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.

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.

This paper presents a new proof of the infinite nature of prime numbers. Grounded in fundamental Set theory and Analysis, the proof uses the method of contradiction to demonstrate the absurdity of assuming the set of all prime numbers to be finite.

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.

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, 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.

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.

To characterize the fecal microbiota of lactating Bactrian camels, this study employed a random selection of camels, assigning them to three groups: the first parity group, the third parity group, and the fifth parity group. The fecal microbial community of lactating camels was assessed using 16S rRNA amplicon sequencing, and the resulting library was sequenced on an Illumina NovaSeq platform. The first parity group was characterized by Verrucomicrobiaceae as a distinctive bi-omarker, whereas Clostridiaceae exhibited a similar role to the third parity group. In terms of functional analysis, the relative abundance of the Steroid biosynthesis pathway was highest in the first parity group, whereas the fifth parity group demonstrated a higher relative abundance of the Tuberculosis pathway compared to the other groups. The first parity group exhibited the greatest presence of seven types of enzymes, whereas the fifth parity group displayed the highest levels of two specific enzymes. Additionally, a positive association was observed between the relative abundance of the Steroid biosynthesis pathway and Verrucomicrobiaceae. Furthermore, the relative abundance of the Tuberculosis pathway displayed positive correlations with 14 enzymes. In conclusion, this study revealed that different parity was associated with distinct fecal microbial ecologies in lactating Bactrian camels.

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}x^{k}W_{k}^{3}$ and $\sum_{k=1}^{n}x^{k}W_{-k}^{3}$ for the cubes of generalized Fibonacci numbers are presented. As special cases, we give sum formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.

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.

This article utilizes the Canny edge extraction algorithm based on contour curvature and the cross-correlation template matching algorithm to extensively study the impact of high-repetition-rate CO2 pulsed Laser on the target extraction and tracking performance of the infrared imaging detector. It establishes a quantified dazzling pattern for lasers on infrared imaging systems. By conducting laser dazzling and damage experiments, a detailed analysis of the normalized correlation between target and dazzling images is performed to quantitatively describe laser dazzling effects. Simultaneously, an evaluation system, including target distance and laser power evaluation factors, is established to determine the dazzling level and whether the target is recognizable. The research results reveal that laser power and target position are crucial factors affecting the detection performance of infrared imaging-guided weapon systems under laser dazzling. Different laser powers are required to successfully interfere with the recognition algorithm of infrared imaging-guided weapons at different distances. And laser dazzling will produce a lot of false edge information, which seriously affects the performance of pattern recognition algorithm. In laser damage experiments, the detector experienced functional damage, with a quarter of the image displaying as completely black. The energy density threshold required for functional damage to the detector is approximately 3 J/cm2. The dazzling assessment conclusions also apply to evaluating damage results. Finally, the proposed evaluation formula aligns with experimental results, objectively reflecting the actual impact of laser dazzling on the target extraction and tracking performance of infrared imaging systems. This study provides an in-depth and accurate analysis for understanding the influence of lasers on the performance of infrared imaging-guided weapons.

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.

Currently, there is a tenacious need to find new ways to purify water by eliminating bacterial biofilms, textile dyes, and toxic water pollutants. These contaminants pose significant risks to both human health and the environment. To address this issue, in this study, we have developed an eco-friendly approach that involves synthesizing Cobalt-doped Cerium Iron Oxide (CCIO) nanocomposite (NC) using an aqueous extract of Gossypium arboreum L. stalks. The resulting nanoparticles can be used to effectively purify water and tackle the challenges associated with these harmful pollutants. Nanoparticles excel in water pollutant removal by providing high surface area for efficient adsorption, versatile design for simultaneous removal of multiple contaminants, catalytic properties for organic pollutant degradation, and magnetic features for easy separation, offering cost-effective and sustainable water treatment solutions. CCIO nanocomposite has been synthesized by green co-precipitation method due to biomolecules and co-enzymes present in the aqueous extract of Gossypium arboreum L. stalk; a single-step procedure completed in 5 h reaction time. Further, the synthesis of nanocomposites was confirmed by various characterization techniques such as Fourier-transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), Field emission scanning electron microscopy (FE-SEM), Transmission electron microscopy (TEM), Thermogravimetric analysis (TGA), Dynamic light scattering (DLS), and Energy Dispersive X-Ray (EDX). CCIO NCs were discovered to have a spherical shape and an average size of 40 nm. Based on DLS zeta potential analysis, CCIO NCs were found to be anionic. Also, CCIO NCs showed significant antimicrobial and antioxidant activity. Overall, considering the physical and chemical properties, the application of CCIO NCs in the adsorption of various dyes (~91 %) and water pollutants (chromium = ~ 60 %) has been considered since they exhibit great adsorption capacity owing to their microporous structure which can be a step forward in water purification.

