In this paper, we study the symmetry between the supersingular prime number according to smallest sphenic number. With this symmetry, we show that the elements of sporadic group generates all prime numbers with the order by a simple application.

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.

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.

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

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.

Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P\bigcap S=\emptyset In this article, we introduce several results concerning graded S-prime ideals. Then we introduce the concept of graded weakly S-prime ideals which is a generalization of graded weakly prime ideals. We say that P is a graded weakly S-prime ideal of R if there exists s\in S such that for all x, y\in h(R), if 0\neq xy\in P, then sx\in P or sy\in P. We show that graded weakly S-prime ideals have many acquaintance properties to these of graded weakly prime ideals.

Integer is either a composite number or a prime number. Therefore, detecting composite numbers is important for solving prime numbers. The study of prime numbers, apart from satisfying human curiosity, can be very important. In this article, the order of composite numbers has been detected. And explained with a simple method and a simple function. And, a method has been developed in which all composite numbers and therefore prime numbers can be determined by using the specified methods, functions and formulas.

Mycobacterium tuberculosis was responsible for 1.3 million deaths worldwide in 2022. Bacillus Calmette-Guérin (BCG) is the only licensed vaccine against tuberculosis (TB); however, it has limited protective efficacy in adults. In this study, we constructed a recombinant vaccinia virus expressing Ag85B from M. tuberculosis using a novel attenuated vaccinia virus (KVAC103). We then analyzed the immunogenicity of prime-boost inoculation strategies using recombinant KVAC103 expressing Ag85B (rKVAC85B) compared to BCG. In both the rKVAC85B prime-boost and the BCG prime-rKVAC85B boost inoculation regimens, rKVAC85B induced the generation of specific IgG and the secretion of IFN-γ by immune cells. In vitro analysis of Mycobacterium growth inhibition revealed a comparable immune-mediated pattern of outcomes. Furthermore, bacterial loads in the lungs were significantly lower in mice inoculated with the BCG prime-rKVAC85B boost, than in the BCG-only group following a rechallenge infection with both H37Rv and HN878 strains of M. tuberculosis. These findings collectively suggest that KVAC103, incorporated into a viral vector, is a promising candidate for a novel TB vaccine platform that is effective against multiple TB strains, including H37Rv and HN878, and that rKVAC85B effectively stimulates immune responses against TB infection.

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.

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of (m,n)-prime ideals which lies properly between the classes of prime and (m,n)-closed ideals. A proper ideal I of R is called (m,n)-prime if for a,b∈R, a^{m}b∈I implies either aⁿ∈I or b∈I. Several characterizations of this new class with many examples are given. Analougus to primary decomposition, we define the (m,n)-decomposition of ideals and show that every ideal in an n-Noetherian ring has an (m,n)-decomposition. Furthermore, the (m,n)-prime avoidance theorem is proved.

In this research first, a sequence of properties called delta is assigned to each prime number and then examined. Deltas are only dependent on the distribution of prime numbers, so the results obtained for the delta distribution can be considered as a proxy for the distribution of prime numbers. The first observation was that these properties are not unique and different prime numbers may have the same value of delta of a given order. It was found that a small number of deltas cover a large portion of prime numbers, so by recognizing repetitive deltas, the next prime numbers can be predicted with a certain probability, but the most important observation of this study is the normal distribution of deltas. This research has not tried to justify the obtained observations and instead of answering the questions, it seeks to ask the right question.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

The maximal prime gaps upper bound problem is one of the major mathematical problems to date. The objective of the current research is to develop a standard which will aid in the understanding of the distribution of prime numbers. This paper presents theoretical results which originated with a researchin the subject of the maximal prime gaps. the document presents the sharpest upper bound for the maximal prime gaps ever developed. The result becomes the Supremum bound on the maximal prime gaps and subsequently culminates with the conclusive proof of the Firoozbakht's Hypothesis No 30. Firoozbakht's Hypothesis implies quite a bold conjecture concerning the maximal prime gaps. In fact it imposes one of the strongest maximal prime gaps bounds ever conjectured. Its truth implies the truth of a greater number of known prime gaps conjectures, simultaneously, the Firoozbakht's Hypothesis disproves a known heuristic argument of Granville and Maier. This paper is dedicated to a fellow mathematician, the late Farideh Firoozbakht.

Extensive genome structure variation, such as copy number variations (CNVs) and presence/absence variations, is the basis for the remarkable maize genetic diversity; however, the effect of CNVs on maize herbivory defense remains largely underexplored. Here, we report that the naturally occurring duplication of the maize 9-lipoxygenase gene, ZmLOX5, leads to increased resistance of maize to herbivory by fall armyworms (FAW). Previously, we showed that ZmLOX5-derived oxylipins are required for defense against chewing insect herbivores and identified several inbred lines, including Yu796, that contained duplicated CNVs of ZmLOX5, referred to as Yu796-2×LOX5. To test whether introgression of the Yu796-2×LOX5 locus into the herbivore-susceptible B73 background that contains a single ZmLOX5 gene is a feasible approach to increase resistance, we generated a series of near-isogenic lines that contained either 2, 1 or 0 copies of the Yu796-2×LOX5 locus in the B73 background by six back crosses (BC6). Droplet digital PCR (ddPCR) confirmed the successful introgression of the Yu796-2×LOX5 locus in B73. The resulting B73-2×LOX5 inbred line displayed increased resistance against FAW associated with increased expression of ZmLOX5, increased wound-induced production of its primary oxylipin product, the α-ketol, 9-hydroxy-10-oxo-12(Z),15(Z)-octadecadienoic acid (9,10-KODA), and the downstream defense hormones regulated by this molecule, 12-oxo-phytodienoic acid (12-OPDA) and abscisic acid (ABA). Surprisingly, wound-induced JA-Ile production was not increased in B73-2×LOX5, resulting from the increased JA catabolism. Furthermore, B73-2×LOX5 displayed enhanced drought tolerance likely due to increased ABA and 12-OPDA content. Taken together, this study revealed that the duplicated CNV of ZmLOX5 quantitively contributes to maize antiherbivore defense and presents proof-of-concept evidence that the introgression of naturally occurring duplicated CNVs of a defensive gene into the productive, but susceptible, crop varieties is a feasible breeding approach for enhancing plant resistance to herbivory and tolerance to abiotic stress.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

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.

Prime period sequences can serve as the fundamental tool to construct arbitrary composite period sequences. This is a review study of prime period perfect Gaussian integer sequence (PGIS). When cyclic group {1,2,…,N−1} can be partitioned into k cosets, where N=kf+1 is an odd prime number, the construction of a degree-(k+1) PGIS can be derived from either matching the flat magnitude spectrum criterion or making the sequence with ideal periodic autocorrelation function (PACF). This is a systematic approach of prime period N=kf+1 PGIS construction, and is applied to construct PGISs with degrees 1, 2, 3 and 5. However, for degrees larger than 3, matching either the flat magnitude spectrum or achieving the ideal PACF encounters a great challenge of solving a system of nonlinear constraint equations. To deal with this problem, the correlation and convolution operations can be applied upon PGIS of lower degrees to generate new PGIS with degree-4 and other higher degrees, e.g., 6, 7, 10, 11, 12, 14, 20 and 21 in this paper. In this convolution based scheme, both degree and pattern of a PGIS vary and can be indeterminant, which is rather nonsystematic compared with the systematic approach. The combination of systematic and nonsystematic schemes contributes the great efficiency for constructing abundant PGISs with various degrees and patterns for the associated applications.

We talk about random when it is not possible to determine a pattern on the observed outcomes. A computer follows a sequence of fixed instructions to give any of its output, hence the difficulty of choosing numbers randomly from algorithmic approaches. However, some algorithms based on mathematical formulas like the Linear Congruential algorithm and the Lagged Fibonacci generator appear to produce "true" random sequences to anyone who does not know the secret initial input [1]. Up to now, we cannot rigorously answer the question on the randomness of prime numbers [2, page 1] and this highlights a connection between random number generator and the distribution of primes. From [3] and [4] one sees that it is quite naive to expect good random reproduction with prime numbers. We are, however, interested in the properties underlying the distribution of prime numbers, which emerge as sufficient or insufficient arguments to conclude a proof by contradiction which tends to show that prime numbers are not randomly distributed. To achieve this end, we use prime gap sequence variation. The algorithm that we produce makes possible to deduce, in the case of a binary choice, a uniform behavior in the individual consecutive occurrence of primes, and no uniformity trait when the occurrences are taken collectively.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

In this outlet, I’ve devised the concept of relation amid two points where these points are coming up to make situation which in that the set of objects are greed to represent the story of how to be in whatever situations when these two points have the styles of being everywhere in the highlights of the concept which are coming from the merits of these points where are eligible to make capable situation to overcome every situation when they’re participant in the hugely diverse situations which mean too styles of graphs with have the name or the general results for the general situation as possible as are.

