New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed independent number I(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously; failed independent neutrosophic-number In(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum neutrosophic cardinality of a set S of vertices such that every two vertices of S are endpoints for an edge, simultaneously. As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-t-partite-neutrosophic graphs. The clarifications are also presented in both sections “Setting of Neutrosophic Failed-Independent Number,” and “Setting of Failed Independent Neutrosophic-Number,” for introduced results and used classes. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhoods of vertices. In path-neutrosophic graphs, two neighbors, form maximal set but with slightly differences, in cycle-neutrosophic graphs, two neighbors forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of all vertices leads us to neutrosophic failed-independent number and failed independent neutrosophic-number. In star-neutrosophic graphs, a set of vertices containing only center and one other vertex, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices including two vertices from different parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of t vertices from different parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set to extend this set to set of all vertices has key role to have these notions in the form of neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of vertices. The cardinality of a set has eligibility to neutrosophic failed-independent number but the neutrosophic cardinality of a set has eligibility to call failed independent neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connections amid each other, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

In this research, assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a “SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a “neutrosophic SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an “δ−SuperHyperForcing” is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : |S∩N(s)|>|S∩(V \N(s))|+δ, |S∩N(s)|<|S∩(V \N(s))|+δ.Thefirst Expression, holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an “δ−SuperHyperDefensive”; a“neutrosophic δ−SuperHyperForcing” is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperForcing. Since there’s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there’s a need to “redefine” the notion of “SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperAlliances and Neutrosophic SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperAlliances, then it’s officially called “SuperHyperAlliances” but otherwise, it isn’t SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperAlliances. For the sake of having neutrosophic SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperAlliances” and “neutrosophic SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperAlliances are redefined “neutrosophic SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperAlliances.] SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperAlliances or the strongest SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperAlliances, called SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $\mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $\mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) \setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$1-failed SuperHyperForcing'' is a \underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotion, namely, 11 Neutrosophic 1-failed SuperHyperForcing. Two different types of SuperHyperDefinitions 12 are debut for them but the research goes further and the SuperHyperNotion, 13 SuperHyperUniform, and SuperHyperClass based on that are well-defined and 14 well-reviewed. The literature review is implemented in the whole of this research. For 15 shining the elegancy and the significancy of this research, the comparison between this 16 SuperHyperNotion with other SuperHyperNotions and fundamental 17 SuperHyperNumbers are featured. The definitions are followed by the examples and the 18 instances thus the clarifications are driven with different tools. The applications are 19 figured out to make sense about the theoretical aspect of this ongoing research. The 20 “Cancer’s Neutrosophic Recognition” are the under research to figure out the challenges 21 make sense about ongoing and upcoming research. The special case is up. The cells are 22 viewed in the deemed ways. There are different types of them. Some of them are 23 individuals and some of them are well-modeled by the group of cells. These types are all 24 officially called “SuperHyperVertex” but the relations amid them all officially called 25 “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic 26 SuperHyperGraph” are chosen and elected to research about “Cancer’s Neutrosophic 27 Recognition”. Thus these complex and dense SuperHyperModels open up some avenues 28 to research on theoretical segments and “Cancer’s Neutrosophic Recognition”. Some 29 avenues are posed to pursue this research. It’s also officially collected in the form of 30 some questions and some problems. Assume a SuperHyperGraph. Then a “1-failed 31 SuperHyperForcing” Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 32 is the maximum cardinality of a SuperHyperSet S of black SuperHyperVertices 33 (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) isn’t 34 turned black after finitely many applications of “the color-change rule”: a white 35 SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white 36 SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred 37 by “1-” about the usage of any black SuperHyperVertex only once to act on white 38 SuperHyperVertex to be black SuperHyperVertex; a “neutrosophic 1-failed 39 SuperHyperForcing” Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) 40 is the maximum neutrosophic cardinality of a SuperHyperSet S of black 41 SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such 42 that V (G) isn’t turned black after finitely many applications of “the color-change rule”: 43 a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only 44 1/128 white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is 45 referred by “1-” about the usage of any black SuperHyperVertex only once to act on 46 white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. 47 Then an “δ−1-failed SuperHyperForcing” is a maximal 1-failed SuperHyperForcing of 48 SuperHyperVertices with maximum cardinality such that either of the following 49 expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s ∈ S : 50 |S ∩N(s)| > |S ∩(V \N(s))|+δ, |S ∩N(s)| < |S ∩(V \N(s))|+δ. The first Expression, 51 holds if S is an “δ−SuperHyperOffensive”. And the second Expression, holds if S is an 52 “δ−SuperHyperDefensive”; a“neutrosophic δ−1-failed SuperHyperForcing” is a maximal 53 neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with maximum 54 neutrosophic cardinality such that either of the following expressions hold for the 55 neutrosophic cardinalities of SuperHyperNeighbors of s ∈ S : |S ∩ N(s)|neutrosophic > 56 |S ∩ (V \ N (s))|neutrosophic + δ, |S ∩ N (s)|neutrosophic < |S ∩ (V \ N (s))|neutrosophic + δ. 57 The first Expression, holds if S is a “neutrosophic δ−SuperHyperOffensive”. And the 58 second Expression, holds if S is a “neutrosophic δ−SuperHyperDefensive”. It’s useful to 59 define “neutrosophic” version of 1-failed SuperHyperForcing. Since there’s more ways to 60 get type-results to make 1-failed SuperHyperForcing more understandable. For the sake 61 of having neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the 62 notion of “1-failed SuperHyperForcing”. The SuperHyperVertices and the 63 SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this 64 procedure, there’s the usage of the position of labels to assign to the values. Assume a 65 1-failed SuperHyperForcing. It’s redefined neutrosophic 1-failed SuperHyperForcing if 66 the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, 67 HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” 68 with the key points, “The Values of The Vertices & The Number of Position in 69 Alphabet”, “The Values of The SuperVertices&The maximum Values of Its Vertices”, 70 “The Values of The Edges&The maximum Values of Its Vertices”, “The Values of The 71 HyperEdges&The maximum Values of Its Vertices”, “The Values of The 72 SuperHyperEdges&The maximum Values of Its Endpoints”. To get structural examples 73 and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph 74 based on 1-failed SuperHyperForcing. It’s the main. It’ll be disciplinary to have the 75 foundation of previous definition in the kind of SuperHyperClass. If there’s a need to 76 have all SuperHyperConnectivities until the 1-failed SuperHyperForcing, then it’s 77 officially called “1-failed SuperHyperForcing” but otherwise, it isn’t 1-failed 78 SuperHyperForcing. There are some instances about the clarifications for the main 79 definition titled “1-failed SuperHyperForcing”. These two examples get more scrutiny 80 and discernment since there are characterized in the disciplinary ways of the 81 SuperHyperClass based on 1-failed SuperHyperForcing. For the sake of having 82 neutrosophic 1-failed SuperHyperForcing, there’s a need to “redefine” the notion of 83 “neutrosophic 1-failed SuperHyperForcing” and “neutrosophic 1-failed 84 SuperHyperForcing”. The SuperHyperVertices and the SuperHyperEdges are assigned 85 by the labels from the letters of the alphabets. In this procedure, there’s the usage of 86 the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. 87 It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And 88 1-failed SuperHyperForcing are redefined “neutrosophic 1-failed SuperHyperForcing” if 89 the intended Table holds. It’s useful to define “neutrosophic” version of 90 SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make 91 neutrosophic 1-failed SuperHyperForcing more understandable. Assume a neutrosophic 92 SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended 93 Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, 94 SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are 95 “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic 96 SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic 97 2/128 SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table 98 holds. A SuperHyperGraph has “neutrosophic 1-failed SuperHyperForcing” where it’s 99 the strongest [the maximum neutrosophic value from all 1-failed SuperHyperForcing 100 amid the maximum value amid all SuperHyperVertices from a 1-failed 101 SuperHyperForcing.] 1-failed SuperHyperForcing. A graph is SuperHyperUniform if it’s 102 SuperHyperGraph and the number of elements of SuperHyperEdges are the same. 103 Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as 104 follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given 105 SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one 106 SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s 107 only one SuperVertex as intersection amid all SuperHyperEdges; it’s 108 SuperHyperBipartite it’s only one SuperVertex as intersection amid two given 109 SuperHyperEdges and these SuperVertices, forming two separate sets, has no 110 SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as 111 intersection amid two given SuperHyperEdges and these SuperVertices, forming multi 112 separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one 113 SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has 114 one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes 115 the specific designs and the specific architectures. The SuperHyperModel is officially 116 called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this 117 SuperHyperModel, The “specific” cells and “specific group” of cells are 118 SuperHyperModeled as “SuperHyperVertices” and the common and intended properties 119 between “specific” cells and “specific group” of cells are SuperHyperModeled as 120 “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, 121 indeterminacy, and neutrality to have more precise SuperHyperModel which in this case 122 the SuperHyperModel is called “neutrosophic”. In the future research, the foundation 123 will be based on the “Cancer’s Neutrosophic Recognition” and the results and the 124 definitions will be introduced in redeemed ways. The neutrosophic recognition of the 125 cancer in the long-term function. The specific region has been assigned by the model 126 [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is 127 identified by this research. Sometimes the move of the cancer hasn’t be easily identified 128 since there are some determinacy, indeterminacy and neutrality about the moves and 129 the effects of the cancer on that region; this event leads us to choose another model [it’s 130 said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s 131 happened and what’s done. There are some specific models, which are well-known and 132 they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves 133 and the traces of the cancer on the complex tracks and between complicated groups of 134 cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, 135 SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). 136 The aim is to find either the longest 1-failed SuperHyperForcing or the strongest 137 1-failed SuperHyperForcing in those neutrosophic SuperHyperModels. For the longest 138 1-failed SuperHyperForcing, called 1-failed SuperHyperForcing, and the strongest 139 SuperHyperCycle, called neutrosophic 1-failed SuperHyperForcing, some general results 140 are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have 141 only two SuperHyperEdges but it’s not enough since it’s essential to have at least three 142 SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of 143 any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, 144 literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph 145 theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, SuperHyperDefensive SuperHyperAlliances and Neutrosophic SuperHyperDefensive SuperHyperAlliances. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The “Cancer’s Recognitions” are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called “SuperHyperVertex” but the relations amid them all officially called “SuperHyperEdge”. The frameworks “SuperHyperGraph” and “neutrosophic SuperHyperGraph” are chosen and elected to research about “Cancer’s Recognitions”. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and “Cancer’s Recognitions”. Some avenues are posed to pursue this research. It’s also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. An “SuperHyperAlliance” is a minimal SuperHyperSet of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the cardinalities of SuperHyperNeighbors of s∈S:,|S∩N(s)|>|S∩(V \N(s))|,and|S∩N(s)|<|S∩(V \N(s))|.Thefirst Expression, holds if S is SuperHyperOffensive. And the second Expression, holds if S is “SuperHyperDefensive”. It’s useful to define “neutrosophic” version of SuperHyperDefensive SuperHyperAlliances. Since there’s more ways to get type-results to make SuperHyperDefensive SuperHyperAlliances more understandable. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a SuperHyperAlliance. It’s redefined neutrosophic SuperHyperAlliance if the mentioned Table holds, concerning, “The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph” with the key points, “The Values of The Vertices & The Number of Position in Alphabet”, “The Values of The SuperVertices&The Minimum Values of Its Vertices”, “The Values of The Edges&The Minimum Values of Its Vertices”, “The Values of The HyperEdges&The Minimum Values of Its Vertices”, “The Values of The SuperHyperEdges&The Minimum Values of Its Endpoints”. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperDefensive SuperHyperAlliances. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there’s a need to have all SuperHyperConnectivities until the SuperHyperDefensive SuperHyperAlliances, then it’s officially called “SuperHyperDefensive SuperHyperAlliances” but otherwise, it isn’t SuperHyperDefensive SuperHyperAlliances. There are some instances about the clarifications for the main definition titled “SuperHyperDefensive SuperHyperAlliances”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperDefensive SuperHyperAlliances. For the sake of having neutrosophic SuperHyperDefensive SuperHyperAlliances, there’s a need to “redefine” the notion of “neutrosophic SuperHyperDefensive SuperHyperAlliances” and “neutrosophic SuperHyperDefensive SuperHyperAlliances”. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there’s the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It’s redefined “neutrosophic SuperHyperGraph” if the intended Table holds. And SuperHyperDefensive SuperHyperAlliances are redefined “neutrosophic SuperHyperDefensive SuperHyperAlliances” if the intended Table holds. It’s useful to define “neutrosophic” version of SuperHyperClasses. Since there’s more ways to get neutrosophic type-results to make neutrosophic SuperHyperDefensive SuperHyperAlliances more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are “neutrosophic SuperHyperPath”, “neutrosophic SuperHyperCycle”, “neutrosophic SuperHyperStar”, “neutrosophic SuperHyperBipartite”, “neutrosophic SuperHyperMultiPartite”, and “neutrosophic SuperHyperWheel” if the intended Table holds. A SuperHyperGraph has “neutrosophic SuperHyperDefensive SuperHyperAlliances” where it’s the strongest [the maximum neutrosophic value from all SuperHyperDefensive SuperHyperAlliances amid the maximum value amid all SuperHyperVertices from a SuperHyperDefensive SuperHyperAlliances.] SuperHyperDefensive SuperHyperAlliances. A graph is SuperHyperUniform if it’s SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It’s SuperHyperPath if it’s only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it’s SuperHyperCycle if it’s only one SuperVertex as intersection amid two given SuperHyperEdges; it’s SuperHyperStar it’s only one SuperVertex as intersection amid all SuperHyperEdges; it’s SuperHyperBipartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it’s SuperHyperMultiPartite it’s only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it’s SuperHyperWheel if it’s only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called “SuperHyperGraph” and “Neutrosophic SuperHyperGraph”. In this SuperHyperModel, The “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperVertices” and the common and intended properties between “specific” cells and “specific group” of cells are SuperHyperModeled as “SuperHyperEdges”. Sometimes, it’s useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called “neutrosophic”. In the future research, the foundation will be based on the “Cancer’s Recognitions” and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it’s called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn’t be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it’s said to be neutrosophic SuperHyperGraph] to have convenient perception on what’s happened and what’s done. There are some specific models, which are well-known and they’ve got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperDefensive SuperHyperAlliances or the strongest SuperHyperDefensive SuperHyperAlliances in those neutrosophic SuperHyperModels. For the longest SuperHyperDefensive SuperHyperAlliances, called SuperHyperDefensive SuperHyperAlliances, and the strongest SuperHyperCycle, called neutrosophic SuperHyperDefensive SuperHyperAlliances, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperGirth, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is an neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as an neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ is excluded in every given neutrosophic SuperHyperGirth. $ \mathcal{C}(NSHG)=\{E_i\}~\text{is an neutrosophic SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^i~\text{is an neutrosophic SuperHyperGirth SuperHyperPolynomial.} \ \ \mathcal{C}(NSHG)=\{V_i\}~\text{is an neutrosophic R-SuperHyperGirth.} \ \ \mathcal{C}(NSHG)=jz^I~{\small\text{is an neutrosophic R-SuperHyperGirth SuperHyperPolynomial.}} $ The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic type-SuperHyperSet with the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperGirth isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth is an neutrosophic SuperHyperSet includes only less than four neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], doesn't have less than four SuperHyperVertices inside the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth isn't up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], isn't the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], is an neutrosophic SuperHyperGirth $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth and it's an neutrosophic SuperHyperGirth . Since it 's the maximum neutrosophic cardinality of an neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices inside the intended neutrosophic SuperHyperSet, thus the obvious neutrosophic SuperHyperGirth, is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperGirth, is: ,is the neutrosophic SuperHyperSet, is: does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperGirth amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the neutrosophic SuperHyperGirth , is only and only. A basic familiarity with neutrosophic SuperHyperGirth theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.