(1) Background: Vitamin K deficiency is a common feature of chronic kidney disease (CKD), leading to impaired bone quality and increased risk of vascular calcifications. A method to indirectly measure Vitamin K status is measuring the blood level of Vitamin K dependent proteins (VKDP)- osteocalcin (OC) and matrix GLA protein (MGP). The aim of this study is to correlate the level of OC and MGP with markers of CKD mineral bone disorder (CKD-MBD). (2) Methods: We conducted a single-center cross-sectional study that included 45 CKD G5D patients and measured blood biochemistry, complete blood count and intact osteocalcin and matrix GLA protein. (3) Results: We found a strong statistically significant correlation of OC with the markers of CKD-MBD such as: iPTH , serum calcium and serum phosphorus and a strong indirect statistically significant correlation with abdominal circumference. There was also a statistically significant correlation of MGP with markers of inflammation (CRP). Higher levels of MGP were found in patients treated with vitamin K antagonists, non-calcium based phosphate binders and vitamin D receptor activator- paricalcitol. (4) Conclusions: In our study, we found that vitamin K deficiency, measured indirectly using the level of VKDP is associated to CKD-MBD. The use of medication such as phosphate binders, that reduce vitamin K absorbtion, Vitamin D that increases Vitamin K requirements and also vitamin K antagonists, seem to have an influence on the blood level of VKDPs.

In this paper, closed forms of the sum formulas $\sum_{k=0}^{n}W_{k}^{2}$ \ for the squares of generalized Tetranacci numbers are presented. We also present the sum formulas $\sum_{k=0}^{n}W_{k+1}W_{k},$ $\sum_{k=0}^{n}W_{k+2}W_{k},$ and $\sum_{k=0}^{n}W_{k+3}W_{k}.$ As special cases, we give summation formulas of the of Tetranacci, Tetranacci-Lucas and some other fourth order linear recurrance sequences.

This article presents a new input device for spastic patients and others with similar symptoms. The sensor consists of a disc used to determine positions and can replace standard joysticks in medical devices such as electric-powered wheelchairs. Using a standard joystick while operating a powered wheelchair can result in dangerous situations when spastic movements occur and extremities cramp making them uncontrollable. To avoid this, a disc was developed that can be controlled with any body part. By shifting weight (x- and y-axis) the disc can tilt in any direction creating a proportional output signal and can also be pushed down in the center (z-axis) to open a menu on a screen for example. When spasms occur it is impossible for users to get stuck on the input device because the disc is flat and can be mounted within a control panel. Body parts coming into contact with the disc would merely slide across the disc without triggering unintentional actions. The sensor presented here is also adaptive and can be adjusted to fit a user’s strength and range of motion. This proposal aims to develop an input device that enables spastic patients to operate sensitive systems safely.

Hereditary hemochromatosis (HH) is the main genetic cause of iron overload and is regarded as metal-related human toxicosis. HH may result from HFE and non-HFE gene mutations causing hepcidin deficiency or hepcidin resistance. The disorder has a high biochemical penetrance, but a low clinical prevalence. Unfortunately, the majority of patients with HH remain undiagnosed at their disease-curable stage. The main aim of HH therapy is to prevent iron overload in the early-phase disease and elimination of excess iron from the body by phlebotomy in its late stage. Raising global awareness of HH among health professionals, their training to pay attention to early HH signs and symptoms, and strict patient monitoring are critical management strategies for preventing treatment delays, upgrading its efficacy, and improving patient prognosis.