VITEK MS PRIME (bioMerieux), a newly developed Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS) system, alongside VITEK PICKME Pen (PICKME), offers easy sample preparation for bacteria and yeast. VITEK MS PRIME also offers two software platforms for filamentous fungi: the IVD database and the RUO database. Our study evaluated its identification agreement on 320 clinical isolates of bacteria and yeasts, comparing PICKME and traditional wooden toothpick sampling techniques against ASTA Mi-croIDSys Elite results. Additionally, we assessed the IVD (v3.2) and SARAMIS (v4.16) RUO data-bases on 289 filamentous fungi against molecular sequencing. The concordant rates for spe-cies-level identification of bacteria and yeasts were about 89.4% (286/320) between the PICKME and wooden toothpick, about 83.4-85.3% between VITEK MS PRIME and ASTA MicroIDSys Elite. Retesting with PICKME improved concordance to 91.9%. For filamentous fungi, species-level identification reached 71.3% with the IVD database and 85.8% with RUO, which significantly enhanced basidiomycetes' identification from 35.3% to 100%. Some strains in the IVD database, like Aspergillus vesicolor, Exophiala xenobiotica, and Nannizzia gypsea failed to be identified. VITEK MS PRIME with PICKME offers reliable and efficient microorganism identification. For fila-mentous fungi, combining the use of the RUO database can be beneficial, especially for basidi-omycetes.

We develop a primality test for Mersenne numbers and investigate the primality of the sequence of Catalan-Mersenne numbers. We use induction as a proof to show that the 5th Catalan-Mersenne number is a prime number, thus demonstrating the infinitude of Mersenne primes.

The Goldbach's conjecture has been described as the most difficult problem in the history of Mathematics. This conjecture states that every even integer greater than 2 can be written as the sum of two primes. This is known as the strong Goldbach's conjecture. The conjecture that all odd numbers greater than 7 are the sum of three odd primes is known today as the weak Goldbach conjecture. A principal complexity class is NSPACE(S(n)) for some S(n). We show if the weak Goldbach's conjecture is true, then the problem PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n). This proof is based on the assumption that if some language belongs to NSPACE(S(n)), then the unary version of that language belongs to NSPACE(S(log n)) and vice versa. However, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples. Since Harald Helfgott proved that the weak Goldbach's conjecture is true, then the strong Goldbach's conjecture is true or this has an infinite number of counterexamples, where the case of infinite number of counterexamples statistically seems to be unlikely. In addition, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Twin prime conjecture is true. Moreover, if PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Beal's conjecture is true. Since the Beal's conjecture is a generalization of Fermat's Last Theorem, then this is also a simple and short proof for that Theorem. In mathematics, the Riemann hypothesis is consider to be the most important unsolved problem in pure mathematics. If PRIMES is not in NSPACE(S(n)) for all S(n) = o(log n), then the Riemann hypothesis is true.

Sickle cell disease is characterized by stiff, “sickled” red blood cells that have difficulty moving through the bloodstream and do not efficiently carry oxygen. It is an inherited disease with severely limited treatment options, and is caused by a point mutation. Its prevalence in black and brown communities makes the already limited treatment options even less accessible. Base editing and prime editing are two relatively recent discoveries in the field of genome editing and were developed after the groundbreaking discovery of the CRISPR Cas9 system. While not fully tested, they hold a lot of promise in providing alternative treatment options for sickle cell disease. Both editing systems are able to install individual point mutations in the beta globin gene, which is where the sickle cell mutation occurs, and can thus cure sickle cell disease (in theory). In this paper we outline the mechanisms of CRISPR-Cas9 systems and base and prime editing, and provide insight into how to apply them to treat SCD. Further investigation should be done on specific editing systems and designs to use to ensure optimal treatment of SCD.

Let G be a finite group. The prime graph Γ(G) of G is defined as follows: The set of vertices of Γ(G) is the set of prime divisors of |G| and two distinct vertices p and p' are connected in Γ(G), whenever G has an element of order pp'. A non-abelian simple group P is called recognizable by prime graph if for any finite group G with Γ(G)=Γ(P), G has a composition factor isomorphic to P. In [4] proved finite simple groups ²D_n(q), where n ≠ 4k are quasirecognizable by prime graph. Now in this paper we discuss the quasirecognizability by prime graph of the simple groups ²D_2k(q), where k ≥ 9 and q is a prime power less than 10⁵.

The UNUSUAL FLORAL ORGANS (UFO) gene is an essential regulatory factor of class B genes and plays a vital role in the process of inflorescence primordial and flower primordial development. We investigated the role of UFO genes in soybean to better understand the development of floral organs through gene cloning, expression analysis, and gene knockout. In situ hybridization demonstrated predominant expression of the GmUFO1 gene in the flower primordium. Phenotypic observation of GmUFO1 knockout mutant lines (Gmufo1) showed obvious alteration in floral organ number and shape, and mosaic organ formation. In contrast, GmUFO2 knockout mutant lines (Gmufo2) showed no obvious difference in floral organs. However, the GmUFO1 and GmUFO2 double knockout lines (Gmufo1ufo2) showed a more severe mutant phenotype than the Gmufo1 lines. Gene expression analysis also showed differences in the expression of major ABC function genes in the knockout lines. Based on the phenotypic and expression analysis, our results suggest the major role of GmUFO1 in the regulation of flower organ formation in soybean and that GmUFO2 does not have any direct effect, but it might have an interaction role with GmUFO1 in the regulation of flower development. In conclusion, the present study identified UFO genes in soybean and improved our understanding of floral development that could be useful for flower design in hybrid soybean breeding.

In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, exponential generating functions for these numbers. Then we define an associate matrix for these numbers. In addition, using this matrix, we present two different versions of Cassini identitiy of these numbers.

A cursory look at Indian prime time news tells us much about the tone and tenor of the people associated with it. Exaggerations, hyperbole, and tempers run wild and news anchors flail in theatrical rage. News channels and news editors display their ideological affiliations subliminally. These affiliations — a factor of personal political stance, funding bodies, and investors — lead to partisan bias in the framing of news and, in some cases, can easily translate into racial prejudice. In this paper, I examine news coverage related to Muslims in India. I study the coverage of two issues specifically– love jihad and triple talaq –in prime time English news of two channels – Times Now and Republic TV. My analysis of the content, tone, and tenor of their coverage shows that these channels propagate associations between Islam and backwardness, ignorance and violence through consistent employment of the following tropes – ‘Muslim women need to be saved from Muslim men’, ‘Hindu women need to be saved from Muslim men’, and ‘Muslims are not fully Indian – they are anti-national’. I place this study of news media within the current political climate in India and briefly touch on the conversations it guides and provokes. This is also a call for further analysis on this subject to examine and evaluate how discourse manipulates public conversations and policy decisions.

This paper considers the direction of arrival (DOA) estimation problem of phase ambiguity for unfolded coprime linear array (UCLA). The existing most common stacking subarray-based method can tackle the phase ambiguity problem. However, the method is not always true. For a given DOA, it has its corresponding steering vector, but if there are two DOAs which have the same steering vectors with the given DOA for different subarrays, the phase ambiguity problem still arises. A modified method, which defines a decision variable and uses the classic beamforming technique to estimate the DOAs is proposed. However, this method needs additional algorithm to distinguish the true DOAs besides multiple signal classification (MUSIC) spectrum. And sometimes this method is not reliable if the decision variable is not chosen appropriately. Therefore, based on the UCLA, we reconstruct the array to design an improved UCLA called IUCLA. With moving the reference element, the linear relationship among the directional vectors can be broken. In this way, we can directly utilize the MUSIC algorithm to estimate with no additional algorithm. The proposed method can solve the phase ambiguity problem and it does not demand other technique to decrease the complexity. Moreover, the Cramer-Rao Bound (CRB), as the lower bound of the unbiased estimation, is provided and numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method.

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. 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.