In this research article, the notions of SuperHyperDominating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHyperDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

in this research, new setting is introduced for new SuperHyperNotion, namely, Neutrosophic SuperHyperStable. In this research article, there are some research segments for ``Neutrosophic SuperHyperStable'' about some researches on neutrosophic SuperHyperStable. With researches on the basic properties, the research article starts to make neutrosophic SuperHyperStable theory more understandable. Assume a neutrosophic SuperHyperGraph. Then a ``neutrosophic SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

In this research, new setting is introduced for new SuperHyperNotions, namely, an SuperHyperStable and Neutrosophic SuperHyperStable. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognitions'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognitions''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognitions''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a``SuperHyperStable'' $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's no SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperStable'' is a \underline{maximal} SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperStable'' is a \underline{maximal} neutrosophic SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. It's useful to define a ``neutrosophic'' version of an SuperHyperStable. Since there's more ways to get type-results to make an SuperHyperStable more understandable. For the sake of having neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of an ``SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume an SuperHyperStable. It's redefined a neutrosophic SuperHyperStable if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points, ``The Values of The Vertices \& The Number of Position in Alphabet'', ``The Values of The SuperVertices\&The maximum Values of Its Vertices'', ``The Values of The Edges\&The maximum Values of Its Vertices'', ``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on an SuperHyperStable. It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyperConnectivities until the SuperHyperStable, then it's officially called an ``SuperHyperStable'' but otherwise, it isn't an SuperHyperStable. There are some instances about the clarifications for the main definition titled an ``SuperHyperStable''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on an SuperHyperStable. For the sake of having a neutrosophic SuperHyperStable, there's a need to ``redefine'' the notion of a ``neutrosophic SuperHyperStable'' and a ``neutrosophic SuperHyperStable''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. Assume a neutrosophic SuperHyperGraph. It's redefined ``neutrosophic SuperHyperGraph'' if the intended Table holds. And an SuperHyperStable are redefined to an ``neutrosophic SuperHyperStable'' if the intended Table holds. It's useful to define ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic SuperHyperStable more understandable. Assume a neutrosophic SuperHyperGraph. There are some neutrosophic SuperHyperClasses if the intended Table holds. Thus SuperHyperPath, SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are ``neutrosophic SuperHyperPath'', ``neutrosophic SuperHyperCycle'', ``neutrosophic SuperHyperStar'', ``neutrosophic SuperHyperBipartite'', ``neutrosophic SuperHyperMultiPartite'', and ``neutrosophic SuperHyperWheel'' if the intended Table holds. A SuperHyperGraph has a ``neutrosophic SuperHyperStable'' where it's the strongest [the maximum neutrosophic value from all the SuperHyperStable amid the maximum value amid all SuperHyperVertices from an SuperHyperStable.] SuperHyperStable. A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyperCycle if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges; it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognitions'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a neutrosophic SuperHyperPath(-/SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite, SuperHyperWheel). The aim is to find either the longest SuperHyperStable or the strongest SuperHyperStable in those neutrosophic SuperHyperModels. For the longest SuperHyperStable, called SuperHyperStable, and the strongest SuperHyperCycle, called neutrosophic SuperHyperStable, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn't any formation of any SuperHyperCycle but literarily, it's the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn't form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

I introduce now for the first time the neutrosophic modal logic. The Neutrosophic Modal Logic includes the neutrosophic operators that express the modalities. It is an extension of neutrosophic predicate logic, and of neutrosophic propositional logic. In order for the paper to be self-contained, I also recall the etymology and definition of neutrosophy and of neutrosophic logic. Several examples are presented as well.

In this research, Assume a neutrosophic SuperHyperGraph. Then a ``Failed SuperHyperStable $\mathcal{I}(NSHG)$ for a SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common; a ``neutrosophic Failed SuperHyperStable'' $\mathcal{I}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's a neutrosophic SuperHyperVertex to have a neutrosophic SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperStable'' is a \underline{maximal} Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperStable'' is a \underline{maximal} neutrosophic Failed SuperHyperStable of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme Failed SuperHyperClique theory, Neutrosophic Failed SuperHyperClique theory, and (Neutrosophic) SuperHyperGraphs theory are proposed.

Background: Acute kidney disease (AKD) is a known risk factor for increased mortality and evolution towards chronic kidney disease (CKD) in adults. The data regarding children are scarce. The purpose of our study is to explore the risk factor for AKD and impact of AKD following an acute kidney injury (AKI) episode in children on mortality and new-onset CKD. Methods: We retrospectively evaluated 736 children with ages between 2 and 18 years old with AKI admitted in a tertiary care hospital from the west Romania over a 9 years period. Results: AKD incidence following AKI was 17%. Patients that developed AKD were older, with higher baseline serum creatinine values, urea, C reactive protein and lower proteins, haemoglobin and sodium. They were more often exposed to sepsis, critical illness and nephrotoxic medications and presented certain susceptibilities like CKD, neoplasia, anemia, heart failure, arterial hypertension, stem cell transplant and female gender. AKI causes that increased the risk of AKD were intrinsic ones. AKD increased the overall mortality by three times. The factors that independently increased the risk of evolution towards CKD were AKD, acute tubular necrosis and higher baseline serum creatinine values. Conclusions: AKD is an independent risk factor for mortality and new-onset CKD in children.

Aiming at the limitations of single-functionality, limited applicability, and complex designs prevalent in current metasurfaces, we propose a terahertz multifunctional and multiband tunable metasurface utilizing a VO2-metal hybrid structure. This metasurface structure comprises a top VO2-metal resonance layer, a middle polyimide dielectric layer, and a gold film reflective layer at the bottom. This metasurface exhibits multifunctionality, operating independently of polarization and incident angle. The varying conductivity states of the VO2 layers, enable the metasurface to achieve various terahertz functionalities, including single-band absorption, broadband THz absorption, and multiband perfect polarization conversion for linear (LP) and circularly polarized (CP) incident waves. Finally, we believe that the functional adaptability of the proposed metasurface expands the repertoire of options available for future terahertz device designs.

In this research, assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. It's useful to define a ``neutrosophic'' version of a SuperHyperMatching . Since there's more ways to get type-results to make a SuperHyperMatching more understandable. For the sake of having neutrosophic SuperHyperMatching, there's a need to ``redefine'' the notion of a ``SuperHyperMatching ''. A basic familiarity with neutrosophic SuperHyperMatching theory, SuperHyperGraphs theory, and neutrosophic SuperHyperGraphs theory are proposed.

New setting is introduced to study quasi-degree and quasi-co-degree arising from co-neighborhood. quasi-degree and quasi-co-degree is about a vertex which are applied into the setting of neutrosophic graphs. . The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs and star-neutrosophic graphs, complete-bipartite-neutrosophic graphs and complete-multipartite-neutrosophic graphs are investigated in the terms of a vertex which is called either quasi-degree or quasi-co-degree. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form quasi-degree and quasi-co-degree. Quasi-degree is a value of a vertex which is maximum amid all values of vertices which are neighbors to a fixed vertex. Quasi-co-degree is a value of an edge which is maximum amid all values of edges which are neighbors to a fixed vertex but corresponded vertex is representative for this notion. Using different values which are related to a vertex inspire us to focus on edge and vertices which are corresponded to a fixed vertex. The notion of neighborhood is used to collect either vertices are titled neighbors or edges are incident to fixed vertex. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definitions are provided. Using fixed vertex has key role to have these notions in the form of vertex or edge. The value of an edge has eligibility to call quasi-co-degree but the value of a vertex has eligibility to call quasi-degree. Some results get more frameworks and perspective about these definitions. The way in that, two vertices have connection together, open the way to define neighborhood and co-neighborhood. The maximum values in neighborhood and co-neighborhood introduces quasi-degree and quasi-co-degree, respectively. New name is chosen from degree. Since amid all vertices with different degrees, one vertex is chosen. In other words, one vertex is fixed and its degree turns out quasi-degree where two degrees could be assigned to a vertex. Degree of edges and degree of vertices. The number of edges which are incident to the vertex and the number of vertices which are neighbors to the vertex. Degree and co-degree are the notions which are transformed to use in quasi-style. Two neutrosophic values introduce two neutrosophic vertices separately in each settings. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to purse this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another de nitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

In this work, an analog front-end (AFE) circuit for Electrocardiogram (ECG) detection system has been designed, implemented, and investigated in an industry-standard Cadence simulation framework using advanced technology node of 45 nm. The AFE consists of an instrumentation amplifier, a Butterworth band-pass filter (with fifth-order low-pass and second-order high-pass sections), and a second-order notch filter- all are based on two-stage, Miller-compensated operational transconductance amplifiers (OTA). The OTAs have been designed employing the $g_m/I_D$ methodology. Both the pre-layout and post-layout simulation were carried out. The layout consumes an area of 0.0058 mm$^2$ without the resistors and capacitors. Analysis of various simulation results were carried out for the proposed AFE. The circuit demonstrates a post-layout bandwidth of 239 Hz with a variable gain between 44 to 58 dB, a notch depth of -56.4 dB at 50.1 Hz, a total harmonic distortion (THD) of -59.65 dB (less than 1\%), an input referred noise spectral density of $

In the era of Big Data and the Internet of Things (IoT), ensuring the security and privacy of patient data within distributed health systems is paramount. This research delves into the challenges posed by these advancements and explores viable solutions, focusing notably on blockchain technology, data encryption methods, and access control mechanisms. Employing a comprehensive literature review approach, the study synthesizes current research findings, complemented by analyses of existing frameworks and case studies from healthcare organizations, offering practical insights. Interviews with cybersecurity experts and healthcare IT professionals provide nuanced perspectives on current security issues and emerging trends. Through qualitative and quantitative data analyses, the study generates recommendations aimed at enhancing patient data security. These include the adoption of new frameworks and innovative technologies to fortify healthcare data systems. By addressing these critical aspects, this research aims to significantly contribute to the advancement of a more secure and efficient healthcare ecosystem in today's digital landscape.