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.

The evolution of human societal dynamics over the course of decades and centuries has led to an ever-increasingly complex digital modern life, one of the hallmark of which is the need for multi-tasking, inclusive of that with media. Is there an empirical mapping between this macroscopic (digital) evolution of the human societal dynamics (in terms of multi-tasking) and the microscopic evolution of the functional molecular units within cells (i.e., proteins) and their manifold cross-talks? Multi-tasking requires a certain degree of intrinsic or adapted flexibility which is as true at the bio-molecular level. Evolutionary diversification of structure-function relationship in proteins emphasizes the functional importance of intrinsically disordered entities (IDPs/IDRs) which are highly dynamic biological soft matters. Multi-functionality is favorably supported by their fluid-like shapes and other new malleable members of the protein family. The new wealth of knowledge coming from recent research on protein intrinsic disorder, fold-switching, moonlighting, hub proteins etc. has given us new insights into protein structure – functional relationship. This has led to a paradigm shift in protein science, clearly diverging from the traditional 'one structure – one function' model applicable to enzyme classes to a more complex understanding of protein functionality. This paradigm shift has caused scientists to delve deeper into the subject, exploring various evolutionary toys and tools to fit the cumulative multi-functional demands in higher organisms. This commentary covers the different evolutionary arsenals to achieve the growing multi-functionality and argues in favor of protein intrinsic disorder as probably the sharpest weapon of all.

This paper will explore analogs of groups formed by the transformations of two ropes as presented by Minh-Tam Quang Trinh.1 The two operations acting on these ropes are T and S, defined as twists and clockwise turns, respectively. These actions intertwine the ropes, creating tangles. T and S also have the ability to untangle the rope when used in certain combinations. In the two-rope case, these actions expressed as a group presentation were shown to be isomorphic to SL₂(Z). We explored the analog of these opera- tions, T and S, and conjectured the corresponding group to which they are isomorphic. Partial proofs for this conjecture are included and future work would include proving our conjecture as well as generalizing results to k ropes.

Peptides, both natural and synthetic, are well suited for a wide range of purposes and offer versa-tile applications in different fields such as biocatalysts, injectable hydrogels, tumor treatment, and drug delivery. The rising prominence of therapeutic peptides encompasses anticancer, antiviral, antimicrobial, and anti-neurodegenerative properties. The metals Na, K, Mg, Ca, Fe, Mn, Co, Cu, Zn, and Mo are ten of the twenty elements that are considered essential for life. Crucial for under-standing the biological role of metals is the exploration of metal-bound proteins and peptides. Aside from essential metals, there are other, non-essential metals that also interact biologically, exhibiting either therapeutic or toxic effects. Irregularities in metal binding contribute to diseases like Alzheimer’s, neurodegenerative disorders, Wilson's, and Menkes disease. Certain metal com-plexes have potential applications as radiopharmaceuticals. The examination of these complexes was done by preforming UV-Vis, IR, EPR, NMR spectroscopy, and X-ray analysis.

Sustainable continuous cover forestry is defined and analyzed in several ways. The differential equation representing growth of the basal areas of individual trees, motivated by fundamental biological production theory by Lohmander (2017a), is analyzed and extended in different directions. From the solution of the differential equation, the basal area and the tree diameter are obtained as explicit functions of time. The diameter is a strictly increasing function of time. In the absence of competitors, the diameter increment is shown to be a strictly decreasing function of time. Hence, the diameter increment can also be interpreted as a strictly decreasing function of the diameter. Alternative forms of adjustment of the differential equation, with consideration of competition, are defined. If the competition is strong, with large trees in the vicinity of a particular tree, then the basal area increment, and the diameter increment, are reduced. The growth of a large tree is less sensitive than the growth of a small tree, to competition from other trees. Under strong competition, the basal area increment, and the diameter increment, are strictly concave functions of the size of the tree. The unique maximum of the diameter increment occurs at a higher diameter, if the competition increases. In dynamic equilibrium, the tree size frequency distribution is stationary. If natural tree mortality can be avoided via the harvest strategy, the tree size frequency distribution is a function of the size and competition dependent growth function, and the harvest strategy. Empirical tree size frequency data are used to simultaneously estimate parameters of a size and competition dependent growth function and the applied harvest strategy, via nonlinear optimization. The properties of the estimated growth function are consistent with the corresponding properties of the production theoretically motivated hypothetical function, and the properties of the estimated harvest strategy confirm the corresponding hypotheses. The R2 of the nonlinear regression exceeds 0.97. With access to an empirically estimated equilibrium tree size distribution, it is possible to: 1. Estimate size frequency relevant parameters of tree size and competition dependent growth functions for individual trees. 2. Estimate the applied harvest strategy. 3. Explain and reproduce the empirically estimated tree size equilibrium distribution.