One of the most important unresolved mysteries in mathematics is the Riemann Hypothesis, which suggests a fundamental connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers. Here, we explore the fascinating union of trigonometric functions, prime numbers, and the Riemann zeta function through an examination of the zeros in the statement ln(sec(π·n log(n))). We demonstrate a strong mathematical connection between these components, providing information on the mysterious properties of prime numbers and their complex relationships to basic mathematical operations. Our thorough investigation adds to the current discussion of the Riemann Hypothesis by offering possible solutions and deepening our comprehension of the intricate relationship between number theory and analytic functions.

It is well established the complex exponential and logarithm are multivalued functions, both failing to maintain most identities originally valid over the positive integers domain. Moreover the general case of complex logarithm, with a complex base, is hardly mentionned in mathematic litterature. We study the exponentiation and logarithm as binary operations where all operands are complex. In a redefined complex number system using an extension of the C field, hereafter named E, we prove both operations always produce single value results and maintain the validity of identities such as log_u (w v) = log_u (w) + log_u (v) where u, v, w in E. There is a cost as some algebraic properties of the addition and subtraction will be diminished, though remaining valid to a certain extent. In order to handle formulas in a C and E dual number system, we introduce the notion of set precision and set truncation. We show complex numbers as defined in C are insufficiently precise to grasp all subtleties of some complex operations, as a result multivaluation, identity failures and, in specific cases, wrong results are obtained when computing exclusively in C. A geometric representation of the new complex number system is proposed, in which the complex plane appears as an orthogonal projection, and where the complex logarithm and exponentiation can be simply represented. Finally we attempt an algebraic formalization of E.

The paper deals with exploration of subsequences of polygonal numbers of different sides derived through step-by-step elimination of terms of the original sequences. Eliminations are based on special rules similarly to how the classic sieve of Eratosthenes was developed through the elimination of multiples of primes. These elementary number theory activities, appropriate for technology-enhanced secondary mathematics education courses, are supported by a spreadsheet, Wolfram Alpha, Maple, and the Online Encyclopedia of Integer Sequences. General formulas for subsequences of polygonal numbers referred to in the paper as polygonal number sieves of order k that include base-two exponential functions of k have been developed. Different problem-solving approaches to the derivation of such and other sieves based on the technology-immune/technology-enabled framework have been used. The accuracy of computations and mathematical reasoning is confirmed through the technique of computational triangulation enabled by using more than one digital tool. A few relevant excerpts from the history of mathematics are briefly featured.

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.

In the paper it is demonstrated that a valid path to a contradiction in complex number theory exists. In the path use is made of Euler’s identity and simple trigonometry. Each step can be easily verified.

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

In this paper, the sequential prime numbers are used as variables for the galactic spiral equations which were developed from the ROTASE model. Special spiral patterns are produced when prime numbers are treated with the unit of radian. The special spiral patterns produced with the first 1000 prime numbers have 20 spirals arranged in two groups. The two groups have perfect central symmetry with each other and are separated with two spiral gaps. The special spiral pattern produced with natural numbers from 1 to 7919 shows 6 spirals in the central area and 44 spirals in the outer area. The whole 7919 spiral points can be plotted with either 6-spiral pattern or 44-spiral pattern. For the spirals only produced by the prime numbers in the 6-spiral pattern plotting, the spiral 2 and spiral 3 each has only one spiral point produced by prime number 2 and 3, respectively, all other spiral points produced by other prime numbers are located on the spiral 1 and spiral 5. The special spiral pattern is well explained with careful analysis, it is concluded that all prime numbers greater than 3 must meet one of the equations: P₁ = 1 + 6 * n (n > 0) P₅ = 5 + 6 * n (n ≥ 0) In other words, every prime number greater than 3 is either a P₁ prime number or a P₅ prime number, no exception. Matching one of the equations is a necessary condition for a number to be a prime number, not a sufficient condition. Hope such sufficient condition can be found in the future. The number of P₁ prime numbers roughly equal the number of P₅ prime number in the first 2 billion prime numbers. The galactic spiral equations with golden angle can duplicate Vogel’s result for the simulation of sunflower seed head pattern, and a pinwheel pattern can be produced also with galactic spiral equations and 1 degree more than golden angle.

Twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the part “twin prime” is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid proof for twin prime conjecture.

Background: Military pilots show high visuo-spatial skills. Previous studies demonstrate that they are better in mental rotating a target, in taking different perspectives, in estimating distances, in travel planning and in topographic memory. Here, we compared navigational cognitive styles between military pilots and people without flight experience. Pilots were expected to be more survey users than non-pilots, showing higher navigational strategies. Method: 106 jet military pilots of Italian Air Force and 92 non-pilots were enrolled in order to investigate group differences in navigational styles. Participants were asked to perform a reduced version of the Spatial Cognitive Style Test – SCST, consisting of six tasks that allow to distinguish individuals in landmark (people orient themselves by using a figurative memory for environmental objects), route (people use an egocentric representation of the space) and survey (people have a map-like representation of the space) users. Results: In line with our hypothesis, military pilots mainly adopt a survey style, whereas non-pilots mainly adopt the route style. In addition, pilots outperformed non pilots in both the 3D-Rotation task and Map Description Task. Conclusion: Military flight expertise influences some aspects of the spatial ability, leading to enhance human navigation. Although, it must be considered that they are a population whose navigational skills were already high at the time of selection at the academy before formal training began.

Dravet syndrome (DS), also known as severe myoclonic epilepsy of infancy, is a rare and drug-resistant form of developmental and epileptic encephalopathies, which is both debilitating and challenging to manage, typically arising during the first year of life, with seizures often triggered by fever, infections, or vaccinations. It is characterized by frequent and prolonged seizures, developmental delays, and various other neurological and behavioral impairments. Most cases result from pathogenic mutations in the sodium voltage-gated channel alpha subunit 1 (SCN1A) gene, which encodes a critical voltage-gated sodium channel subunit involved in neuronal excitability. Precision medicine offers significant potential for improving DS diagnosis and treatment. Early genetic testing enables timely and accurate diagnosis. Advances in our understanding of DS's underlying genetic mechanisms and neurobiology have enabled the development of targeted therapies, such as gene therapy, offering more effective and less invasive treatment options for patients with DS. Targeted and gene therapies provide hope for more effective and personalized treatments. However, research into novel approaches remains in its early stages, and their clinical application remains to be seen. This review addresses the current understanding of clinical DS features, genetic involvement in DS development, and outcomes of novel DS therapies.

Cystic Fibrosis is a rare genetic disease that affects the transmission of chloride ions due to mutations in the CFTR (cystic fibrosis transmembrane conductance regulator) gene. Even though there are nearly 2000 mutations identified to be related to the condition, the most common mutation is F508del; deletion of a phenylalanine residue at 508. On the other hand, G542X which is a Class I mutation is also found very commonly and there are no modulator treatments available for it. Furthermore, it was investigated that R553X mutation can as well be corrected simultaneously with G542X mutation. Therefore, the main focus is on designing a gene therapy project that can correct all these three mutations at once by utilizing the prime editing technique via lipid-based delivery. In this way, the mutations can be edited through plasmids that were designed containing 2 pegRNAs and the Cas enzyme. To implement such an approach efficiently, both ex vivo, an animal model, and in vivo steps are to be designed. For the cell line, fibroblasts are selected due to their simplicity and low cost. The animal model of the experiment is determined to be a ferret concerning the high similarity to the human's CFTR protein and finally, the procedure will follow on a direct application in human Cystic Fibrosis patients. The plasmids are thought to be delivered through a cationic liposome that will reach the lungs with the aid of a nebulizer. At the last stage of the experimental procedure, Sanger Sequencing will be done to see if the desired edit within the CFTR has been performed successfully, and Next Generation Sequencing will be executed to see if there has been an off-target mutation in the remainder of the genome. Whereas for detecting the presence and expression of CFTR protein in humans, immunodetection with flow cytometry will be conducted.