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

We introduce a full binary directed tree structure to represent the set of natural numbers, further categorizing them into three distinct subsets: pure odd numbers, pure even numbers, and mixed numbers. We adopt a binary string representation for natural numbers and elaborate on the composite methodology encompassing odd- and even-number functions. Our analysis focuses on examining the iteration sequence (or composition) of the Collatz function and its reduced variant, which serves as an analog to the inverse function, to scrutinize the validity of the Collatz conjecture. To substantiate this conjecture, we incorporate binary strings into an algebraic formula that captures the essence of the Collatz sequence. By this means, we transform discrete powers of 2 into continuous counterparts, ultimately culminating in the smallest natural number, 1. Consequently, the sequence generated through infinite iterations of the Collatz function emerges as an eventually periodic sequence, thereby validating an enduring 87-year-old conjecture.

This research discusses the challenges faced by university students in group work assignments and the importance of effective project management. This article introduces Tasknest, a project management platform that helps teams organize tasks, track progress, and improve communication. This article also reviews related studies on project management applications and discusses the Agile methodology used in the development of Tasknest. The implementation of the task management system was done using Agile methods and Typescript programming language. This web-based system includes a landing page, dashboard page, board page, and settings page. Black box testing was conducted to ensure the system functions as expected, with tests on login, board creation, adding columns and cards, and others. Overall, the system was successfully implemented and tested. Tasknest application development includes user stories, acceptance criteria, sprint backlogs, sprint planning, reviews, and retrospectives. System design analysis includes usecase diagram, activity diagram, sequence diagram, and entity relationship diagram. Application features include task list management, team member management, real-time collaboration, notification system integration, task enhancement, in-task checklists, user authentication, UI optimization, performance improvement, collaboration feature enhancement, database design, front-end implementation, and UI design. The Agile Alliance outlines 12 principles for implementing Agile methodologies, which prioritize customer satisfaction, collaboration, and continuous improvement. Agile methodologies offer high flexibility, rapid iteration, responsiveness to change, improved product quality, stakeholder involvement, transparency, and clear responsibilities. Scrum is a framework that supports Agile principles, with a focus on transparency, inspection, and adaptation. Scrum improves team collaboration, rapid adaptation to change, transparency, visibility, product quality, and team motivation. In the development of the Tasknest application, the Scrum methodology is used, with roles such as Product Owner, Scrum Master, and Development Team. Data collection techniques include interviews, observations, and literature studies, while data testing techniques involve black box testing. Planning using Scrum involves creating a Product Backlog with prioritized features and fixes. Prioritization determines the duration of each sprint.

Transcranial magnetic stimulation, TMS, has been an innovative method of demure neuromodulation. This paper aims to delve into the different forms of its existence and to evaluate the use of TMS in five psychiatric disorders; Parkinson’s disease, schizophrenia, obsessive-compulsive disorder, major depressive disorder, and major anxiety disorder. Literature pertaining to the use of TMS in treating these specific diseases will be analyzed, and its efficacy and mechanisms will be explored. The literature will be evaluated through sources with established facts and research studies demonstrating function, potency, or inefficacy. TMS poses a method to have a more explicit effect on the regions of the brain, and the exploration of its use in the treatment of psychiatric diseases poses new possibilities in the treatment of psychiatric disorders. Venturing into the options it could have in a sole or combinatorial setting could provide penetrating insight into innovative forms of treatment and research.

The severe acquired respiratory coronavirus–2 (SARS–CoV-2) infection has initiated both acute and chronic COVID–19 disease between 2020 and 2023, currently evolving with other homologous prior coronavirus strains of the Nidoviridae order, which encompasses other prevalent alpha/ beta coronaviruses, but also the Middle East Respiratory Syndrome (MERS-CoV) and SARS-CoV-1, with recent SARS–CoV–2 variants, increasing demands for effective immunogens and therapeutic approaches that will reduce global disease burden and further infection from SARS–CoV-2 affected individuals that may experience post acute sequelae (PASC) or “Long COVID”. Following a worldwide programme of prophylactic vaccination, there is still a dilemma in the efforts to find prophylactic and early therapeutic approaches that would treat novel SARS-CoV-2 variants and prevent future epidemics or pandemics within host human and animal populations, where zoonotic or cross species transfer naturally occurs. Concerns about viral immune escape intersect at a specific point; a gained evolutionary ability of several viruses to co–infect and compete against previous scientific advances since 1796 that remain undetected or asymptomatic during the early stages of infection progressing to symptomatic and severe disease via the double methylation of the 5' end of eukaryotic DNA or RNA-based viral genomes, the 7-MeGpppA2’-O-Me cap, and its double methylation capping process is performed by the activated viral 2’ - O - Methyltransferase (MTase) enzyme, a complex of two viral non-structural proteins (NSPs) joined together through an activation process (NSP10/16) and by N7-Methyltransferase (N7-MTase/NSP14), respectively. Moreover, it was discovered that polymorphic viruses translate NSP1, which prevents the activation of various Pattern Recognition Receptors (PRRs), and consequently, detection of Pathogen-Associated Molecular Patterns (PAMPs) and Damage-Associated Molecular Patterns (DAMPs) alike. NSP1 also silences important interferon-encoding genes (INGs) and interferon-stimulated genes (ISGs), is signalled in a paracrine manner to neighbouring cells, and that induces the apoptosis of host cells, inducing an effect of “trace erase” effect and making the viral infection as immunologically “invisible” as possible during the initial, key stages of viral replication and distribution, all such mechanisms occurring independently of the viruses in cause. Another important viral NSP is NSP14, as it plays two functional roles that are independent of each other; to produce new viral genetic material for the purpose of maintaining the validity of the viral genome as well, and not just transfer a methyl group to the 5’ end of the viral genome. Other viral NSPs share a role with NSP1, 10, 14 and 16 in directly suppressing the activation of PRRs and ISGs, and all such viral proteins help the virus in its process of self-camouflaging against first- and second-line immunity, thereby often severely impacting the quality of the produced adaptive immune responses. The outcome of all such phenomena is the sharp decrease in the host Type I and Type III interferons' (IFNs) rate of synthesis by the host cells, that would usually occur and affect homeostatic cellular pathways, resulting in further viral replication and induced apoptosis. Nonetheless, effects of microbial immune evasion during the development of other viral or carcinogenic pathologies are not widely known. In short, polymorphic viruses developed a proportionate evolutionary response against developed adaptive immune responses, by currently relying on gaps mostly situated in the natural immune system in their process of molecular self-camouflaging. Scientists developed numerous approaches of early treatment that generally showed good success rates and fewer risks of adverse events, and the still early present stages of COVID-19 research should also be taken into consideration whilst filtering for the most appropriate solutions. For example, the administration of recombinant human interferons I and III into the nasal mucosa cellular layer, as key mediators of anti–viral activity, can simulate intracellular infection and stimulate cellular activity in a timely manner, training the innate and adaptive immune system cells to develop and appropriately stimulate an adequate immune response through B and T cells. Another example could involve the treatment of natural and adaptive lymphocytes with a low dose of IFNs I and possibly III, prior to their insertion into the host lymphatic system, possibly alongside additional recruitment of plasmacytoid dendritic cells (pDCs) as further interferon “factories”, all with the purpose of early infection management. It might be that focusing on directly offering the immune system the information about the genetics and protein structure of the pathogen, rather than training its first-line mechanisms to develop faster, excessively increases its specificity, making it reach a level that brings the virus the opportunity to evolve and escape previously-developed host immune mechanisms. It is until the scientific community realises this potentially crucial aspect that large proportions of the world population will probably continue to face serious epidemics and pandemics of respiratory diseases over the coming several decades, evidenced with dengue fever and more recently, monkeypox and possibly avian flu. Of note, it has been indicated that IFN I and / or III display significant immunising, early therapeutic and clinical disease onset-attenuating effects for many other microbial evoked diseases, as well as for a number of oncological diseases.

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtain chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing representatives of the colors are applied in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about number, degree and co-degree in the way that some number, degree and co-degree get understandable perspective. Neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are studied to investigate about the notions, coloring, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs. In this way, sets of representatives of colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, notions chromatic number, the representatives of the colors, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges are applied into neutrosophic hypergraphs, especially, neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

This qualitative research explores the transformative impact of technological innovations on retail marketing effectiveness. Through thematic analysis of interviews with industry professionals, the study identifies key themes including enhanced customer engagement, personalized marketing strategies driven by AI and machine learning, data-driven decision-making leveraging big data and analytics, the rise of e-commerce platforms, integration of mobile technologies, adoption of augmented reality (AR) and virtual reality (VR), development of omnichannel strategies, and implementation of loyalty programs. These themes illustrate how technology has reshaped retail marketing by enabling real-time customer interactions, personalized shopping experiences, and targeted marketing campaigns that enhance customer satisfaction and loyalty. The findings highlight the critical role of digital platforms like social media in fostering community engagement and brand loyalty. AI and machine learning facilitate personalized marketing efforts, tailoring product recommendations and enhancing customer experiences. Data-driven strategies optimize marketing ROI by providing insights into consumer behavior and market trends. E-commerce platforms expand market reach and streamline transactions, while mobile technologies and AR/VR innovations create immersive shopping experiences that captivate consumers. Omnichannel strategies integrate physical and digital channels, delivering seamless brand experiences and enhancing customer retention through CRM systems and loyalty programs. Looking ahead, retailers must navigate challenges such as rapid technological change, the need for continuous adaptation, and concerns about data privacy. By embracing technological advancements strategically and maintaining ethical standards, retailers can sustain competitive advantage, meet evolving consumer expectations, and drive growth in the digital era.

The Jakarta LARP community, established in March 2020 and primarily active in Gelora Bung Karno, fosters inclusivity, diversity, and physical role-playing activities. It adheres to a policy of excluding ultra-nationalist ideologies and integrates new members despite language barriers. Bruhn (2011) defines this kind of community sharing the same goals, values, and lifestyles, while McMillan & Chavis (1986) outline four aspects of the sense of community.The research discovered that communities endure by utilizing solidarity built on the basis of their peculiarities. This study employed ethnographic methods alongside grounded research to identify the community's culture and their efforts to sustain and utilize it as community solidarity.

The advent of 5G technology represents a transformative leap in the realms of retail marketing and supply chain operations, offering unprecedented enhancements and posing unique challenges. This study explores the multifaceted impacts of 5G, focusing on its influence on customer experiences, operational efficiency, and supply chain management. The integration of 5G enables advanced technologies such as augmented reality (AR) and virtual reality (VR), significantly enhancing the interactivity and personalization of the shopping experience. Real-time data collection and analysis, facilitated by 5G, allow for more precise inventory management and optimized store operations, leading to improved customer satisfaction and reduced operational costs. In the supply chain domain, 5G technology offers enhanced visibility and control through real-time tracking and environmental monitoring, which improves logistics efficiency and product quality management. Despite these advancements, the adoption of 5G technology involves considerable challenges, including high infrastructure costs, data security concerns, and global disparities in technology deployment. Businesses must navigate these obstacles while leveraging the benefits of 5G to achieve competitive advantage. The study also highlights the role of 5G in integrating with other advanced technologies, such as artificial intelligence (AI) and blockchain, to drive further innovation. Additionally, 5G supports sustainability efforts by optimizing energy use and reducing waste. Overall, the successful implementation of 5G requires strategic investment and adaptability, but it holds the potential to revolutionize retail and supply chain operations, enhancing efficiency, customer engagement, and sustainability in a rapidly evolving digital landscape.

This research explores the impact of 5G technology on supply chain efficiency and marketing innovations, highlighting its transformative potential and associated challenges. The study delves into how 5G enhances real-time tracking and monitoring within supply chains, significantly improving inventory management, reducing stockouts and overstocking, and ensuring optimal conditions during product transit. The advanced communication capabilities of 5G enable seamless collaboration among supply chain partners, facilitating quicker decision-making and improved risk management. Additionally, the integration of 5G technology with data analytics has optimized processes, improved forecasting accuracy, and led to cost reductions, showcasing the value of data-driven decision-making. In the marketing domain, 5G technology has driven the development of immersive augmented reality (AR) and virtual reality (VR) applications, enhancing customer engagement through interactive and experiential content. Personalized and targeted marketing strategies, supported by real-time data and deeper customer insights, have led to higher customer satisfaction and increased sales. The proliferation of connected devices, such as smart speakers and wearables, has further enabled personalized interactions and convenience, fostering brand loyalty and driving growth. Despite these advancements, the implementation of 5G presents challenges, including significant infrastructure investment, cybersecurity risks, and privacy concerns. Companies must navigate these issues by investing in robust security measures and developing comprehensive policies. The research concludes with an optimistic outlook on the future impact of 5G technology, emphasizing its potential to drive innovation, enhance operational efficiency, and transform customer experiences, ultimately shaping the future of business operations.