Liver X receptors (LXR) are deemed as potential drug targets for atherosclerosis, whereas a role in adipose tissue expansion and its relation to insulin sensitivity remains unclear. To assess the metabolic effects of LXR activation, C57BL/6 mice on a high-fat diet (HFD) were treated with the dual LXRα/β agonist T0901317 (30 mg/kg per day) for 3 weeks. Differentiated 3T3-L1 was used for analysing the effect of T0901317 on glucose uptake.T0901317 reduced fat mass, accompanied by a massive fatty liver and lower adipokine levels in circulation of HFD mice. Increased adipocyte apoptosis and macrophage infiltration were found in epididymal fat of T0901317-treated HFD mice. In addition, T0901317 treatment promoted basal lipolysis, but blunted the anti-lipolytic action of insulin. Furthermore, LXR activation antagonized PPARγ target genes in epididymal fat and PPARγ-PPRE binding activity in 3T3-L1 adipocytes. Although the glucose tolerance was comparable to that in vehicle-treated HFD mice, the insulin tolerance was significantly decreased in T0901317-treated HFD mice, indicating decreased insulin sensitivity by T0901317 administration, and which was further supported by impaired insulin signalling found in epididymal fat and decreased insulin-induced glucose uptake in 3T3-L1 by T0901317administration. These findings reveal that LXR activation impairs adipose expansion which contributes to decreased insulin sensitivity.

By repeated unloading and loading of the excavation dynamic and static loads, repeated train dynamic and static loads of multi-factors, the underpass tunnel, cross tunnel engineering influence area rock layer, the existing tunnel structure of the three constitutes a multifaceted structure, multi-factor interaction system. Existing tunnels into the prediction theory model of the new tunnel excavation process of dynamic and static loads, dynamic and static loads of existing tunnels are mostly analyzed individually, the results of synergistic analysis needs to be improved. Based on the theory of the current layer method, the paper comprehensively considers the stiffness of the existing tunnel, the stiffness of the new tunnel, the excavation method load and the existing tunnel load, coupled with Peck's empirical formula, the theoretical model of deformation prediction for excavation of a two-lane highway tunnel under the tunnel through the existing railroad is proposed, and verified and optimized by numerical calculations and monitoring data, which proves the applicability and reliability of the theoretical model in the similar strata and the project promotion.

In this paper, we present sums and partial sums of Horadam sequences via generating functions which extends a recent result of Prodinger.

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.

Recent data suggest that K-Ras4B (hereafter K-Ras) can drive cancer cell stemness via calmodulin (CaM)-dependent, non-canonical Wnt-signalling. Here we examined whether another Ca2+-binding protein, the CaM-related centrin1, binds to K-Ras and could mediate some K-Ras functions that were previously ascribed to CaM. While CaM and centrin1 appear to distinguish between peptides that were derived from their classical targets, they both bind to K-Ras in cells. Cellular BRET-data suggest that CaM engages more with K-Ras than centrin1 and that the interaction with the C-terminal membrane anchor of K-Ras is sufficient for this. Surprisingly, binding of neither K-Ras nor its membrane anchor alone to CaM or centrin1 is sensitive to inhibition of prenylation. In support of an involvement of the G-domain of K-Ras in cellular complexes with these Ca2+-binding proteins, we find that oncogenic K-RasG12V displays increased engagement with both CaM and centrin1. This is abrogated by addition of the D38A effector-site mutation, suggesting that K-RasG12V is held together with CaM or centrin1 in complexes with effectors. When treated with CaM-inhibitors the BRET-interaction of K-RasG12V with centrin1 was also disrupted in the low micromolar range, comparable to that with CaM. While CaM predominates in regulating functional membrane anchorage of K-Ras, it has a very similar co-distribution with centrin1 on mitotic organelles. Given these results, a significant overlap of the CaM- and centrin1-dependent functions of K-Ras is suggested.