A symbolic analysis of Archimedes’ periodical number system is developed, from which a natural link emerges with the modern positional number systems with zero. After the publication of Fibonacci’s Liber Abaci, the decimal Indo-Arabic positional system was the basis of the algorithmic and algebraic trend of modern mathematics, but even if zero plays a crucial role in algebra and mathematical analysis, zeroless positional systems show the same capability of producing efficient arithmetical algorithms based on operation tables over digits. The crucial role of digits is assessed, by considering a representation of numbers based on strings in lexicographic order. A new algorithm for the determination of decimal periods is presented,, by remarking the cruciality of this topic in number theory. Periods of ordinal numbers, and enumerations of recursive enumerability are shortly recalled. Concluding remarks are formulated about the deep relationship among numbers and information, which shed new light on a red line passing through the whole history of mathematics

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

Bacillus Calmette-Guérin (BCG) is the only widely used prophylactic tuberculosis (TB) vaccine that can prevent severe TB in infants. However, it provides poor protection in adults, and therefore, there in ongoing research on new TB vaccines and immunization strategies with more durable immune effects. The recombinant BCG and BCG prime-protein booster are two important vaccine strategies that have recently been developed based on BCG and could improve immune responses. In this study, three immune strategies based on four protective antigens, namely, ESAT-6, CFP-10, nPPE18, and nPstS1, were applied to construct recombinant rBCG-EPCP009, EPCP009 subunit protein, and BCG prime-EPCP009 booster vaccine candidates. The short- and long-term immune effects after vaccination in Balb/c mice were evaluated based on humoral immunity, cellular immunity, and the ability of spleen cells to inhibit in vitro mycobacterial growth. At 8 and 12 weeks after the initial immunization, splenocytes from mice inoculated with the BCG prime-EPCP009 protein booster secreted higher levels of PPD- and EPCP009-specific IFN-γ, IL-2, TNF-α, IL-17, GM-CSF, and IL-12 and had a higher IFN-γ⁺CD4⁺ TEM:IL-2⁺CD8⁺ TCM cell ratio than splenocytes from mice inoculated with the rBCG-EPCP009 and EPCP009 proteins. In addition, the EPCPE009-specific IgG2a/IgG1 ratio was slightly higher in the BCG prime-EPCP009 protein booster group than in the other two groups. The in vitro mycobacterial inhibition assay showed that the splenocytes of mice from the BCG prime-EPCP009 protein booster group exhibited stronger inhibition of Mycobacterium tuberculosis （M. tuberculosis）growth than the splenocytes of mice from the other two groups. These results indicate that the BCG prime-EPCP009 protein booster exhibited superior immunogenicity and M. tuberculosis growth inhibition to the parental BCG, rBCG-EPCP009, and EPCP009 proteins under in vitro conditions. Thus, the BCG prime-EPCP009 protein booster may be important for the development of a more effective adult TB vaccine.

The enhancement of health-beneficial omega-3 long chain polyunsaturated fatty acid (n-3 LC-PUFA) contents in the muscle, liver, heart and kidney of Australian prime lambs through pasture grazing and supplementation with oil infused pellets was investigated. Forty-eight first-cross prime lambs were randomly assigned into a split-plot design with pasture type as the main plot effect and pellet supplementation as a sub-plot effect in a feeding trial that lasted for nine weeks. The n-3 LC-PUFA content in Longissimus dorsi muscle of all lambs was well above the 30 mg threshold for “omega-3 source” nutrition claim under the Australian Food Standards and Guidelines. Pasture type impacted the fatty acid contents in muscle, heart and kidney of prime lambs. Lambs grazing cocksfoot only had the highest 18:3n-3 (ALA) and n-3 LC-PUFA contents (67.1 mg/100g and 55.2 mg/100 g, respectively). Supplementation of pellets with or without oil infusion to grazing lambs decreased the ALA and n-3 LC-PUFA contents and increased n-6/n-3 ratio in Longissimus dorsi muscle. The fatty acid content in internal organs of grazing lambs was also affected by pellet supplementation. The liver and kidney of grazing lambs were both “good sources” (60 mg/100 g) of omega-3. The cocksfoot grass showed considerable potential for producing healthy, premium quality meat with high contents of n-3 and n-3 LC-PUFA which may consequently enhance the omega-3 intake of Australian lamb consumers.

We report the first correction by Prime editing of a mutation in the RYR1 gene, paving the way to gene therapies for RYR1-related myopathies. The RYR1 gene codes for a calcium channel named Ryanodine receptor 1, which is expressed in skeletal muscle fibers. The failure of this channel causes muscle weakness in patients, which degenerates into motor disabilities. Currently, there are no effective treatments for these diseases, which are mainly caused by point mutations. Prime editing allows the modification of precise nucleotides in the DNA. Our results showed a 59% correction rate of the T4709M mutation in the RYR1 gene in human myoblasts by RNA delivery of the Prime editing components. It is to be noted that the T4709M is recessive, and thus, persons having a heterozygous mutation are healthy. These results are the first demonstration that it is possible to correct mutations in the RYR1 gene.

Prime number-related issues can be viewed from drastically different perspectives by examining the close connections between prime numbers and composite numbers. We think that multiple perspectives are the pillars on the path to solutions so we have created this study. As a result of the study, we proposed two new formulas by presenting three theorems and one proof for each theorem, a total of three proofs. We proved that the formula p · n + p returns a composite number in the first of the theorems, which is the preliminary theorem. Our first theorem except the preliminary theorem is that the formula p · n + p returns all composite numbers, and we proved that too. Finally, we created Theorem II using Theorem I to use in our other work and proved that the formula 2 · n · p + p returns all odd composite numbers, which is Theorem II. Afterward, we presented the similarities of the 2 · n · p + p formula we put forth with another known formula.

Therapeutic vaccine studies should be designed to elicit durable, high magnitude, and efficacious T cell responses, all of which can be impacted by the choice of vaccination schedule. Here, we compare different prime-boost intervals (PBI) in a human papillomavirus (HPV) model using HPV16E6E7 Venezuelan equine encephalitis virus replicon particle (VRP) vaccination to address the optimal boosting schedule, quality of immune response, and overall in vivo efficacy. Six different vaccine regimens were tested with each group receiving booster vaccinations at different time intervals. Analysis of T-cell responses demonstrated a significant HPV16 E7 specific CD8+T cell response with minimally a one-week PBI between antigen re-exposure. Significant E7-specific in vivo cytotoxicity was also observed with longer PBIs. Additionally, longer PBIs led to an enhanced memory recall response to tumor challenge, which correlated with differential expansion of T cell memory subsets. Our findings imply that when using alphavirus vector platforms as a vaccination strategy, a one-week PBI is sufficient to induce high magnitude effector T cells with potent anti-tumor activity. However, longer PBIs lead to enhanced long-term protective anti-tumor immunity. These findings have implications for therapeutic vaccine clinical trials in which shorter intervals of prime-boost regimens may lead to suboptimal durable immune responses.

Phytoalexins are naturally-occurring molecules with antimicrobial activity deriving from the secondary metabolism of plants, which are synthesized in response to physical agents or stresses, phytopathogenic agents (fungi, bacteria and viruses) as well as numerous chemical compounds and biological control agents. Among these, grapevine phytoalexins, which belong to the chem-ical group of stilbenes, exhibit biocidal activity against a large number and a variety of plant pathogens. An important issue in research on these compounds is to be able to stimulate their synthesis in planta and to determine whether the induction of their production can serve as a basis for protecting that plant against its pathogens. Quite a few chemical compounds, derivatives of phytohormones bio-elicitors as well as biocontrol agents have been used to induce the synthesis of stilbene phytoalexins with the aim of conferring protection to grapevine against its main dis-eases (gray mold, downy mildew, powdery mildew and esca). This article reviews the experi-ments that have been carried out in this direction during the last thirty years and shows that the observed protective effects towards pathogens are generally linked to induction and priming of the grapevine phytoalexin response, confirming the interest of using, in a more general way, stimulation of the production of phytoalexins in plants as a basis for crop protection.

This study investigated live animal performance and carcass characteristics of Australian prime lambs fed oil based polyunsaturated fatty acid (PUFA) enriched pellets in a feedlot system. The tested hypothesis was that supplementation of lambs with a variety of dietary oil based PUFA enriched pellets would enhance growth and carcass characteristics compared with the control lambs on lucerne only. Seventy-two, 6 months old White Suffolk x Corriedale first-cross prime lambs with an average liveweight (LWT) of 35.7 ± 0.9 kg were allocated to six treatment groups in a completely randomised experimental design. The treatments were: (1) control: lucerne hay only; or lucerne hay plus wheat-based pellets infused with 50 ml/kg DM of oils from (2) rice bran (RBO); (3) canola (CO); (4) rumen protected (RPO); (5) flaxseed (FO) and (6) safflower (SO) dietary sources. All lambs had ad libitum access to lucerne hay and clean fresh water. Supplemented lambs were fed 1kg of pellet/head/day for 10 weeks. Feed intake, final LWT, average daily gain (ADG), body conformation and carcass characteristics of lambs in the supplemented groups were all greater than for the control group. SO lambs had the lowest ADG of 190.3 g/day. RBO and CO treatments had the lowest feed cost per unit gain of AU$ 3.0/kg. Supplemented lambs had similar over the hooks (OTH) incomes that were all higher than that of the control group. This empirical evidence-based data demonstrated that supplementation of lambs with RBO and CO had comparatively lower feed costs without compromising ADG, carcass characteristics and OTH income.