This research explores the pivotal role of big data analytics in enhancing retail marketing and supply chain optimization. As the retail industry undergoes rapid digital transformation, big data analytics has emerged as a critical tool for gaining competitive advantage and improving operational efficiency. The study delves into the various applications of big data analytics, including customer segmentation, personalized marketing, demand forecasting, inventory management, dynamic pricing, and supply chain optimization. It highlights how retailers leverage data from diverse sources to gain insights into consumer behavior, market trends, and operational performance, leading to more informed decision-making. The findings underscore the significant benefits of big data analytics in enhancing customer experiences through targeted engagement and personalized service. Additionally, the research addresses the ethical considerations and challenges associated with data privacy, security, and potential biases in analytics models. It emphasizes the importance of maintaining high standards of data quality and ethical practices to ensure the responsible use of data. The conclusion reiterates the transformative impact of big data analytics in the retail sector, suggesting that while it offers substantial advantages, careful management of its challenges is crucial. The study provides valuable insights into how retailers can harness the power of big data analytics to drive growth, innovation, and long-term success in an increasingly competitive and data-driven market environment.

Presence detection is essential in many applications, including smart homes, office automation, and public space management. Traditional technologies like infrared sensors and cameras frequently encounter obstacles due to privacy concerns, high costs, and complexity. The study provides a novel way to detect presence based on Wi-Fi signals and machine learning algorithms, utilizing the ESP8266 microcontroller. The suggested system attempts to reliably detect the presence of people in a given place by evaluating fluctuations in Wi-Fi signal strength and patterns. The theoretical basis of this strategy is investigated, including the ESP8266’s capabilities for Wi-Fi data gathering and the use of machine learning methods for data analysis. The methodology includes data collecting with the ESP8266, preprocessing, feature extraction, and training and evaluating machine learning models. This system’s potential uses include smart home automation, office occupancy tracking, and crowd management in public settings. The paper also discusses potential issues such as signal interference, data privacy concerns, and the limitations of Wi-Fi detection. Future work is also mentioned, including the suggested system’s installation and testing and enhancement proposals to improve accuracy and scalability. This research aims to provide a cost-effective, non-intrusive, and scalable presence detection system by harnessing the power of Wi-Fi signals and machine learning, enhancing intelligent environments

Background: Population studies have shown that prehypertension is associated with adverse cardiometabolic risk profile even among apparently healthy populations. Although associations between serum triglyceride (TG) concentrations and the risk of atherosclerotic cardiovascular disease have been reported, there are lack of data on the association of hypertriglyceridemia with cardiovascular risk (CVR) in a low risk prehypertensive population. Aim: Our aim was to analyze the cardiorenometabolic characteristics of prehypertensives (PHT) compared to normotensives (NT) and untreated hypertensives (HT) and its associations with CVR. Materials and methods: In our cross-sectional study we included 323 apparently healthy untreated subjects 18-45 years who underwent basic anthropometric and standardized blood pressure measurement, fasting blood sampling, spot urine collection and transthoracic echocardiogram. Results: Higher BMI, waist circumference, HOMA-IR, LDL-cholesterol, TG, uric acid and LVMI contribute to higher CVR in PHT compared to true NT (p

In this article, we present two topics related to mathematical economics. We offer an intriguing proposal for securing cost and production functions in the face of uncertainty and risk. We discuss the relationship between individual and social preferences. This is important because traditional revealed preference theory does not account for such factors.

Additive manufacturing (AM) has revolutionized the field of biopolymers by providing a range of opportunities to create complex and intricate structures. Here we provide an overview of developments in biopolymer AM, first in the context of how natural systems have impacted the synthetic processes of AM, and secondly in the context of how synthetically derived structures can be used for biomedical applications. In particular, we explore the range of biopolymers developed for AM, AM techniques for biopolymers, and potential biocompatible medical applications with a focus on four categories of tissue in the human body: skin, bone, heart, and nerve. Despite the current challenges of the technology, exciting results in tissue regeneration, synthetic replacements for natural grafts, and complex dynamic organoids have already come to pass - with many more possible in the future.

This study aims to examine the non-volatile Particle Number (PN) emissions of a retrofitted Heavy-Duty Spark-Ignition (HD-SI) engine powered by liquefied petroleum gas (LPG) under both steady-state and transient conditions. The engine was tested under seven steady-state operating points to investigate the PN behavior and Particle Size Distribution (PSD) upstream and down-stream of the Three-Way Catalyst (TWC). This analysis intends to assess the impact of including particles with diameters ranging from 10 nm to 23 nm in the total particle count, a consideration for future regulations. The study employed the World Harmonized Transient Cycle (WHTC) for transient conditions to encompass the same engine working region used in the steady-state analysis. A Dekati FPS-4000 diluted the exhaust sample to measure the PSD and PN for particle diameters between 5.6 nm and 560 nm using the TSI-Engine Exhaust Particle Sizer (EEPS) 3090. Findings indicate that PN levels tend to increase downstream of the TWC under steady-state conditions in operating points with low exhaust gas temperatures and flows (equal to or less than 500 °C and 120 kg/h). Furthermore, the inclusion of particles with diameters between 10 nm and 23 nm leads to an increase in PN emissions by 17.70% to 40.84% under steady conditions and by an average of 40.06% under transient conditions, compared to measurements that only consider particles larger than 23 nm. Notably, in transient conditions, most PN emissions occur during the final 600 seconds of the cycle, linked to the most intense phase of the WHTC.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

New setting is introduced to study the global powerful alliance. Global powerful alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global powerful alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs excluding empty, path, star, and wheel and containing complete, cycle and r-regular-strong are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is used in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-powerful-alliance number and minimal-global-powerful-alliance-neutrosophic number. Two different types of sets namely global-powerful alliance and minimal-global-powerful alliance are defined. Global-powerful alliance identifies the sets in general vision but minimal-global-powerful alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-powerful-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-powerful alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs has an open avenue, in the way that, the family only contains same classes of neutrosophic graphs. The results are about minimal-global-powerful alliance, minimal-global-powerful-alliance number and its corresponded sets, minimal-global-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-powerful alliances, minimal-t-powerful alliance, minimal-t-powerful-alliance number and its corresponded sets, minimal-t-powerful-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-t-powerful alliances. The connections amid t-powerful-alliances are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications and closing remarks. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global powerful alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set and reversely for non-members of set with less members in the way that the set is simultaneously t-offensive and(t-2)-defensive. A set is global if t=0. It leads us to the notion of global powerful alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

New setting is introduced to study the global offensive alliance. Global offensive alliance is about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define this notion. Also, neighborhood is defined based on strong edges. Strong edge gets a framework as neighborhood and after that, too close vertices have key role to define global offensive alliance based on strong edges. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, star, and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. Neutrosophic number is defined in new way. It’s first time to define this type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number. It’s called “modified neutrosophic number”. Summation of three values of vertex makes one number and applying it to a set makes neutrosophic number of set. This approach facilitates identifying minimal set and optimal set which forms minimal-global-offensive-alliance number and minimal-global-offensive-alliance-neutrosophic number. Two different types of sets namely global-offensive alliance and minimal-global-offensive alliance are defined. Global-offensive alliance identifies the sets in general vision but minimal-global-offensive alliance takes focus on the sets which deleting a vertex is impossible. Minimal-global-offensive-alliance number is about minimum cardinality amid the cardinalities of all minimal-global-offensive alliances in a given neutrosophic graph. New notions are applied in the settings both individual and family. Family of neutrosophic graphs is studied in the way that, the family only contains same classes of neutrosophic graphs. Three types of family of neutrosophic graphs including m-family of neutrosophic stars with common neutrosophic vertex set, m-family of odd complete graphs with common neutrosophic vertex set, and m-family of odd complete graphs with common neutrosophic vertex set are studied. The results are about minimal-global-offensive alliance, minimal-global-offensive-alliance number and its corresponded sets, minimal-global-offensive-alliance-neutrosophic number and its corresponded sets, and characterizing all minimal-global-offensive alliances. The connection of global-offensive-alliances with dominating set and chromatic number are obtained. The number of connected components has some relations with this new concept and it gets some results. Some classes of neutrosophic graphs behave differently when the parity of vertices are different and in this case, path, cycle, and complete illustrate these behaviors. Two applications concerning complete model as individual and family, under the titles of time table and scheduling conclude the results and they give more clarifications. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study deeply and with more results but it seems that analogous results are determined. Slight progress is obtained in the family of these models but there are open avenues to study family of other models as same models and different models. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on strong edges illustrate open way to get results. A set is global offensive alliance when two sets partitioning vertex set have uniform structure. All members of set have more amount of neighbors in the set than out of set. It leads us to the notion of global offensive alliance. Different edges make different neighborhoods but it’s used one style edge titled strong edge. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for these notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

This article presents a new method of segmenting images with gray levels. The method is based on determining several thresholds for separation of gray levels. The determination of these thresholds is done using the certainty of the neutrosophic information. The concept of this method can be stated simply: to choose the local maximums for the neutrosophic certainty.

In this paper, a geometric model is introduced for Neutrosophic data problem for the first time. This model is based on neutrosophic sets and neutrosophic relations. Neutrosophic control points are defined according to these points, resulting in neutrosophic Bézier curves.

In this paper, we propose an assumption of which the relation between electron and phonon is discussed and investigated based on the experiment of γ photon and electric interconverting with each other. We calculated the charge of a particular standing wave topology with Maxwell’s equation rotated in accordance space with the SO3 transformation. The derived charge value is 1.6035 × 10E−19C around 0.0826% different from the experimental data, indicating the proposal is a promising theory to explain the origin of charge and spin of electron particle. Electron spin angular momentum comes from the orbital angular momentum of photon rotation (electromagnetic field rotation), and electron charge comes from photon, that is, the space-time rotation effect of electromagnetic wave.

Weathering and erosion transport minerals and organics toward the sea or lake bottoms over geologic time. The finest solids are deposited in lower, less turbulent areas, such as lake bottoms and continental shelves. They sometimes stack up to thicknesses of kilometers, and begin compacting. These sediment sections are called shales, and as initially deposited in water, shales can have porosities up to 50-80{\%} water, As they are buried, many alteration products from oil to slate are produced due to overburden and temperature increasess, making them important to study. A preceeding paper \cite{1} showed that pressure solution is the primary mechanism for porosity reduction, with possible mechanical compaction at shallow depths. Without naming the mineral(s) involved, it postulated that the greater the product of the water and pore interfaces, the faster the reaction would proceed. This term is $ \varphi^{4m/3}(1-\varphi)^{4n/3}$ , where $\varphi$ is porosity and m and n are numbers close to unity. The large exponents, {\em 4/3}, recognize that the reaction occurs at the molecular scale at which the surfaces are rough. A second term, $\exp^{(-E/RT)}$ , indicates that the reaction is impeded by a quantum energy barrier, E, with diminished impeding power as increased available thermal energy, represented by the absolute temperature, T, becomes available at greater depths in the Earth. These two factors combine to allow porosity $\varphi$ to reduce with time, or equivalently for the fraction of solids, $(1-\varphi)$, to increase with time,$\left. \frac{\partial(ln(1-\varphi) ) }{\partial t } \right |_{\sigma} = (\varphi )^{4m/3}( 1-\varphi )^{4n/3}Ae^{-E/(RT)}$. { \em Here it is shown that this equation can cover quantitatively any actual deposition rates which may have been experienced by the six sections studied, the actual deposition rates being unknown for these cases. Hence a time-depth depositional history for any new shale section, known in detail, would allow determination of the parameters m, n, E and a lumped proportionality constant A. This was accomplished by showing that, for a wide range of depositional rates, r, the range of E for any of the studied sections is small compared to laboratory measurements of quartz solution\cite{2}, 24+-15kJ/mol. Results were obtained over this range of r's using the previously determined m and n, and porosity and temperature profiles. The presently existing porosity profiles necessarily incorporate any overpressure or underpressure conditions that may have existed in the past or currently, as the net difference between overburden and pore pressure is a primary driving force for pressure solution. $SiO_2$ usually comprises 20-50{\%} of shales. In conclusion, pressure solution of quartz can account for vertical compaction of shales quantitatively in the studied examples. Separately, a quasi-eqivalent method for discussing reduced porosities in Macron 2 versus Macron 1 as increased vertical stress, rather than additional horizontal stress, is illustrated. Experiments are suggested to clarify the pressure solution mechanism. The role of horizontal forces is discussed. From a global point of view, shale compaction by pressure solution is a quantified step in the cycling of continental rocks, beginning with rifting.