In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

While lidar-based forest inventory methods have been widely demonstrated, prediction of tree diameters with lidar is not well understood. The performance metrics typically used in studies for prediction of diameters can be difficult to interpret and may not support comparative inferences between sampling designs or study areas. We evaluate a variety of lidar and k nearest neighbor (k-NN) strategies for prediction of tree diameter distributions using two indices which are easier to interpret and compare. The indices are based on the coefficient of determination (R²), and root mean square deviation (RMSD). These indices facilitate comparisons with alternative (non-lidar) inventory strategies, and with other project areas. We evaluate k nearest neighbors (k-NN) dbh density (relative frequency by dbh class) prediction strategies with lidar for 190 training plots distribute across the 800 km² Savannah River Site in South Carolina, USA. We evaluate the performance of k-NN with respect to distance metrics, number of neighbors, predictor sets, and response sets. Amongst the examined strategies we found Mahalanobis distance with k = 3 neighbors performed best according to a number of criteria.

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.

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.

Systemic inflammation and coronary microvascular endothelial dysfunction are essential pathophysiological factors in heart failure with preserved ejection fraction (HFpEF) that support the use of statins. The pleiotropic properties of statins, such as anti-inflammatory, antihypertrophic, antifibrotic, and antioxidant effects, are generally accepted and may be beneficial in HF, especially in HFpEF. Numerous observational clinical trials have consistently shown a beneficial prognostic effect of statins in patients with HFpEF, while the results of two larger trials in patients with HFrEF have been controversial. Such differences may be related to a more pronounced impact of the pleiotropic properties of statins on the pathophysiology of HFpEF and pro-inflammatory comorbidities (arterial hypertension, diabetes mellitus, obesity, chronic kidney disease) that are more common in HFpEF. This review discusses the potential mechanisms of statin action that may be beneficial for patients with HFpEF, as well as clinical trials that have evaluated the statin effects on left ventricular diastolic function and clinical outcomes in patients with HFpEF.

The intestinal microbial community of aquatic animals is closely related to the environment and thus affects the health of aquatic animals. Here we investigated annual variation of intestinal bacteria community structures of Ruditapes philippinarum cultured using two different methods, bottom sown and raft hanging. Bacterial diversity of seawater and sediment in different seasons was examined as well. Correlation between R. philippinarum intestinal bacteria community structures and environmental factors was analyzed. The results showed that in the two aquculture areas where R. philippinarum was differentially cultured, bacteria community structure of seawater and sediment both altered with seasons. However, neither seasonal changes nor difference in culture methods could significantly affect the intestinal bacteria community structures of R. philippinarum. Additionally, in terms of the alpha diversity of intestinal bacteria communities, there was no significant difference in R. philippinarum cultured using the two methods. For benthic cultured clams, alpha diversity of the intestinal bacterial communities was often higher than that of the environmental bacterial communities. For raft hanging cultured calms, Alpha diversity of the intestinal bacterial communities was normally comparable with that of the environmental counterparts. Beta diversity analysis showed that the intestinal bacterial community structure of R. philippinarum was mainly determined by both deterministic and stochastic processes. Correlation analysis showed that the intestinal bacterial community structures of R. philippinarum were determined by a variety of environmental factors. For clams collected from the benthic culture area, the intestinal bacterial structure was more correlated with the physicochemical properties of sediment in comparing with those of seawater. For clams collected from the raft-culture area, the intestinal bacterial structure was mainly determined by the phsicochemical characteristics of seawater. This study helps us to better understand the bacterial community structure in complex aquaculture ecosystems, providing a reference for healthy shellfish aquaculture and ecosystem protection in aquaculture area.