Analysis of complex DNA mixtures is limited by the selected genetic markers characterized and assay technology. Small panels of short tandem repeats (STRs) are the current standards in most countries. Extension of STRs with hundreds of single nucleotide polymorphisms (SNPs) is now commercially available. The current set of extension SNPs focus on phenotypic and biogeographic ancestry informative SNPs. Larger panels with thousands of SNPs have been developed that can identify up to 10 contributors to forensic DNA samples. Herein, multiple sets of SNPs were selected with the focus of increasing the upper limit of detectable contributors. Larger SNP panel sets with lower minor allele frequency (MAF) alleles can detect large numbers of contributors to in silico mixtures of randomly selected profiles from the 1,000 Genomes project. These results provide a path to enable characterization of complex DNA mixtures that are currently impossible to analyse.

Data from DR17 of the SDSS in the g, i, r, u, z bands were used to compute galaxy number counts and galaxy density per square degree in the composite bJ band over two areas of sky centred on the North Galactic Cap (NGC) and above the South Galactic Cap (SGC), with areas of 5,954 and 859 sq. deg. respectively and a combined count of 622,121 galaxies within the limits of redshift ≤0.4 and bJ≤20. The comparative densities confirmed an extensive void in the Southern sky with a deficit of 26% out to a redshift z∼0.15. Number counts in the K−, R−, I−, H−, B− and U−bands were derived from the Durham Extragalactic Astronomy and Cosmology catalogue and were well fitted to a general relativity (GR) cosmological model over their whole range, requiring only modest luminosity evolution, except for a steeper curve in the B−band at faint magnitudes required a star-burst evolutionary model to account for the excess faint number counts. Extending the SDSS redshift-number count survey to fainter and more distant galaxies with redshift ≤1.20 and bJ≤24 showed a secondary peak in the number counts that may account for this observed apparent excess of faint blue galaxy counts. Individual examination of a sample of these galaxies suggested that many were QSOs, bright X-ray or radio sources, or evolving irregular galaxies with rapid star formation rates. This sub-population at redshifts 0.45−0.65 may account for the excess counts observed in the B− optical band.

Nowadays the practice of developing algorithms to maintain the confidentiality of data shows that there is a lack of some features, such as velocity, predictability, etc. Generating pseudorandom numbers is one such problem that lies in the basement of many algorithms, even in hardware microprograms. An unreliable generator can cause cyberattacks on it, despite the security in the upper layers. At the same time, the algorithm should be fast enough to provide uninterrupted circuit work for the entire system. The paper presents a new algorithm generating pseudorandom numbers on cellular automata, which is not only fast and easy-repeating, but unpredictable enough and can be used in cryptographic systems. Using the NIST statistical test suite for random and pseudorandom number generators (PRNG), it is shown that the presented algorithm is more than three times superior to the state-of-the-art methods and algorithms in terms of ? − ?????. A high level of the presented algorithm’s parallelization allows for implementation it effectively on calculators with parallel structure. CPU-based architecture, FPGA-based architecture, CUDA- based architecture of PRNG and different PRNG implementations are presented to confirm high performance of the proposed solution.

The Ramanujan primes are the least positive integers Rn having the property that if m ≥ Rn, then π_m − π_(m/2) ≥ n. This document develops several bounds related to the Ramanujan primes, sharpening the currently known results. The theory presented is by no means exhaustive, however it provides insights for future research work. Alternatively, we may say that it is a road map which may be followed to make further discoveries.

The heavy demand of water resources from the Zarqa River Basin (ZRB) has resulted in a base-flow reduction of the River from 5m³/s to less than 1m³/s. This paper aims at predicting Curve Numbers (CN) as a baseline scenario and proposing restoration scenarios for ZRB. The method includes classifying the soil type and land use, predicting CNs, and proposing CN restoration scenarios. Prediction of existing CNs will be in parallel with the runoff prediction using the US Army Corps of Engineers HEC-1 Model, and Rainfall-Runoff Model (RRM). The models have been set up at the land use distribution of 0.3% water body, 9.3% forest and orchard, 71% mixture of grass, weeds, and desert shrubs, 7.0% crops, 4.0% urban areas, and 8.4% bare soil. The results show that CN under dry condition are 59, 78 under a normal condition and 89 under a wet condition. During vegetation period, CN are 52, 72 and 86 for the dry, normal and wet condition respectively. The restoration scenarios; CN decreases runoff, and increases soil moisture when using the contours, terraces and crop residues. Analyzing results of CN scenarios will be a fundamental tool to support end-users related to their targets to achieve watershed restoration.

ATP and other nucleoside phosphates have specific receptors named purinergic receptors. Purinergic receptors and ectonucleotidases regulate various signaling pathways that play a role in physiological and pathological processes. Extracellular ATP in the tumor microenvironment (TME) has a higher level than in normal tissues and plays a role in cancer cell growth, survival, angiogenesis, metastasis, and drug resistance. In this review, we investigated the role of purinergic receptors in the development of resistance to therapy through changes in tumor cell metabolism. When a cell transforms to neoplasia, its metabolic processes change. The metabolic reprogramming modified metabolic feature of the TME, that can cause impeding immune surveillance and promote cancer growth. The purinergic receptors contribute to therapy resistance by modifying cancer cells' glucose, lipid, and amino acid metabolism. Limiting the energy supply of cancer cells is one approach to overcoming resistance. Glycolysis inhibitors which reduce intracellular ATP levels, may make cancer cells more susceptible to anti-cancer therapies. The loss of the P2X7R through glucose intolerance and decreased fatty acid metabolism reduces therapeutic resistance. Potential metabolic blockers that can be employed in combination with other therapies will aid in the discovery of new anti-cancer immunotherapy to overcome therapy resistance. Therefore, therapeutic interventions that are considered to inhibit cancer cell metabolism and purinergic receptors simultaneously can potentially reduce resistance to treatment.

This research proposes an algorithm to sign messages using the ElGamal asymmetric cryptosystem, called: Digital signature algorithm based on ElGamal, Diffie-Hellman protocol and the number π (DSAπ). This proposal has a high level of security like the DSA standard, in addition, execution times are reduced in relation to it. The Diffie-Hellman protocol and the number π were used in the construction of the digital signature algorithm in conjunction with the Hash-Sha-512 function. Some experiments are presented to provide evidence that the bits on the right side of the decimal point of π appear randomly, such as: a color image was constructed of a string of consecutive bits chosen at random, of the number π. Subsequently, parameters such as: entropy, correlation, discrete Fourier transform, goodness-of-fit test χ2 were evaluated. It is mentioned that an S-box 8×8 is involved in the signature. The sensitivity of the signature was measured, that is, when small changes are made to the sender’s private key, or small changes to the message. Finally, an image was constructed using the signatures of random texts, and subsequently the randomness of its pixels was obtained, to verify that there is no relationship between the different signatures.

: The objective of this work is to elucidate the role of partnerships and the number of partners necessary for lead user innovation outcomes. Lead user theory identifies these users as being ahead of market trends and experiencing significant benefits from innovating. So far, most lead user research has concentrated on firms and not individual lead users’ perspective. Data were obtained using a quantitative design during which 321 respondents participated. The SPSS software was used to analyze the data and determine significance. These findings indicate a connection between number of partners and lead user innovation success. This demonstrates that number of partners is significant in determining the success or failure of an innovation. This study provides empirical evidence that the number of partners is an essential factor that influences the success of innovation, and establishes the absolute numbers for achievement of successful innovation. Future studies must investigate the possible implications of integrating the partner variables with other characteristics of the lead user.