Background and aims: Brain metastases are prevalent in the late stages of malignant melanoma. Multimodal therapy remains challenging. Patient-derived organoids (PDOs) represent a valuable pre-clinical model, faithfully recapitulating key aspects of the original tumor, including the heterogeneity and the mutational status. This study aimed to establish PDOs from melanoma brain metastases (MBM-PDOs) and to test the feasibility of using them as a model for in vitro targeted-therapy drug testing.Methods: Surgical resection samples from eight patients with melanoma brain metastases were used to establish MBM-PDOs. Samples were enzymatically dissociated followed by seeding into low-attachment plates to generate floating organoids. The MBM-PDOs were characterized genetically, histologically, immunohistologically and compared with the parental tissue. The MBM-PDO cultures were exposed to dabrafenib (BRAF inhibitor) and trametinib (MEK inhibitor) followed by cell viability assessment.Results: Seven out of eight cases were successfully cultivated, maintaining the histological, immunhistological phenotype, and the mutational status of the parental tumors. Five out of seven cases harbored BRAF V600E mutations and were responsive to BRAF and MEK inhibitors in vitro. Two out of seven cases were BRAF wild type, one case harboring an NRAS mutation and the other harboring a KIT mutation, and both were resistant to BRAF and MEK inhibitor therapy. Conclusion:We successfully established PDOs from melanoma brain metastases surgical specimens, which exhibited a consistent histological and mutational profile with the parental tissue. Using FDA-approved BRAF and MEK inhibitors, our data demonstrates the feasibility of employing MBM-PDOs for targeted-therapy in vitro testing.

This article is some review of results that were obtained at 2007-2021 years development of “The Information as Absolute” concept and the informational physical model, which is based on the concept; including a number of fundamental physical problems are briefly considered in framework of the conception and the model. Recently in physics there are several publications, that present lists of the problems. However, those lists are essentially incomplete, for at least two reasons. Firsts of all, a number of phenomena are studied traditionally by philosophy, and so corresponding problems are usually considered to be “metaphysical”. However, they relate also to some concrete physical phenomena. For example, physics evidently studies Matter, and so the metaphysical problems “what is ontology of Matter”, “what is “Space”, “Time” and a few other physical phenomena and notions as well, are really a Meta-physical problems “what does physics study?” There are other fundamental physical problems, which are not considered as such in physics, and are absent in the “fundamental problems lists”. Those include the problems, which really exist, yet are incorporated into standard physical theories, and so are fundamental “implicitly”, which in physics are “solved by default” ‒ and mostly erroneously. Note, though, that a number of “Meta-physical”, and concrete fundamental, problems more in detail are considered in the paper “The Informational Conception and Basic Physics”, https://arxiv.org/abs/0707.4657, v5 (2021), so this paper is, in certain sense, an expanded conclusion of this paper, which includes, correspondingly, more in detail consideration of some more general physical problems; and, besides, in this article, the problem “what are Gravity and Electric Forces” is essentially clarified comparing with the arXiv 2021 paper version above, and additionally initial model of Nuclear Force is presented. Besides, the concrete problem “What is Life”, and the rational cosmological model, where a few vague points in standard cosmology rather probably are rationally clarified, while the fundamental problem “matter – antimatter asymmetry” in Matter is solved with rather large probability, are considered, and one of recently published rather complete “lists of fundamental problems” is commented in Appendix.

The inherited ‘EIA’ process at Brexit is based on a ‘Project’ period from Inception tothe start of construction works. The ‘Incompleteness’ of the process covers andidentifies stages that will impact on the environmental cycle: construction period,operational life, de-commissioning and a return to acceptable environmental footprint.A master environment structure-plan framework is required to commence with theupgrading of the complete ‘EIA’ process, embracing separate limbs for the UK’spriority environmental targets for climate change, and other major adverse effectswhich result in serious ‘harm’ to the UK environment. The identification of the processfor ‘incompleteness’ requires effective sustainability, and inclusion of effectivemanagement tools, for the essential ‘monitoring/control/recording’ proceduresthroughout the project life and the natural environmental cycle. This will allow theopportunity for a new approach to a structured ‘Suite of EIAR Directives’, to enable a‘EIAR’ regime that ‘will remain fit and proper for UK purpose’.

Wearable antennas are increasingly vital in modern healthcare, facilitating continuous monitoring and communication for medical purposes. These antennas are integrated into wearable devices, allowing for the transmission and reception of vital health data, such as heart rate, body temperature, and blood pressure, to medical professionals or monitoring systems in real time. This instantaneous data transmission enables timely interventions, thus improving the quality of healthcare services. This review aims to comprehensively synthesize recent research from reputable databases, focusing on the functionality and effectiveness of wearable antennas in medical applications. The primary objectives of each study were categorized, including antenna design and integration, the performance of medical wearable antenna technology, safety considerations in wearable antenna biomedicine, and the use of antennas in clinical applications and their impact. This synthesis provides valuable insights for researchers and practitioners aiming to develop and deploy wearable antennas in medical settings, ultimately enhancing healthcare delivery and patient outcomes.

This article argues that philosophy and its influential narrative should take and think "food" - the gastro-world - in order to radically renew itself and develop a gastrocentric view of the world and the future of humanity. It discusses first some of the basic ideas of a gastrocentric understanding of the world, second the adventure of becoming a Terran, and third the daily practice of what I will call "terra madre forming". It tells us this: If there is to be a future of human survival and well-being on Earth, if we are to achieve the goals of sustainable development, then we have a clear agenda for tomorrow with the re-humidification of the soil - madre terra - that nourishes us. What needs to be done is quite simple and down-to-earth: We, each of us, if possible, must participate in the regeneration of the earth. In conclusion, it is time for the Slow Food movement to blossom into a geo-gastro-activism. The future task of this organization is to make itself electable as a political party to support the much-needed transformation of humans into Terrans.

In this research, assume a SuperHyperGraph. Then a ``Failed SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$Failed SuperHyperClique'' is a \underline{maximal} Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$Failed SuperHyperClique'' is a \underline{maximal} neutrosophic Failed SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Neutrosophic Failed SuperHyperClique theory, SuperHyperGraphs theory, and Neutrosophic SuperHyperGraphs theory are proposed.

This study investigates the pivotal areas where Artificial Intelligence (AI) integration in healthcare warrants further exploration, leveraging insights from Boston Specialists, a forefront healthcare provider in AI adoption. Employing a qualitative case study approach, enriched by in-depth interviews and comprehensive literature reviews, we identify three main domains for potential AI expansion: scheduling efficiency, clinical documentation, and AI-driven medical research. Our results underscore the substantial enhancements AI brings to operational workflows and patient care, notably through improved scheduling systems, accuracy in medical documentation, and the facilitation of data-driven research methodologies. These findings suggest a critical need for healthcare institutions to further invest in AI technologies, focusing on these key areas to harness AI's full potential in personalizing care, optimizing efficiency, and advancing medical knowledge. The study concludes with a call for continued investigation into AI's integration within healthcare settings, emphasizing the importance of a supportive organizational infrastructure, ethical considerations, and data security in realizing AI's transformative impact on healthcare delivery and patient outcomes.

In this paper we investigate some properties of square-free numbers. In particular, we study a function that counts the number of square-free numbers no larger than the given number n. We show that this function has asymptotics consistent with the predictions of the Riemann hypothesis and use this to obtain new and better estimates of the density of square-free numbers. Finally, we present a well-known generalization of the concept of a square-free number to monoids and research on square-free factorizations.

In this article, we present solutions for one of the oldest mathematical problems, the Collatz Conjecture, and provide a proof for the Riemann Hypothesis, utilizing a new number theory based on newly discovered number properties, which will also be presented in this paper. This is made possible through the Sophy-Peter mathematical framework, built upon this new number theory. The Collatz Conjecture will be disproven, but as an alternative, the Oscillating Theorem will be introduced, with its correctness proven within this article. Furthermore, we present the general version of the Riemann zeta function, developed based on the new number theory. The correctness of this function is verified by comparing it with existing results of the zeta function. Using this approach and the Sophy-Peter framework, we have successfully proven the Riemann Hypothesis, long considered a millennium problem. Moreover, since the general zeta function is proven, this implies the correctness of the new number theory and the Sophy-Peter framework.

Background: Sexual dysfunction is the most common side effect encountered by cervical cancer patients during and after treatment, and rehabilitation strategies are needed to improve their quality of life. A variety of rehabilitation strategies have been reported in previous studies, varying by country, race and even continent. However, the common rehabilitation strategies used by cervical cancer survivors in Tanzania and their outcomes are unknown. The study aimed to unfold sexual rehabilitation strategies and outcome practiced by cervical cancer survivors who experienced sexual dysfunction during and after treatment in North-western Tanzania. Methods: Descriptive qualitative study were employed. Phenomenology study design used with a sample of 7 participants and data corrected via in-depth interview guided by 11 questions. Audiotaped and transcribed to get main themes and sub themes through deductive analysis. Results: Most participants reported inability to achieve an orgasm and low libido and dyspareunia after treatment. Most participants were eagerly to have their sexual activity recovered. However, they were not familiar with any rehabilitation strategy after the experience of sexual dysfunction. Even though, some of the participants attempted various interventions, but all were unsatisfactory leading to a significant decline in sexual interest and activity. Conclusion: Cervical cancer survivors are not familiar with any sexual rehabilitation strategies. Health education concerning various sexual rehabilitation strategies should be provided to survivors during and even after treatment.

Independent Learning Independent Campus (MBKM) is a program to develop an educational ecosystem that is in harmony with learning in higher education and the needs of industry. The limited link and match between universities and the business and industrial world in Indonesia are obstacles in realizing Indonesia as a developed country in the Industrial Revolution 4.0 era. The purpose of this study is to analyze the impact of the Independent Learning Independent Campus (MBKM) program on improving the performance of Ibn Khaldun University Bogor. The method used in this study is descriptive statistics with quantitative analysis. The sample that participated in this study consisted of all active students, lecturers, and administration staff. The research data was obtained through distribution to 6100 students, 233 lecturers, and 150 education staff. The research stages include socializing the understanding of MBKM, filling out the survey, calculating the distribution of respondents' filling, and concluding the assessment category using the weighted mean score (WMS) method. Based on the result, the implementation of MBKM in University of Ibn Khaldun Bogor based on all indicators can conclude that MBKM improve the performance of Ibn Khaldun Bogor University in the good category with an average percentage assessment criteria above 75%

Abstract: Qatar and other Gulf States have a diverse range of marine vegetation that is adapted to the stressful environmental conditions of seawater. The industrial wastewater produced by oil and gas activities adds further detrimental conditions for marine aquatic photosynthetic organ-isms on the Qatari coastlines. Thus, these organisms experience severe stress from both seawater and industrial wastewater. This review discusses the biodiversity in seawater around Qatar, as well as remediation methods and metabolic pathways to reduce the negative impacts of heavy metals and petroleum hydrocarbons produced during these activities. These methods include phyto-stabilization phyto-accumulation, phyto-volatilization, and phyto-degradation. Phy-to-degradation in particular is discussed in detail, including metabolic pathways such as alkane and aromatic-compound degradation pathways. The role of microorganisms that are adjacent to or associated with these aquatic marine organisms is discussed, including rhizosphere biodeg-radation. In this type of biodegradation, exudates are released by plant roots and supply nutrients to microorganisms in the rhizosphere, which enhances their ability to degrade organic pollutants. Special attention is paid to mangrove forests and their roles in remediating shores polluted by industrial wastewater. Seagrasses (Halodule uninervis, Halophila ovalis, and Thalassia hemprichii) and seaweeds (Chlorophyta, Phaeophyta, and Rhodophyta) around the peninsula of Qatar are also discussed.

This study provides an evaluation of a web-based platform for game management and sales, developed using PHP, MySQL, and SASS. The development process utilized the SCRUM methodology, concentrating on essential modules such as user management, game catalog, payment processing, and technical support. The platform's performance was assessed using Google's Lighthouse tool, which evaluates four critical areas: performance, accessibility, best practices, and SEO. The results demonstrated exceptional performance with a score of 99/100 and perfect adherence to best practices with a score of 100/100, reflecting high efficiency and compliance with web development standards. Accessibility received a score of 83/100, indicating potential areas for improvement, while SEO achieved a score of 91/100, suggesting effective search engine optimization. The findings reveal that the platform exhibits high levels of optimization and operational efficiency. However, there remains an opportunity to enhance accessibility features. This study highlights the significance of rigorous web development practices and optimization efforts in achieving superior performance and user experience in web-based systems.

Cosmetic surgery is the subfield of plastic surgery that enhances appearance mainly for aesthetic reasons. Currently, cosmetic surgery interventions are highly considered appealing and popular all around the world. Several factors have contributed in this rapidly evolving field such as scientific and economic development, breaking down barriers and cultural norms, globalization, social media and mental disorders. Nowadays, the morality of cosmetic surgery is facing many dilemmas due to its benefits and drawbacks. It is proven that the advantages of cosmetic surgery include improved body confidence, mental health, and function. Additionally, aesthetic corrections can upscale the quality of life and create career opportunities for special targeted groups. Also, cosmetic surgery has a major impact in gender affirmation procedures. Although, herein we also describe the disadvantages of this widely developing field such as minor and major medical complications, potential postoperative risks and addiction in plastic surgeries associated with damaging economic issues. Lack in self-confidence, altered mental health status and ethical crisis consist another negative aspects of aesthetic surgery’s impact.