In the paper, the authors find closed forms for derangement numbers in terms of the Hessenberg determinants, discover a recurrence relation of derangement numbers, present a formula for any higher order derivative of the exponential generating function of derangement numbers, and compute some related Hessenberg and tridiagonal determinants.

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.

In standard construction of hyperrational numbers using ultra-power we assume that the ultra lter is selective. It makes possible toassign real value to any nite hyperrational number. So, we can consider hyperrational numbers with selective ultra lter as extension of traditional real numbers. Also proved the existence of strictly monotonic or stationary representing sequence for any hyperrational number.

(1) Background: In this work, a series of benzimidazole derivatives containing colchicine-like and cathechol-like moieties with methyl group substitution in the benzimidazole ring were evaluated for their in vitro antiproliferative, pro-apoptotic and antioxidative activity against highly invasive breast cancer cell line MDA-MB-231 and related impairment of tubulin dynamics; (2) Methods: MTT assay was used to evaluate the antiproliferative activity. In vitro tubulin polymerization assay as well as docking analysis was applied to prove the alterations in tubulin polymerization. Immunofluorescent and DAPI staining reveal the pro-apoptotic potential of benzimidazole derivatives and the effect on tubulin’s dynamics in living cells. The antioxidant activity was evaluated by scavenging of H2O2 and hypochlorite ion and ortho-phenanthroline tests; (3) Results: The compounds containing colchicine-like moiety displayed significant growth inhibitory effect against cancer cell line as was highlighted the role of methyl functional group on the tubulin aggregation and blockage of mitosis. All compounds showed an ability to scavenge H2O2, while the compounds with cathecol-like moiety were more effective against hypochlorite ion and chelation of iron; (4) Conclusions: The benzimidazole derivative containing colchicine-like moiety and methyl group substitution in benzimidazole ring is a potential antiproliferative and microtubule destabilizing agent.

The main goal of the present paper is to construct some families of the Carlitz’s q-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and investigate their some explicit properties and identities arising from the bosonic q-Volkenborn integral on ℤ_p. We then define the modified degenerate Carlitz’s q-Bernoulli polynomials and numbers with weight (α, β) and obtain some recurrence relations and other identities. Moreover, we derive some correlations with the modified Carlitz’s q-Bernoulli polynomials with weight (α, β), the modified degenerate Carlitz’s q-Bernoulli polynomials with weight (α, β), the Stirling numbers of the first kind and second kind.

The current study aims to produce a material that has a dual effect of healing and anti-inflammatory. For this target k-carrageenan/polyacrylamide hydrogel film loaded with cetrimide (k-CAR/PAAm/CI) was performed by manual casting technique. Definite concentrations of k-CAR and AAm was heated at 80°C for 2 hours, CI and glycerol were added. The solution was cast without using initiator and cross-linker. The reaction of the sulfonic acid group -SO3H of k-CAR with -CONH2 group of PAAm lead to the formation of a sulfonamide (-SO2NH-) linkage. The characteristics of the produced films were investigated by FTIR, TGA, contact angle, and mechanical properties. Improvement in the thermal stability was performed in k-CAR/PAAm/CI2 film containing 1.5% CI compared to the film has 0.5% CI (k-CAR/PAAm/CI1). The contact angle measurement proved the films are hydrophobic that enhanced by increasing CI content. The tensile strength and elongation percent values are considered adequate for materials used in wound care. k-CAR/PAAm/CI2 (1.5% CI) film showed superior antimicrobial activity against P. aeruginosa, moderate activity against S. aureus, and low activity against E. coli. The film k-CAR/PAAm/CI2 was effectively inhibiting the heat-induced hemolysis and may offer a promising approach for the development of effective wound dressings.