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the average lower 2-domination number of a graph is a measure of the graph vulnerability and it is defined by ${\gamma }_{2av}\left(G\right)=\frac{1}{\left|V\left(G\right)\right|}{\sum }_{v\in V\left(G\right)}{\gamma }_{2v}\left(G\right)$, where the lower 2-domination number, denoted by ${\gamma }_{2v}\left(G\right)$, of the graph G relative to v is the minimum cardinality of 2-domination set in G that contains the vertex v. In this paper, the average lower 2-domination number of wheels and some related networks namely gear graph, friendship graph, helm graph and sun flower graph are calculated. Then, we offer an algorithm for computing the 2-domination number and the average lower 2-domination number of any graph G.

The rapid growth of the smart Internet of Things (IoT) and massive propagation of wireless technologies revealed the recent opportunities for development in various domains of real life such as smart cities and E-Health applications. A slight defense against different forms of attacks is offered for the current secure and lightweight Routing Protocol for Low Power and Lossy Networks (RPL) of IoT resource-constrained devices. Data packets are highly likely to be exposed while transmitting them during data packets routing. The RPL rank and version number attacks, which are two forms of RPL attacks, can have critical consequences for RPL networks. The studies conducted on these attacks have several security defects and performance shortcomings. The research proposes a Secure RPL Routing Protocol (SRPL-RP) for rank and version number attacks. It mainly detects, mitigates and isolates attacks in the RPL networks. The detection is based on a comparison of ranks strategy. The mitigation uses threshold and attacks status tables, and the isolation adds them to a blacklist table and alerts relevant nodes to skip them. SRPL-RP supports diverse types of network topologies and is comprehensively analyzed with multiple studies such as Standard RPL with Attacks, SBIDS and RPL+ Shield. The analysis results showed that the SRPL-RP achieves great improvements with Packet Delivery Ratio (PDR) of 98.48%, control message value of 991 packets/second, and average energy consumption of 1231.75 joules. It provides a better accuracy rate with 98.17% under the attacks.

The following system of equations {x_1 \cdot x_1=x_2, x_2 \cdot x_2=x_3, 2^{2^{x_1}}=x_3, x_4 \cdot x_5=x_2, x_6 \cdot x_7=x_2} has exactly one solution in ({\mathbb N}\{0,1})^7, namely (2,4,16,2,2,2,2). Hypothesis 1 states that if a system of equations S \subseteq {x_i \cdot x_j=x_k: i,j,k \in {1,...,7}} \cup {2^{2^{x_j}}=x_k: j,k \in {1,...,7}} has at most five equations and at most finitely many solutions in ({\mathbb N}\{0,1})^7, then each such solution (x_1,...,x_7) satisfies x_1,...,x_7 \leq 16. Hypothesis 1 implies that there are infinitely many composite numbers of the form 2^{2^{n}}+1. Hypotheses 2 and 3 are of similar kind. Hypothesis 2 implies that if the equation x!+1=y^2 has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(4,5),(5,11),(7,71)}. Hypothesis 3 implies that if the equation x(x+1)=y! has at most finitely many solutions in positive integers x and y, then each such solution (x,y) belongs to the set {(1,2),(2,3)}. We describe semi-algorithms sem_j (j=1,2,3) that never terminate. For every j \in {1,2,3}, if Hypothesis j is true, then sem_j endlessly prints consecutive positive integers starting from 1. For every j \in {1,2,3}, if Hypothesis j is false, then sem_j prints a finite number (including zero) of consecutive positive integers starting from 1.

Italy suffered heavily with the new pandemic crisis caused by the novel coronavirus SARS-CoV-2. Given the low number of tests performed on the early stages of the outbreak, Italy lost track of most of infections. We use a modified SEIR model to reconstruct the most realistic infection curve using the hospitalization curve of the registered data. Using this method we estimated that, by the end of the first infection wave, about 3-4% of the population will have been infected by the virus. Following the same process, the number of deaths is projected to be between 100000 to 115000. We also find a significant correlation between the number of tests performed, the fraction of undocumented infections and the rate of change dI/dt of the real infection curve. We conclude that herd immunity is not enough to contain further spread of the disease inside the country.

We investigate the flow structure and dynamics of moderate-Rayleigh-number ($Ra$) thermal convection in a two-dimensional inclined porous layer. Direct numerical simulations (DNS) confirm the emergence of $\mathit{O}(1)$ aspect-ratio large-scale convective rolls, with one `natural' roll rotating in the counterclockwise direction and one `antinatural' roll rotating in the clockwise direction. As the inclination angle $\phi$ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Moreover, our DNS reveal---for the first time in single-species porous medium convection---the existence of \emph{spatially-localized} convective states at large $\phi$, which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different $\phi$, we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the DNS at different values of $\phi$.

This study investigates the magnetization of Cobalt (Co) nanoparticles with two different crystal structures: a centered cubic (fcc) and an hexagonal close packed (hcp), under the magnetic field of the Earth. For that reason, the hysteresis loops of the two material samples are exported and compared with the corresponding value by experimental procedure in the laboratory under the Earth’s magnetization. For both samples, the nanoparticle number variation and the nearest neighbor distance effect, in the Co hysteresis loop are investigated, structural information that is useful for the sample preparation. For the simulations the Finite Element Method (FEM) was used, while experiments are conducted using a measurement set-up based on fluxgate magnetometers. From the simulation, it is proven that, for both samples, the nanoparticle number effect does not change the hysteresis loop. In contrast, when the distance between the nanoparticles increases, the magnetization obtains smaller value. This study aims to build a novel, simple and economical measurement arrangement enabling in situ magnetic measurements for ferromagnetic nano-material characterization. As the need for continuous knowledge of the condition and the phase of ferromagnetic nanoparticles that is crucial in many applications, like catalytic processes, this work aims to introduce an alternative approach that will add another dimension to conventional chemical reaction engineering this of the magnetic state of the material resolved in time and space and to contribute in the field of the monitoring and the early fault diagnosis of nanoparticle materials.

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.

Although Lov\'{a}sz introduced the graph exponential $G^K$ in 1967, this product has received little attention. This paper focuses on the number of components in $G^K$ when exponent $K$ is a complete graph $K_n$. For a connected bipartite $G$, when $K$ is $K_2$, $G^{K_2}$ has three components; and when $K$ is $K_n$ with $n>2$, $G^{K_n}$ produces $\lceil\frac{n+1}{2}\rceil$ components. A connected $G$ with an odd cycle produces one component in $G^{K_n}$.

The paper proposes an approach to determine the optimal number of medical specialists in the region. According to the author's theoretical model, in order to maximize public welfare, the marginal contribution of the last physician recruited to the growth of the public utility function should be equal to the marginal cost of attracting him and providing conditions for his work. To empirically assess the contribution of physicians to the number of lives saved, the CVD mortality rate is modeled using the instrumental variable method. On average, a 1% increase in the number of cardiologists is associated with a 0.6% decrease in cardiovascular mortality. At the level of provision with cardiologists in the amount of 1 per 100 thousand people, their marginal contribution to the number of lives saved is not less than 129 per 100 thousand people, with a further decrease by 5 people with the increase in the level of provision by 1 unit. The use of the obtained results will increase the validity of managerial decisions and in determining the optimal level of doctors when choosing between alternative possibilities of spending money on hiring doctors of different profiles or other expenses, especially in the case of limited resources.

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix which in turn constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2 x 2 block preconditioner, provides convergence of the GMRES method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated showing its great potential.

Real-time estimation of the parameters characterising infectious disease transmission is important for optimization quarantine interventions during outbreaks. One of the most significant parameters is the effective reproduction number - number of secondary cases produced by a single infection. The current study presents an approach for estimating the effective reproduction number and its application to COVID-19 outbreak. The method is based on fitting SIR epidemic model to observation data in a sliding time window and allows to show real-time dynamics of reproduction number at any phase of epidemic for countries globally. Online data on COVID-19 daily cases of infections, recoveries, deaths are used.Finally, time-dependent reproduction number is explored in connection with dynamics of peoples mobility. The method allows to assess the disease transmission potential and understand the effect of interventions on epidemics spread. It also can be easily adapted to future outbreaks of different pathogens. The tool is available online as Python code from the Github repository.