In this digital era, laundry applications come as an innovative solution to meet the laundry needs of modern people who often have busy schedules and limited time. This research aims to make a significant contribution to our broader understanding of how digital innovations can revolutionize mundane tasks. This research uses the Waterfall model, which is one of the methods in the Software Development Life Cycle (SDLC). The development process begins with the Requirement Analysis stage, where application requirements and specifications are collected and thoroughly analyzed to ensure that the developed application will meet user expectations. After that, the System Design stage is conducted, where the application architecture, user interface design, and database structure are designed in detail to ensure conformity with the previously identified needs.The next stage is Implementation, where program code is written and application features are developed according to the design that has been made. The final stage is Integration and Testing, where all application components are combined and tested thoroughly to detect and fix any errors or bugs that may exist. The results of this study produced a web-based shuttle laundry service application using the Laravel framework called "All Fresh Laundry". This application can order clothes washing services according to its membership, where there are 3 types of membership based on price and of course have different benefits. In addition, the testing phase of this application using black box testing shows that all menu features function properly according to their functions. Each component of the "All Fresh Laundry" app was thoroughly tested to ensure that no errors or malfunctions occurred. The results of this testing make it clear that every feature, from online ordering to laundry status tracking, works well and meets the specifications that have been set, so that this application can provide an optimal and reliable user experience.

Camping offers invaluable experiences in nature exploration, but the expense of acquiring camping gear can deter potential enthusiasts. To mitigate this, camping gear rental services emerge as a practical solution, promoting accessibility and reducing financial barriers. However, existing rental systems often encounter issues such as limited payment options, inconvenient pickup/return processes, and opaque management. In response, this paper introduces "Rent-n-Play," a web-based camping gear rental platform built on Laravel framework. It enables cashless transactions, offers pickup/delivery services, and employs a real-time admin system for transparent management. User feedback guided platform enhancements, including review systems and responsive support. The "Rent-n-Play" platform enhances user experience, fosters trust, and promotes sustainable camping practices, thus contributing to a more accessible and enjoyable camping culture.

The issue of sufficient nutrition and appropriate distribution in school lunch programs presents a significant challenge that must be addressed. Many schools struggle to provide food that meets all of their students’ nutritional needs. Additionally, inconsistencies in nutritional information and administrative difficulties often hinder the efficient operation of these programs. Developing technology to better manage school lunch programs is critical to addressing these issues. The goal of this project is to create a web application that ensures the fair distribution of nutritional information while also increasing the efficiency of lunch program administration. The methodology used in this research is Agile. Agile approaches are employed throughout the development process, allowing for rapid iteration and responsiveness to user feedback. The end result is a web tool called Nourishify, designed to streamline the management and dissemination of nutritional information. Implementing Nourishify led to substantial improvements in access to nutrition information and operational efficiency, making it an innovative solution for school lunch programs. This project demonstrates that integrating technology can significantly enhance the administration and transparency of nutrition programs, ultimately benefiting students' health and well-being. Moreover, Nourishify’s user-friendly interface and real-time data capabilities ensure that all stakeholders, including parents, administrators, and nutritionists, can easily collaborate and access crucial information.

This article presents a new method of segmenting grayscale images by minimizing Shannon's neutrosophic entropy. For the proposed segmentation method, the neutrosophic information components, i.e., the degree of truth, the degree of neutrality and the degree of falsity are defined taking into account the belonging to the segmented regions and at the same time to the separation threshold area. The principle of the method is simple and easy to understand and can lead to multiple thresholds. The efficacy of the method is illustrated using some test gray level images. The experimental results show that the proposed method has good performance for segmentation with optimal gray level thresholds.

Point of Sales (POS) systems are an important component of sales and inventory management for many businesses. This article discusses the development of a POS application designed to simplify the process of selling products in stores. The application uses PHP for the server, JavaScript for the client, Bootstrap for responsive design, and MySQL as the database. Its main features include a dashboard with daily sales summary, visual graphs, product category management, product addition and editing, admin and access rights management, ease of sales transaction processing, access to sales reports and analyses by leaders, and provision of sales reports in various formats. The clean and easy-to-use interface is expected to improve the efficiency of sales and inventory management, and assist businesses in making data-driven decisions.

The research is on the SuperHyperGirth and the neutrosophic SuperHyperGirth. A SuperHyperGraph has SuperHyperGirth where it’s the longest SuperHyperCycle. To get structural examples and instances, I’m going to introduce the next SuperHyperClass of SuperHyperGraph based on SuperHyperGirth. It’s the main. It’ll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. This SuperHyperClass is officially called “SuperHyperFlower”. If there’s a need to have all SuperHyperCycles until the SuperHyperGirth, then it’s officially called “SuperHyperOrder” but otherwise, it isn’t SuperHyperOrder. There are two instances about the clarifications for the main definition titled “SuperHyperGirth”. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on SuperHyperGirth and they’re called “SuperHyperFlower.” A SuperHyperGraph has “neutrosophic SuperHyperGirth” where it’s the strongest [the maximum value from all SuperHyperCycles amid the minimum value amid all SuperHyperEdges from a SuperHyperCycle.] SuperHyperCycle. In “Cancer’s Recognitions”, the aim is to find either the longest SuperHyperCycle or the strongest SuperHyperCycle in those neutrosophic SuperHyperModels. For the longest SuperHyperCycle, called SuperHyperGirth, and the strongest SuperHyperCycle, called neutrosophic SuperHyperGirth, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it’s not enough since it’s essential to have at least three SuperHyperEdges to form any style of a SuperHyperCycle. There isn’t any formation of any SuperHyperCycle but literarily, it’s the deformation of any SuperHyperCycle. It, literarily, deforms and it doesn’t form. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

New setting is introduced to study the alliances. Alliances are about a set of vertices which are applied into the setting of neutrosophic graphs. Neighborhood has the key role to define these notions. Also, neighborhood is defined based on the edges, strong edges and some edges which are coming from connectedness. These three types of edges get a framework as neighborhood and after that, too close vertices have key role to define offensive alliance, defensive alliance, t-offensive alliance, and t-defensive alliance based on three types of edges, common edges, strong edges and some edges which are coming from connectedness. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs containing complete, empty, path, cycle, bipartite, t-partite, star and wheel are investigated in the terms of set, minimal set, number, and neutrosophic number. In this study, there’s an open way to extend these results into the family of these classes of neutrosophic graphs. The family of neutrosophic graphs aren’t study but it seems that analogous results are determined. There’s a question. How can be related to each other, two sets partitioning the vertex set of a graph? The ideas of neighborhood and neighbors based on different edges illustrate open way to get results. A set is alliance when two sets partitioning vertex set have uniform structure. All members of set have different amount of neighbors in the set and out of set. It leads us to the notion of offensive and defensive. New ideas, offensive alliance, defensive alliance, t-offensive alliance, t-defensive alliance, strong offensive alliance, strong defensive alliance, strong t-offensive alliance, strong t-defensive alliance, connected offensive alliance, connected defensive alliance, connected t-offensive alliance, and connected t-defensive alliance are introduced. Two numbers concerning cardinality and neutrosophic cardinality of alliances are introduced. A set is alliance when its complement make a relation in the terms of neighborhood. Different edges make different neighborhoods. Three types of edges are applied to define three styles of neighborhoods. General edges, strong edges and connected edges are used where connected edges are the edges arising from connectedness amid two endpoints of the edges. These notions are applied into neutrosophic graphs as individuals and family of them. Independent set as an alliance is a special set which has no neighbor inside and it implies some drawbacks for this notions. Finding special sets which are well-known, is an open way to purse this study. Special set which its members have only one neighbor inside, characterize the connected components where the cardinality of its complement is the number of connected components. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

This study focuses on the creation and implementation of a platform to improve personal financial management for scholarship students of the National Program of Scholarships and Educational Credit (Pronabec) in Peru. Using a mixed methodology that combines qualitative and quantitative techniques, the effectiveness and user satisfaction with the platform were evaluated. The results indicated that 50\% of users found the tool useful, 55\% considered it easy to use, 70\% reported a positive impact on their personal budget planning, and 85\% expressed high overall satisfaction. In addition to providing tools for financial recording and analysis, the platform promotes financial education among its users, significantly contributing to improving their financial management skills.

This study provides a thorough examination of the introduction of 5G technology in Bangladesh's agriculture sector, providing insights into the problems and potential implications related to its adoption. Focusing on the contextual landscape of Bangladesh, the study evaluates the effectiveness, efficiency, scalability, and ease of implementation of 5G technology concerning key challenges faced by the agricultural sector. Drawing comparisons with global perspectives, including countries such as China, Taiwan, Colombia, Netherlands, and India, the analysis provides a nuanced understanding of the diverse technological landscapes. The examination encompasses the evolution from 4G to 5G, emphasizing the commitment of major telecommunications providers in Bangladesh to advance technological capabilities. The challenges in rural adoption, limited technology literacy among farmers, and high smartphone costs are discussed, highlighting potential barriers to seamless integration. To address the creation of a more comprehensive technological infrastructure, the study also explores the efforts and regulatory support provided by the government and the Bangladesh Telecommunication Regulatory Commission (BTRC). Furthermore, the comparative analysis sheds light on the unique characteristics and advancements in other countries, contributing to a holistic understanding of 5G's role in transforming global agricultural practices. By exploring the anticipated socio-economic factors influencing the pace and success of 5G adoption in the agricultural sector, this paper emphasizes the need for collaborative efforts, infrastructure development, and addressing accessibility challenges to achieve widespread agricultural technology integration.

RNA sequencing techniques, like bulk RNA-seq and Single Cell (sc) RNA-seq, are critical tools for the biologist looking to analyze the genetic activity/transcriptome of a tissue or cell during an experimental procedure. Platforms like Illumina's next-generation sequencing (NGS) are used to produce the raw data for this experimental procedure. This raw FASTQ data must then be prepared via a complex series of data manipulations by bioinformaticians. This process currently takes place on an unwieldy textual user interface like a terminal/command line that requires the user to install and import multiple program packages, preventing the untrained biologist from initiating data analysis. Open-source platforms like Galaxy have produced a more user-friendly pipeline, yet the visual interface remains cluttered and highly technical, remaining uninviting for the natural scientist. To address this, SeqMate is a user-friendly tool that allows for one-click analytics by utilizing the power of a large language model (LLM) to automate both data preparation and analysis (differential expression, trajectory analysis, etc). Furthermore, by utilizing the power of generative AI, SeqMate is also capable of analyzing such findings and producing written reports of upregulated/downregulated/user-prompted genes with sources cited from known repositories like PubMed, PDB, and Uniprot.

The integration of solar energy systems with agricultural practices, known as agrivoltaic systems, presents a promising solution for advancing sustainable food and energy production. This approach involves installing photovoltaic panels on agricultural lands, which allows for simultaneous crop cultivation and energy generation. Agrivoltaic systems offer a dual benefit: they enhance land use efficiency by utilizing the same area for both solar power generation and crop production, and they contribute to sustainable energy transitions. This abstract explores the benefits and challenges associated with agrivoltaic systems. Key advantages include increased land productivity, reduction in water usage due to shading effects, and potential economic gains from dual income streams. Furthermore, these systems can mitigate land use conflicts by combining food production with renewable energy generation. However, there are challenges to address, including the potential for decreased crop yields under solar panels, the need for appropriate system design to balance energy generation and agricultural needs, and the economic feasibility of initial investment and maintenance. The integration of agrivoltaic systems represents a critical step toward achieving sustainable development goals by promoting environmental stewardship and resource efficiency. Future research and advancements in technology are essential to optimize system performance and maximize benefits for both agriculture and energy sectors.

this paper we present approaches for generating random numbers along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses as well as their potential application domains so as the reader can judge what would be the best approach for the application in hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed, then suitable preprocessing can enhance its randomness and then the output of the preprocessing can feed different types of generators, e.g. a linear congruential generator, a cryptographically secure one and one based on the combination of one way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined giving the final random sequence. Moreover, we present a set of practical randomness tests which can be applied on the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e. eLotteries and cryptographic key generation.

The use of credit cards and online banking is expanding exponentially. As more individuals use debit cards, credit cards, and internet banking, the likelihood of falling victim to various forms of fraud also rises. Due to ignorance, credit card company customers have provided their card details, personal information, and one-time password to an unknown bogus caller on several occasions in the recent past. One of the biggest issues facing financial institutions and customers alike is credit card theft. It may result in large financial losses and harm to the financial institution's image. While there are several ways to identify credit card fraud, one of the best is machine learning.By using past data, machine learning algorithms may be trained to recognize trends and abnormalities that point to fraud. The state-of-the-art in machine learning for credit card fraud detection is reviewed in this study. Numerous research on the same subject have been conducted in the past with a variety of well-known machine-learning techniques. However, with a grasp of the notion of hybrid machine learning, we will now examine how well hybrid machine learning performs on the same problem statement.

Abstract: Comorbidities of patients may be related to the duration of mechanical ventilation, survival, and Candida isolation during intensive care unit (ICU) stay. To examine the frequency of Candida isolation and significant comorbidities in the surgical intensive care unit (ICU) in Osijek University Hospital, Croatia, the data from the electronic database from May 2016 to June 30, 2023, were analyzed. In a cross-sectional study examining 15,790 microbiological samples, different strains of Candida were observed in 581 samples from 236 patients. The control group was 160 consecutive patients from March-May 2019, and 161 in the same months of 2020 (pre- and post-COVID-19). Comorbidities, duration of mechanical ventilation and survival were compared. Patients with isolated Candida were more often non-elective, had significantly more heart, kidney, liver diseases and sepsis (P<0.001). The duration of mechanical ventilation was 9.2 [2.2-9.24], 96 [24-146], 160 [19.5-343] and 224 [73.5-510] hours in controls, and patients with Candida albicans, non-albicans, and in patients with ³2 Candidas isolated. The mortality was significantly higher and reached 42% in patients with Candida isolated, while in the control group, it was 19% (P<0.001). In a multivariate analysis adjusted for patient’s age, SAPS II score, days of ICU, and type of admission, only sepsis was independent predictor of mortality (OR = 2.27).

Visualising textual content could be helpful to professionals as well as amateurs across several fields. However, training a text-to-image generator in the mainstream domain requires large amounts of paired text-image and data, which is too expensive to collect since labeling millions of images and videos can be tiresome. GANs like StackGAN and StyleGAN can be considered as solutions to generate images from text. But the images generated may be of low accuracy and resolution, and the entire processing can be highly time-consuming. Moreover, image generation is a notion that is still being researched. Hence, the process of developing a Video Generation model necessitates substantial research. Despite the need for such a model, modern technology has lagged behind the solutions to this problem. This proposal suggests combining two methods, Text modification for Action Definition (TexAD) and SeQuential Image Generation for Video Synthesis (SQIGen). The proposed solution synthesises a sequence of images from textual information feeds and combines these images to create a video. TexAD uses Natural Language Processing and Deep Learning techniques to process, classify and modify text data. SQIGen is an extension of the VQGAN+CLIP neural network architecture that generates a sequence of images from the modified text data

Influencer marketing has become a pivotal component of digital marketing strategies, offering brands a unique way to connect with audiences through trusted voices. However, measuring the return on investment (ROI) from influencer marketing campaigns can be challenging due to the intangible nature of brand influence and engagement. This abstract explores various techniques and strategies to measure and optimize ROI in influencer marketing. Measurement Techniques: The paper delves into both quantitative and qualitative methods for assessing influencer marketing ROI. Quantitative techniques include tracking metrics such as impressions, clicks, conversions, and sales, using tools like Google Analytics and social media insights. Additionally, advanced attribution models, such as multi-touch attribution and econometric modeling, are discussed for more accurately linking influencer activities to business outcomes. Qualitative approaches involve sentiment analysis and brand awareness studies, which help gauge the impact of campaigns on brand perception and customer loyalty. Optimization Strategies: To maximize the effectiveness of influencer marketing, the paper outlines several optimization strategies. These include selecting the right influencers based on audience alignment and engagement rates, setting clear and measurable campaign goals, and employing A/B testing to refine content and strategies. The importance of long-term partnerships and content diversification is also emphasized, as they can enhance authenticity and sustain audience interest. The abstract concludes that a comprehensive approach combining rigorous measurement techniques and strategic optimization can significantly enhance the ROI of influencer marketing campaigns. By continuously analyzing data and refining strategies, brands can better leverage influencer partnerships to achieve their marketing objectives.

The convergence of digital twin technology with additive manufacturing (AM) represents a transformative advancement in the fields of design, simulation, and production. Digital twins—virtual replicas of physical assets—enable real-time monitoring, simulation, and optimization of manufacturing processes by mirroring their physical counterparts. When integrated with additive manufacturing, which allows for the creation of complex geometries and rapid prototyping, digital twins enhance the ability to design, test, and refine products with unprecedented precision and efficiency. This integration facilitates iterative design improvements, predictive maintenance, and real-time process adjustments, leading to more accurate simulations and optimized production workflows. By leveraging data from digital twins, manufacturers can anticipate issues, reduce material waste, and shorten development cycles. This abstract explores how the fusion of digital twin technology with AM not only refines traditional manufacturing paradigms but also paves the way for more innovative and adaptive manufacturing practices.

Emission trading schemes (ETSs) have become vital tools in striving toward global emission reduction objectives and promoting a sustainable economy. This paper empirically investigates the impact of market conditions on interconnectedness within precious metals, clean energy, green bonds, and carbon markets, focusing on China and the EU ETSs as the study subjects. A TVP-VAR-based asymmetric connectedness approach is adopted to capture the evolving relationships between the variables of interest in the time–frequency domain. The empirical findings reveal that: First, time-varying asymmetric connectedness and spillover effects among clean energy, precious metals, green bonds, and carbon markets are identified in both time and frequency domains under diverse market conditions, with long-term connectedness asymmetry being particularly sensitive, although spillovers exhibit variations. Second, the role and intensity of net transmitters or receivers vary across market conditions and frequency domains, indicating the complex and nuanced nature of market interactions. The EU ETS demonstrates a higher level of connectivity with global markets for clean energy, precious metals, and green bonds when compared to the Chinese ETS. However, it also shows greater susceptibility to fluctuations in market conditions. These results have significant implications for both investors striving to build sustainable diversified portfolios and regulators endeavoring to craft effective policies for risk regulation and sustainable development.

Large Language Models (LLMs) have proved significant proficiency when comes to code generation especially in Structured Query Language (SQL) for databases and recent successful Text-to-SQL method involves fine-tuning pre-trained LLMs for SQL generation tasks. Transforming natural language text into SQL queries, has been attempted to solve with various learning techniques including Few-shot learning[1], fine tuning. In this paper we propose Supervised fine-tuning (SFT) as a better alternative for learning technique for text-to-SQL generation task using Code-Llama that pushes state of art accuracy on spider test suite to 89.6% on dev set which represent first instance of surpassing the earlier best-in-class with 5.5% higher score and 86.8% of exact match accuracy on dev set. Furthermore, we demonstrate that properly prompted LLM along with SFT provides far fewer hallucinations and much more robust LLM that can be used as a general tool for any text-to-SQL generation use case.

The advent of artificial intelligence (AI) has revolutionized digital marketing, offering unprecedented levels of personalization. AI-driven personalization leverages machine learning algorithms and data analytics to tailor content, advertisements, and recommendations to individual consumers based on their behavior, preferences, and demographics. This paper explores the effectiveness of AI-driven personalization in enhancing customer engagement, increasing conversion rates, and improving overall marketing efficiency. It also examines the ethical considerations associated with these technologies, including data privacy, consent, and the potential for manipulation or bias. While AI-driven personalization can lead to more relevant and engaging consumer experiences, it raises critical ethical questions that must be addressed to ensure responsible and fair use. The study concludes with recommendations for marketers and policymakers to balance the benefits of AI personalization with the need for ethical standards and consumer protection.

Background: The effectiveness of the anti-COVID-19 vaccine remains a matter to be clarified. Methods: The humoral and cellular immunity after the administration of three doses of the Pfizer–BioNTech and Oxford AstraZeneca vaccines against SARS-CoV-2 over one year and the appearance of post-vaccination COVID-19 have been studied. Results: Anti-SARS-CoV-2 IgG and IgA antibodies showed a progressive increase throughout the vaccination period. This increase was greatest after the third dose. The highest levels were observed in subjects who had anti-SARS-CoV-2 antibodies prior to vaccination. There was an increase in CD4+ αβ, CD8+ γδ and TEM CD8+ γδ T cells, and a decrease in apoptosis in CD4+CD8+ and CD56+ αβ and γδ T cells. Post-vaccination SARS-CoV-2 infection was greater than 60%. The symptoms of COVID-19 were very mild and were related to γδ T cell deficit, specifically CD8+ TEMRA and CD56+ γδ TEM, as well as lower pre-vaccine apoptosis levels. Conclusions: Those results demonstrate the important role that γδ T cells play in SARS-CoV-2 vaccine immunization.

The transition to renewable energy sources is critical for sustainable development, particularly in rural regions with limited access to electricity. Solar-powered microgrids offer a promising solution for rural electrification by providing reliable, clean energy that can enhance economic opportunities and improve quality of life. This paper presents a techno-economic analysis of solar-powered microgrids for rural areas, evaluating their feasibility, costs, and benefits. The analysis encompasses technological aspects, such as solar panel efficiency, battery storage, and grid management, alongside economic factors including initial investment, maintenance costs, and potential returns. Additionally, the study assesses the social impact of solar-powered microgrids, exploring their effects on local communities, including improvements in education, health, and economic activities. The findings indicate that solar microgrids can be a viable and impactful solution for rural electrification, with significant long-term benefits for both economic development and social well-being.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making problem.

This qualitative research explores the impact of Artificial Intelligence (AI) on Customer Relationship Management (CRM), providing a comprehensive analysis of how AI technologies are transforming CRM practices. AI integration in CRM has revolutionized customer interactions, enabling enhanced personalization, efficiency, and customer engagement. By leveraging machine learning, natural language processing, and predictive analytics, organizations can create highly tailored customer experiences, automate routine tasks, and anticipate future customer needs with precision. The study identifies the significant benefits of AI, including improved customer insights, faster response times, and proactive engagement strategies. However, it also highlights the challenges associated with AI adoption in CRM, such as data privacy and security concerns, algorithmic bias, high implementation costs, and resistance to change. The findings emphasize the need for robust data protection measures, strategies to mitigate biases, significant investments in technology and training, and effective change management to overcome these challenges. The thematic analysis reveals key areas where AI is making an impact, including customer service, customer segmentation, and personalized marketing strategies. Additionally, the study discusses the organizational implications of AI adoption, such as enhanced decision-making, increased productivity, and the necessity for staff reskilling. Future directions for AI in CRM suggest further advancements in AI algorithms, greater integration with other business systems, enhanced customer experiences, and a focus on ethical AI practices. This research underscores the transformative potential of AI in CRM and provides insights for organizations aiming to leverage AI for improved customer relationship management.

This study explores the influence of social media marketing on brand loyalty, employing a qualitative research approach to gain in-depth insights into the key factors that drive consumer engagement and commitment. Through semi-structured interviews with 20 active social media users and a comprehensive analysis of social media content, the research identifies several critical elements affecting brand loyalty. Personalization emerged as a central theme, with tailored content, customized offers, and personalized recommendations significantly enhancing users' emotional connection with brands. High-quality content, characterized by engaging visuals and valuable information, was found to reinforce positive brand perceptions and sustain loyalty. Influencer marketing also plays a pivotal role, with authentic endorsements from relevant influencers boosting brand credibility and trust. Effective community management, involving active engagement, responsive feedback, and relationship-building, contributes to a positive brand experience and strengthens user loyalty. Targeted and relevant social media advertising supports brand loyalty, although excessive or irrelevant ads can lead to disengagement. The study also highlights the importance of balancing interaction frequency and content quality to maintain user interest without causing fatigue. Addressing social media fatigue by delivering relevant and valuable content is crucial for preventing user disengagement. Content that resonates with users' values and emotions further strengthens brand attachment. Consistency in brand voice, visual identity, and values ensures a coherent and positive brand experience. The findings emphasize the need for a strategic approach to social media marketing, integrating personalization, content quality, influencer partnerships, community management, advertising relevance, and consistency to build and sustain strong brand loyalty.

This study investigates the adoption of Robotic Process Automation (RPA) in marketing operations, exploring its impact on efficiency, data accuracy, and overall effectiveness. RPA has emerged as a transformative technology, automating routine tasks such as data entry, report generation, and campaign management, which has significantly enhanced operational efficiency within marketing departments. By automating repetitive processes, RPA enables marketing professionals to focus on strategic and creative tasks, resulting in accelerated campaign execution and improved productivity. Additionally, the integration of RPA with Customer Relationship Management (CRM) systems has led to more accurate and consistent data, providing valuable real-time insights that enhance decision-making and personalization in marketing strategies. Despite these benefits, the study also highlights several challenges associated with RPA adoption. These include concerns about workforce implications, such as job displacement and the need for reskilling, as well as implementation difficulties related to system compatibility and workflow design. Ethical and regulatory considerations, particularly regarding data privacy and compliance, are also critical factors that organizations must address to maintain customer trust and adhere to legal standards. The study further explores the potential of integrating artificial intelligence (AI) with RPA to drive future innovations in marketing automation. AI-driven RPA offers advanced capabilities, including predictive modeling and personalized marketing, which promise to enhance the effectiveness of automation strategies. The findings underscore the need for organizations to adopt best practices in RPA implementation and remain adaptable to technological advancements to fully leverage the benefits of automation and maintain a competitive edge in the dynamic marketing landscape.