Information-theoretically provable unique true random numbers, which cannot be correlated or controlled by an attacker, can be generated based on quantum measurement of vacuum state and universal-hashing randomness extraction. Quantum entropy in the measurements decides the quality and security of the random number generator (RNG). At the same time, it directly determines the extraction ratio of true randomness from the raw data, in other words, it obviously affects quantum random bits generating rate. In this work, we commit to enhancing quantum entropy content in the vacuum noise based quantum RNG. We have taken into account main factors in this proposal to establish the theoretical model of quantum entropy content, including the effects of classical noise, the optimum dynamical analog-digital convertor (ADC) range, the local gain and the electronic gain of the homodyne system. We demonstrate that by amplifying the vacuum quantum noise, abundant quantum entropy is extractable in the step of post-processing even classical noise excursion, which may be deliberately induced by an eavesdropper, is large. Based on the discussion and the fact that the bandwidth of quantum vacuum noise is infinite, we propose large dynamical range and moderate TIA gain to pursue higher local oscillator (LO) amplification of vacuum quadrature and broader detection bandwidth in homodyne system. High true randomness extraction ratio together with high sampling rate is attainable. Experimentally, an extraction ratio of true randomness of 85.3% is achieved by finite enhancement of the laser power of the LO when classical noise excursions of the raw data is obvious.

In this study, using information theory tools, we investigate the quantum degree of mixedness, particle number fluctuations, and temperature variations in the paradigmatic Lipkin model, focusing on the interplay between these factors in a system of many fermions. Our analysis reveals intriguing dependencies of quantum mixedness on the total fermion number, showcasing distinct behaviors at different temperatures. Notably, we find that the degree of quantum mixedness exhibits a strong dependence on the total fermion number, with varying trends observed across different temperature regimes. Remarkably, this dependence remains unaffected by the strength of the fermion-fermion interaction (if it does not vanish, of course), underscoring the robustness of the observed phenomena. Through comprehensive numerical simulations, we provide illustrative graphs that depict these dependencies, offering valuable insights into the fundamental characteristics of many-fermion systems. Our findings shed light on the intricate dynamics of quantum degree of mixedness and particle number fluctuations in fermionic systems, with potential implications for diverse fields ranging from condensed matter physics to quantum information science.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.

In this paper for every number field K generated by a root α of a trinomial x⁷ + ax + b ∈ Z[x] and for every prime integer p, we calculate ν_p(i(K)), the highest power of p dividing the index i(K) of the field K. In particular, we calculate the index i(K). As application, when the index of K is not trivial, then K is not monogenic.

Abstract: The Mediterranean diet, a widely studied and highly beneficial diet, underpins my research. Initially, the Mediterranean diet included Wild Edible Plants (WEPs). According to numerous research reports, this diet 1) promotes health and longevity and 2) prevents various modern diseases, including coronary and Alzheimer’s disease. A vital component of this diet is consuming locally available green plants, which are rich in health-promoting substances. In Åhlberg (2021, 2022b), I presented evidence for 56 health-promoting substances that all green vascular WEPs contain. While reading research reports of these five species, I found eight more health-promoting substances that all green vascular wild edible plants have. This article adds eight new substances to the earlier 56, bringing the total to 64. This is a novel and groundbreaking finding for which I provide research evidence. Each WEP has 1) health-promoting substances that all green vascular plants share and 2) species-specific health-promoting substances. I present the latest research on five invasive wild edible plants (WEPs) species. Each contains at least 64 health-promoting substances and varying species-specific health-promoting substances. I also present the experimental research results showing how many of these substances prevent Alzheimer’s disease. Keywords: wild edible plants (WEPs); wild food plants; Mediterranean diet; functional foods; good health, longevity; Alzheimer’s disease; alimurgic plants; invasive species; sustainability

We extend the concept of metallic ratios to the real argument n considered as a dimension by analytic continuation showing that they are defined by an argument of a normalized complex number, and for rational n ≠ {0, ±2}, they are defined by Pythagorean triples. We further extend the concept of metallic ratios to metallic angles.

In the following article, we analyse the determinants of the number of physicians in the context of ISTAT BES-Benessere Equo Sostenibile data among twenty Italian regions in the period 2004-2022. We apply Panel Data with Random Effects, Panel Data with Fixed Effects, and Pooled OLS-Ordinary Least Squares. We found that the number of Physicians among Italian regions is positively associated, among others, to “Trust in the Police and Firefighters”, “Net Income Inequality”, and negatively associated, among others, to “Research and Development Intensity” and “Soil waterproofing by artificial cover”. Furthermore, we apply the k-Means algorithm optimized with the Silhouette Coefficient and we find the presence of two clusters. Finally, we confront eight different machine-learning algorithms to predict the future value of physicians and we find that the PNN-Probabilistic Neural Network is the best predictive algorithm.

A formula for the turbulent Prandtl number is derived in terms of local variables available from two-equations turbulence models. The derivation is a direct consequence of the expected square additivity of the molecular and turbulent parameters defining the effective viscosity and the effective conductivity. The formula does not degenerate and leads to a Kays like formulation if approximated. Its utility and its limitation are discussed.

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.

Based on three assumptions of our 4G model of final unification, we have developed simple logics for estimating the unified atomic mass unit, atomic electrochemical equivalents, Faraday constant and Avogadro number. We appeal the science community to review the following points. 1) Unified atomic mass or energy unit can be considered as ‘average rest energy of nucleons minus average binding energy per nucleon of all atomic nuclides plus electron rest energy’. 2) Electrochemical equivalent of any atomic ion is nothing but the ratio of its mass to its charge. 3) Faraday charge is nothing but the ratio of elementary charge to unified atomic mass unit. 4) Faraday mass can be considered as the inverse of Faraday charge. 5) Avogadro number is nothing but the inverse of unified atomic mass unit. 6) Number of atoms per kg can be called as Kg-mole and number of atoms per gram can be called as gram-mole. Following our 4G model, starting form A=5 to 340, for isobars, ‘average binding energy per nucleon’ having maximum binding energy can be estimated with a simple relation of the form, BE/A=A^-1[1-(0.5+0.000935A²)-A^1/3]10.1MeV. It needs a review and fine tuning.

We propose a method that enables precise determination of the number of atoms in a Dick-noise-free optical lattice clock, by effectively addressing quantum projection noise. Our approach relies on conducting stability measurements at three distinct parameter sets, allowing us to differentiate between quantum projection noise, photon shot noise, and technical noise. Importantly, our method enables accurate extraction of the atom number, even in the presence of photon shot noise and technical noise. To validate the effectiveness of our approach, we employ numerical simulations and optimize the modulation parameters to achieve the smallest uncertainty possible. The numerical simulations show the validity of our method and demonstrate a measurement uncertainty in the atom number that is below 4% across a wide range of atom numbers, provided that the standard deviation of atom number fluctuation is kept below 0.23 times the average atom number.

Today, the most powerful approach to detect distant homologs of a protein is based on structure prediction and comparison. Yet this approach is still inapplicable to many viral proteins. Therefore, we developed a powerful sequence-based procedure to identify distant homologs of viral proteins. It relies on 3 main principles: 1) Traces of sequence similarity with a protein can persist beyond the significance cutoff of homology detection programs; 2) Candidate homologs can be identified among proteins with weak sequence similarity to the query, by using "contextual" information, e.g. taxonomy or type of host infected; 3) These candidate homologs can be validated using highly sensitive profile-profile comparison.As a test case, we applied our approach to a protein without known homologs, ORF4 of Lake Sinai virus (which infects bees). We discovered that ORF4 is composed of a domain that has homologs in proteins from >20 taxa of viruses infecting arthropods. We called it “Widespread, Intriguing, Versatile” (WIV) domain because it is found in proteins with a wide variety of domain organizations and functions. For example, WIV is encoded by the NSs protein of tospoviruses, a global threat to food security, which infect plants through arthropod vectors; by the protein encoded by RNA2 ORF1 of chronic bee paralysis virus, a widespread virus of bees; and by various proteins of cypoviruses, which infect the silkworm bombyx mori. WIV has a previously unknown structural fold, according to Alphafold predictions. In some viral species, WIV facilitates infection of arthropods, according to bibliographical evidence

Multiple sclerosis (MS) is a chronic autoimmune inflammatory disease that affects the nervous system. Peripheral blood leukocyte telomere length (LTL) and mitochondrial DNA copy number (mtDNA-CN) are potential biomarkers of disability and neurological damage. The present work evaluated LTL and mtDNA-CN in 75 relapsing-remittent MS (RRMS) patients 50 of whom had an Expanded Disability Status Scale (EDSS) 0 to 3 (mild-moderate disability), and 25 had an EDSS of 3.5 to 7 (severe disability). Absolute LTL and absolute mtDNA-CN were measured via real-time polymerase chain reaction (qPCR). The LTL and mtDNA-CN were significantly lower in RRMS severe disability than in RRMS mild-moderate disability (3.924 ± 0.124 vs 2.854 ± 0.092, p<00001; 75.14 ± 1.77 vs 68.06 ± 1.608, p<0.00001, respectively). The LTL and mtDNA-CN showed a linear correlation in RRMS with mild-moderate disability (r=0.2986, p=0.0351). In addition, in a binary logistic regression model the LTL can predict severe disability (AUC=0.697, p=0.0031, cutoff ≤ 3.0875 Kb, sensitivity= 73.1%, specificity=62.5%), the prediction is improved by including age to the model (AUC=0.765, <0.0001, sensitivity=78.26%, specificity=81.25%). Aging is closely linked to the development of disability in RRMS and can be evaluated through LTL and mtDNA-CN absolute quantification.