Big data analytics has fundamentally transformed how organizations enhance customer experience by leveraging vast amounts of data to tailor interactions, streamline services, and drive strategic decisions. This research explores the multifaceted role of big data in improving customer experiences, focusing on its impact on personalization, customer service, operational efficiency, and strategic decision-making. By analyzing recent advancements and applications, the study highlights how big data analytics enables highly personalized recommendations, targeted marketing efforts, and dynamic content that significantly enhance customer engagement. Additionally, it examines the improvements in customer service through real-time support, sentiment analysis, and predictive assistance, which collectively contribute to a more responsive and customer-centric approach. The research also addresses how big data analytics optimizes operational efficiency by streamlining workflows, improving resource allocation, and reducing costs, thus enhancing overall organizational performance. Strategic decision-making benefits from data-driven insights into market trends, pricing strategies, and competitive positioning, allowing organizations to adapt and thrive in a competitive environment. However, the study also acknowledges the challenges associated with data quality, privacy, and investment, emphasizing the need for robust measures to address these issues. Furthermore, the integration of big data with emerging technologies such as artificial intelligence, the Internet of Things, and blockchain presents new opportunities and complexities in enhancing customer experience. Overall, this research underscores the transformative potential of big data analytics while highlighting the importance of addressing its associated challenges to fully capitalize on its benefits.

This study explores consumer perceptions of virtual reality (VR) in marketing, aiming to understand how immersive technology impacts engagement and brand perception. As VR continues to evolve and integrate into various marketing strategies, it becomes crucial to examine its effectiveness and the factors influencing consumer attitudes. Through a detailed thematic analysis, this research identifies key themes such as familiarity with VR technology, immersion and engagement, technical quality, accessibility, personalization, storytelling, social interaction, purchase intentions, and brand perception. The findings reveal that familiarity with VR enhances enthusiasm and comfort, leading to more positive attitudes towards VR marketing. The immersive and multi-sensory nature of VR provides a significant advantage over traditional advertising methods, fostering stronger emotional connections and increasing memorability. However, the quality of the VR experience is critical; high-quality graphics and seamless interactions are essential for maintaining positive consumer perceptions. Technical issues, such as lag and motion sickness, can negatively impact the experience, especially for those less acquainted with VR technology. Accessibility remains a challenge, with limited access to VR headsets restricting the reach of VR marketing campaigns. Personalization of VR content is highly valued, though it must be balanced with ethical considerations related to data privacy. The power of storytelling in VR enhances engagement by allowing consumers to actively participate in narratives. Social interaction within VR experiences adds an extra layer of enjoyment. The study also highlights the practical applications of VR marketing in high-involvement sectors and underscores the need for continuous innovation and consumer feedback to maximize the technology's impact. Overall, VR holds significant potential to transform marketing practices by offering immersive, engaging, and memorable experiences that deepen consumer connections and drive positive outcomes.

This study explores the role of chatbots in enhancing customer service, examining their benefits, limitations, and overall impact on modern support systems. Chatbots have emerged as a transformative technology in customer service, offering significant advantages such as increased efficiency through automation of routine tasks, reduced response times, and the ability to provide 24/7 support. By handling high volumes of inquiries and managing repetitive tasks, chatbots alleviate the workload of human agents, allowing them to focus on more complex issues. Additionally, chatbots employ advanced data analytics and machine learning to deliver personalized interactions, enhancing user engagement and satisfaction. Despite these benefits, the research identifies several challenges, including chatbots' difficulty in managing complex queries and their lack of emotional intelligence, which often necessitates escalation to human agents. The study also highlights the importance of well-designed chatbots and seamless integration with existing systems to ensure effective user experiences. Privacy and security concerns are critical, as chatbots handle sensitive customer data, requiring robust measures to protect against breaches and ensure compliance with data protection regulations. Looking ahead, advancements in technologies such as augmented reality (AR), virtual reality (VR), and artificial intelligence (AI) are expected to further enhance chatbot capabilities, addressing current limitations and expanding their role in customer service. The findings suggest that a hybrid approach, combining chatbots with human support, offers the most effective solution for delivering high-quality customer service. Overall, chatbots have proven to be valuable assets, and their continued evolution promises to significantly impact the future of customer service.

This study investigates the influence of digital marketing on consumer purchasing decisions, focusing on how various strategies impact consumer behavior. By analyzing data collected from in-depth interviews and thematic analysis, the research highlights several key factors driving consumer engagement and purchases. Personalized content emerged as a significant factor, with tailored recommendations and customized email campaigns creating a sense of individual attention and enhancing consumer involvement. Social media platforms played a pivotal role, with advertisements, influencer endorsements, and user-generated content significantly affecting purchasing decisions. The impact of visual content, including high-quality images and videos, was also notable, as these elements helped consumers better understand products and increased their confidence in making purchases. Email marketing proved effective, particularly when offering exclusive discounts and creating a sense of urgency. Mobile marketing demonstrated its growing influence, with consumers valuing the convenience of mobile-friendly websites and app notifications. The integration of artificial intelligence further improved the shopping experience by providing instant assistance and personalized recommendations. Ethical considerations, such as data privacy and honest advertising, were essential for maintaining consumer trust and loyalty. User-generated content provided authentic insights that influenced purchasing decisions, while omnichannel strategies offered a seamless and flexible shopping experience. Gamification elements, including reward programs and interactive challenges, enhanced consumer engagement and motivation. The study concludes that a multifaceted approach to digital marketing, incorporating these strategies, is crucial for effectively engaging consumers and driving sales. The findings offer valuable insights for marketers aiming to optimize their digital marketing strategies in the evolving digital landscape.

This study explores the transformative impact of machine learning on predictive analytics within supply chain management. As supply chains become increasingly complex and dynamic, traditional methods of forecasting and management are proving inadequate. Machine learning offers advanced algorithms capable of analyzing vast datasets to uncover patterns and trends that enhance decision-making processes. This research investigates how machine learning improves demand forecasting accuracy, optimizes inventory management, strengthens supplier relationships, and enhances risk management. The study employs a qualitative approach, analyzing data from industry case studies and expert interviews to identify key themes and challenges associated with the adoption of machine learning. Findings reveal that machine learning significantly improves forecasting precision, reduces inventory costs, and enables proactive supplier and risk management. However, challenges such as ensuring data quality, acquiring specialized skills, integrating new technologies with existing systems, and addressing ethical considerations are critical. The study also highlights the potential of emerging technologies like blockchain, IoT, and 5G to further enhance machine learning applications in supply chain management. This research contributes to a deeper understanding of how machine learning can drive innovation and efficiency in supply chains, while also addressing the hurdles that organizations must overcome. The results underscore the need for a balanced approach that incorporates technological advancements and ethical practices to fully leverage the benefits of machine learning.

This study explores the impact of artificial intelligence (AI) on digital marketing strategies, emphasizing how AI technologies have transformed marketing practices. AI's ability to analyze vast amounts of data has significantly enhanced targeting and personalization, enabling marketers to deliver highly relevant and tailored content to specific consumer segments. The integration of AI in content creation has streamlined processes, improving efficiency while maintaining high standards of quality and relevance. Customer engagement has also been revolutionized through AI-driven tools such as chatbots and predictive assistance, which provide real-time, personalized support and enhance overall user satisfaction. Despite the numerous benefits, the adoption of AI in digital marketing presents challenges, including data privacy concerns, algorithmic bias, high implementation costs, and the complexity of integrating AI with existing marketing systems. The shortage of skilled professionals further complicates effective AI utilization. Looking forward, the potential for AI to drive innovation in digital marketing is substantial, with opportunities for advancements in personalization, predictive analytics, and the integration of emerging technologies like virtual and augmented reality. However, it is essential for businesses to navigate these developments carefully, addressing ethical considerations and ensuring responsible use of AI to maintain consumer trust and achieve sustained success. This study provides insights into the transformative effects of AI on digital marketing and offers a comprehensive overview of the associated benefits and challenges, highlighting the need for a balanced approach to leveraging AI technology.

This research explores the adoption of advanced analytics in supply chain decision-making, emphasizing its transformative impact on organizational efficiency and strategic advantage. The study investigates the key drivers behind the adoption of advanced analytics, including the growing complexity of data, the need for agility, and the pursuit of competitive advantage and cost reduction. It identifies significant challenges such as data integration difficulties, high implementation costs, and a shortage of skilled professionals, which organizations face when integrating these sophisticated tools. Despite these challenges, the research highlights the substantial benefits of advanced analytics, including enhanced forecasting accuracy, improved supply chain visibility, optimized processes, and cost savings. The findings indicate that while the implementation of advanced analytics varies across different sectors—such as retail, manufacturing, logistics, and healthcare—the overarching themes of improved efficiency and better decision-making are consistently observed. The study also discusses future trends, noting the integration of emerging technologies such as artificial intelligence, machine learning, and blockchain, which promise to further enhance analytics capabilities and accessibility. The successful adoption of advanced analytics relies not only on technological advancements but also on fostering a data-driven organizational culture, investing in continuous learning, and ensuring robust data governance. As supply chain management continues to evolve, advanced analytics will play a crucial role in driving strategic success and maintaining a competitive edge in a complex and dynamic market environment.

The integration of Augmented Reality (AR) in e-commerce has emerged as a transformative development, reshaping how consumers interact with online retail environments. This research explores the impact of AR on e-commerce by examining its effects on consumer behavior, purchase decisions, and overall shopping experience. Through a series of interviews with industry experts, the study uncovers key insights into how AR enhances product visualization, leading to improved consumer confidence and a reduction in return rates. The immersive and interactive nature of AR applications has been shown to significantly increase consumer engagement and conversion rates, as users are able to interact with products in a virtual setting that simulates real-world experiences. Despite these advantages, the research also highlights several challenges associated with AR implementation, including the high costs of development and maintenance, difficulties in integrating AR technology with existing e-commerce platforms, and concerns regarding privacy and data security. The study further explores the varying applications of AR across different sectors within e-commerce, such as fashion, furniture, and cosmetics, each benefiting from unique AR functionalities. Looking ahead, the potential for AR to be enhanced by emerging technologies like Artificial Intelligence and the Internet of Things is discussed, with implications for future advancements in the field. Overall, the research demonstrates that while AR offers significant benefits for enhancing online shopping experiences, addressing its associated challenges is crucial for its successful and widespread adoption.

This study explores the application of data mining techniques in marketing strategies, highlighting their impact on customer segmentation, predictive analytics, and personalization. Data mining has emerged as a transformative tool for businesses seeking to enhance their marketing effectiveness by providing deep insights into customer behavior and preferences. Techniques such as clustering, predictive modeling, and personalization are examined for their roles in improving marketing outcomes. Clustering methods, including K-means and hierarchical clustering, enable businesses to categorize customers into meaningful segments, allowing for more targeted marketing efforts. Predictive analytics, utilizing models like decision trees and neural networks, offers the capability to forecast future customer behaviors and trends, thereby optimizing resource allocation and strategy planning. Personalization techniques, such as collaborative filtering and dynamic recommendations, enhance customer engagement by delivering tailored content and offers. Despite these advantages, the study also addresses the challenges associated with data mining, including data privacy concerns, data quality issues, and the shortage of skilled personnel. These challenges underscore the need for effective data management practices and ethical considerations in the application of data mining. Furthermore, the integration of emerging technologies like artificial intelligence and real-time analytics is discussed as a means to overcome existing obstacles and drive future advancements in marketing strategies. The findings underscore the significant role of data mining in revolutionizing marketing practices and highlight the ongoing need for adaptation and innovation in response to evolving market dynamics.

This research explores the transformative impact of artificial intelligence (AI) on personalizing marketing campaigns, highlighting how AI technologies are reshaping modern marketing practices. AI tools such as machine learning, natural language processing (NLP), predictive analytics, deep learning, and computer vision are integral to enhancing customer engagement and optimizing marketing strategies. Machine learning algorithms enable precise customer segmentation and personalized recommendations, leading to more targeted and effective marketing messages. NLP facilitates the analysis of customer sentiment and enhances communication through advanced language processing and AI-powered chatbots. Predictive analytics and deep learning provide businesses with the capability to forecast customer behaviors and recognize complex data patterns, further refining marketing efforts. Computer vision technology contributes to personalization through innovations like visual search and augmented reality, creating immersive customer experiences. Despite the numerous benefits, the adoption of AI in marketing presents several challenges. Data privacy and security concerns, integration complexities, and the potential for algorithmic bias are critical issues that need to be addressed. Ethical considerations, including transparency and fairness in data usage, are also paramount to maintaining customer trust and ensuring responsible AI application. The future of AI in marketing promises continued advancements, with trends such as hyper-personalization and enhanced integration with technologies like the Internet of Things and voice search expected to drive further innovation. Overall, AI significantly enhances marketing effectiveness by offering tailored solutions and strategic insights while necessitating a thoughtful approach to ethical and practical challenges.