Successive-addition-of-digits-of-a-number(SADN) refers to the process of adding up the digits of an integer number until a single digit is obtained. Concept of SADN has been occasionally identified but seldom employed in extensive mathematical applications. This paper discusses SADN and its properties in terms of addition, subtraction and multiplication. Further, the paper applies the multiplication-property of SADN to understand the distribution of prime numbers. For this purpose the paper introduces three series of numbers -S1, S3 and S5 series- into which all odd numbers can be placed, depending on their SADN and the rationale of such classification. Extending the analysis the paper explains how composite numbers of the S1 and S5 series can be derived. Based on this discussion it concludes that even as the concept of SADN is rather simple in its formulation and appears as an obvious truism but a profound analysis of the properties of SADN in terms of fundamental mathematical functions reveals that SADN holds a noteworthy position in number theory and may have significant implications for unfolding complex mathematical questions like understanding the distribution of prime numbers and Goldbach-problem.

This study describes the seasonal course of denitrifying and nitrate reducing bacteria in a dimictic mesotrophic lake (Lake Scharmützelsee, Brandenburg, Germany) within a three-year period from 2011 to 2013. The bacterial cell numbers were quantified by fluorescence microscopy, most probable number (MPN) and PCR dependent quantification of the chromosomal 16S rDNA and of the nirS and nirK gene copy number. The highest seasonal differences (up to three orders of magnitudes) has been measured by MPN in the epilimnion. This variation was not reflected by PCR dependent approaches or direct microscopical enumeration. At adverse conditions (low temperature and/or low nitrate concentrations), the differences between MPN and gene copy numbers increased up to five orders of magnitudes and decreased to one magnitude at favorable environmental conditions. These results can be explained best by an increasing ratio of viable but not cultivable (VBNC) cells or dead cells at impairing conditions. In the hypolimnion, the courses of MPN and nir gene copy numbers were similar. This can be explained by higher feeding pressure and therefore smaller amounts of dormant cells. In the pelagial in general, the total cell numbers enumerated by either microscopical or molecular approaches were similar. In the sediment, more than 99 % of the DNA was obviously not related to viable bacteria but was rather “dead DNA” in dead cells or adsorbed to particle surfaces.

In this paper, a plasmonic refractive index sensor based on MIM waveguide (metal_insulation_metal) with two plasmonic waveguides and five rings and two teeth and four rectangular cavities is proposed and designed. The refractive index of the resonators as well as the resonant wavelengths will be investigated by the time difference finite difference method. To achieve an optical sensor with excellent quality and performance, we change the number and type of amplifiers and their dimensions. In each stage of the simulation, we will only change the refractive index of the middle ring located in the middle of the two waveguides, and the refractive index of the other amplifiers remains the same. This challenge will help to form a more appropriate structure for optical sensors. The sensor built in this simulation has a balanced and suitable function for integrated circuits and helps researchers to better understand the design of plasmonic structures. It also has important applications in medical research, health care, drug manufacturing, security monitoring and environmental protection, internal security of countries and the battlefield.

The declining and aging population, as well as the downsizing of households, poses problems for the simultaneous occurrence of vacant houses and the construction of new housing units. The objective of this study was to examine countermeasures for the future occurrence of vacant houses. The relationship between population, households, vacant houses, and newly constructed housing was reviewed according to prefecture, and the occurrence of vacant houses and distribution of newly constructed housing were mapped out. The results revealed that the increase in the number of elderly single-person households is a source of vacant houses, while middle-aged single households tend to promote the construction of new housing due to the lack of housing stock. In Setagaya ward, Tokyo, one of the reasons for the increase in new housing construction may be that many of the elderly single households have old wooden detached houses facing qualitative problems. In Wakayama central city, it was inferred that old, detached houses built for households with children during an economic growth period do not meet the needs of middle-aged single households, due to factors such as age, size, and floor plan, which has promoted vacancy and new construction, resulting in a stagnation of the housing cycle.

The sustainability of cities often changes as rapid urban developments and population growth affect the carrying capacity. Understanding the dynamics of carrying capacity then becomes crucial for tourist-oriented cities. This study focused on Baguio City, the "Summer Capital of the Philippines," attracting large crowds on holidays and actively promoting various events on non-holidays, thereby having temporal context variations classified as regular days, days with events, and holidays. Using the enhanced urban carrying capacity load number (EUCCLN) model, load number (LN) changes for different temporal contexts are calculated based on spatial indicators grouped into air, traffic, economy, and waste. The city experiences the worst pressures on air quality during holidays with $99.23\%$ districts under very high to critical levels followed by regular and days with events. However, the total LN is balanced by favorable economic conditions with only $9.23\%$ at critical. EUCCLN effectively pinpoints areas experiencing critical states at any time, advocating targeted government monitoring. We demonstrate that Night Time Light, for places with no economic data available, can be used as a proxy to highlight areas requiring improved urban vibrancy. This work suggests that EUCCLN monitoring urban pressures can easily be expanded to nowcasting with real-time data.

We present a mixing length based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

Automatic Number Plate Recognition is a computer vision technology that provides a way to recognize the vehicles number plates without direct human intervention. Developing Automatic Number Plate Recognition methodologies is a widely studied topic among the computer vision community to increase the accuracy rates. Although there are many studies, the research in character segmentation and improving the recognition accuracy remains limited. In this study, a new methodology is proposed to reduce the character recognition errors of Automatic Number Plate Recognition systems. To achieve this, it will be determined whether the characters are letters or numbers, and the number plates will be expressed in the form of letters - digit. The method suggested for segmenting blobs correctly worked with an accuracy of 96.12% on the test dataset. The method suggested for generating letter-digit expression for the number plates correctly worked with an accuracy of 99.28% on the test dataset. The proposed methodology can work only on Turkish number plates. In the future studies, the proposed methodology can be expanded by using the number plate dataset of a different country.

A number of chemical modifications were carried out in order to synthesize new compounds based on the triterpenoid betulonic acid. Triazolation reactions were carried out for the synthesis of new 1,2,3-triazole derivatives based on betulonic acid. Chemical changes were made on the carbonyl group at the C-3 position of the initial molecule and on the carboxyl and hydroxyl groups at the C-28 position. Chromatographic methods were used to separate and purify the formed products. Spectroscopic (NMR-, mass-) methods were used to establish the structure of synthesized compounds. As a result of the chemical transformations carried out, a number of new derivatives of betulonic acid were obtained. All synthesized compounds were tested for antimicrobial and cytotoxic activity. As a result, compounds with pronounced antimicrobial activity were identified.

Accurately monitoring insecticide resistance in target mosquito populations is important to combating malaria and other vector-borne diseases, and robust methods are key. The “WHO susceptibility bioassay” has been used for +60 years: mosquitoes of known physiological status are exposed to a discriminating concentration of insecticide. Several changes to the test procedures have been made historically which may seem minor but could impact bioassay results. The published test procedures and literature for this method were reviewed for methodological details. Areas where there was room for interpretation in the test procedures or where the test procedures were not being followed were assessed experimentally for impact on bioassay results: covering or uncovering of the tube end during exposure, number of mosquitoes per test unit, and mosquito age. Many publications do not cite the most recent test procedures, methodological details are reported which contradict the test procedures referenced or methodological details are not fully reported. As a result, the precise methodology is unclear. Experimental testing showed that using fewer than the recommended 15-30 mosquitoes per test unit significantly reduced mortality, covering the exposure tube had no effect, and using mosquitoes older than 2-5 days old increased mortality, particularly in the resistant strain. Recommendations are made for better reporting of experimental parameters.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.