Understanding morphological and genetic diversity of forest trees is essential to facilitate their conservation, sustainable management and genetic improvement for addressing the economic and environmental demands and challenges. We have examined variation in morphometric seed and pod traits and seed germination of multipurpose and widely distributed forest tree Albizia lebbek (Indian siris) from 12 provenances covering the species’ range in northern India and its relationships with bioclimatic factors. Highly significant inter-provenance variation was observed in seed size (seed length (SL), seed width (SW), SW/SL, SL×SW), seed mass (1000 seed weight), pod size (pod length (PL), pod width (PW), PW/PL), seed germination, number of seeds per pod, and insect infected seeds (IIS). The provenance effect contributed a major portion to the total phenotypic variance. Morphometric variation in all traits except for IIS was not clinal related to longitude, latitude, altitude or rainfall. There was an indication of the presence of ecotypic variation. IIS showed clinal variation with significant negative correlation with latitude. Most seed size and pod size traits showed positive correlations with several temperature bioclimatic factors and negative correlations with several precipitation bioclimatic factors. Our results have significance for genetic improvement, population genetics and genomics studies and conservation and sustainable management of A. lebbek genetic resources.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

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 the achievement of the Sustainable Development Goals (SDGs), education plays a fundamental role. However, traditional methodologies do not favor the enrichment and personal development essential to promote global awareness. The use of active methodologies based on experiences improve the quality of learning. This work describes the design, implementation, and evaluation of the acquired knowledge of a didactic proposal for non-formal education as a support for regulated education based on botany content. Firstly, a workshop was held, where young people participated directly in developing field work with a real scientific methodology. Subsequently, a group of students was chosen to be interviewed to obtain a global vision of the learning they obtained. The motivation of the students was quite positive, which allowed us to obtain voluntary participation in the field work and gave the students a participative attitude throughout the development of the workshops. Four months later, this positive attitude remained during their direct involvement in various activities, and the students still remembered the fundamental content discussed. Relating the didactic proposal to its immediate environment was shown to increase interest in learning and value in its own context. The results of this educational experience have been very positive, as knowledge was acquired, and interest in the preservation of the environment and the profession of a researcher was promoted.

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.

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.

Phage therapeutics offer a potentially powerful approach to combat multidrug-resistant bacterial infections. However, to be effective, phage therapy must overcome existing and developing phage resistance. While phage cocktails can reduce this risk by targeting multiple receptors in a single therapeutic, bacteria have mechanisms of resistance beyond receptor modification. A rapidly growing body of knowledge describes a broad and varied arsenal of antiphage systems encoded by bacteria to counter phage infection. We sought to understand the types and frequencies of antiphage systems present in a highly diverse panel of Pseudomonas aeruginosa clinical isolates utilized to characterize novel antibacterials. Using web-server tool PADLOC (Prokaryotic Antiviral Defense Locator), putative antiphage systems were identified in these P. aeruginosa clinical isolates based on sequence homology to a validated and curated catalog of known defense systems. Coupling this host bacterium sequence analysis with host range data for 70 phages, we observed a correlation between existing phage resistance and the presence of higher numbers of antiphage systems in bacterial genomes. We were also able to identify antiphage systems that were more prevalent in highly phage-resistant P. aeruginosa strains, suggesting their importance in conferring the resistance.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

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.

Cervical cancer is one of the ailments that endangers the health of women all over the world and causes infertility. Fortunately, this disease can be avoided. Both the results and participation rates of the current preventative strategy remain poor. Hence, preventative or early detection methods remain challenging and open. In gynecology and computer science fields, few studies on identifying cervical cancer are based on behavior risk factor and machine learning. Moreover, various social and behavioral aspects might often make it more difficult to detect cervical cancer especially in low‑ and middle‑income countries (LMICs). Accordingly, focus on predicting the presence of cervical cancer through behavioral risk factors is the basic structure of this research. We proposed an approach to classify cervical cancer from a social-behavioral perspective using logistic regression to predict cervical cancer. We got significantly improved outcomes than the existing methods. Moreover, we used feature engineering to formulate less dimensionality as a pre-processing step and optimized parameters to be prepared for classification phase. The results proved that using the logistic regression with regularization type L1 had a promising performance. The accuracy of Logistic Regression (LR) L1 was 97.2%. Such results support the proposed work as a reliable classification predictive tool.

Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden. Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.

Image recovery by dictionary learning is of potential interest for many possible applications. To learn a dictionary, one needs to solve a minimization problem where the solution should be sparse. The K-SVD formalism, which is a generalization of the K-means algorithm, is one of the most popular methods to achieve this aim. We explain the preprocessing that is needed to bring images into a manageable format for the optimization problem.The learning process then takes place in terms of solving for sparse representations of the image batches. The main contribution of this paper is to give an experimental analysis of the recovery for highly textured imagery. For our study, we employ a subset of the Brodatz database. We show that the recovery of sharp edges plays a considerable role. Additionally, we study the effects of varying the number dictionary elements for that purpose.

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.

In the first part of this article, we discuss and generalize the complete convergence introduced by Hsu and Robbins (1947) to the r-complete convergence introduced by Tartakovsky (1998). We also establish its relation to the r-quick convergence first introduced by Strassen (1967) and extensively studied by Lai (1976). Our work is motivated by various statistical problems, mostly in sequential analysis. As we show in the second part, generalizing and studying these convergence modes is important not only in probability theory but also to solve challenging statistical problems in hypothesis testing and changepoint detection for general stochastic non-i.i.d. models.

We review time expansion wave theory and refine our model showing it to accurately match observed cosmological luminosity data. The theory augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension that we observe as the expansion of the universe. This leads us to explain mass creation, the speed of light limit, gravity, black holes without singularities and other macroscopic effects. Our model leads to an expansion velocity of 6.87 0.36 × 106 ms-1, which results in a Hubble expansion rate constant of 71.3 3.7 km/s/Mpc. Because of the finite window of time in which we exist, an extra a degree of freedom is available leading to interesting interpretations at the subatomic level. At this size range, then a spin is allowed within the time dimension explaining why wave particle duality occurs and explains the electromagnetic force and other quantum mechanical properties. It provides a solution to the double slit conundrum and can explain how quantum entangled partners can behave in a quantum way and pass seemingly time-defying information. The potential quantitative origin of the fine structure constant which governs the size of the electromagnetic force is also strongly indicated by this theory.

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.

Severe early childhood caries remains the most common chronic disease affecting children. Its multifactorial etiology has established a controversy about which risk factors were more significant to its development. Therefore our study aimed through meticulous statistical analysis to arrange the “well agreed upon” common risk factors in order of significance, to aid the clinician in tailoring an adequate preventive program for this affected age group. The study reshuffled the risk factors contributing to severe early childhood caries and placed them in the order of their significance as follows: snacking of sugary food several times a day, increased number of siblings to 3 or more, night feeding, child self-employed brushing, mother caries experience, 2 siblings, on demand feeding, once/day sugary food, sharing utensils, 1 Sibling, male gender, father’s education, late first child dental visit, brushing time, mother’s education, no dental visit, decreased brushing frequency & no night brushing.

The KcsA is a prokaryotic potassium-oriented channel, which is sourced from the Streptomyces lividans soil bacteria. From extensive studies that have been carried over the KcsA potassium channel, it has been proved that various factors enable the gating and shuttling of the potassium ions into and out of the cells. Some of the factors include the different concentration of protons in the inside and outside membrane. The other factor is the existence of the selectivity filter equipped in the exit of channel pore, which enables the movement of the K⁺ ions. Not only are potassium ions present in the channel but also sodium ions. Potassium and sodium ions are the ions that are essential in the conductivity of a cell because of their charge. An intuitive idea about why K⁺ ions are at least 10,000 times more permeant than Na⁺ ions is presented in various entities. The hypothesis is that the selectivity ratio is probably related to the successive entry of Na⁺ ions, based on the premise that the ratio seems to be relevant to unpredictable quantities caused by Brownian corrosion of ions.

The excessive intake of sodium (Na) and insufficient intake of potassium (K) are major concerns to prevent hypertension. Using low-Na/K seasonings (reducing 25% of the NaCl and adding K salt) may improve the dietary Na/K ratio and help prevent hypertension. To devise an intervention study using low-Na/K seasonings at a company cafeteria, we calculated the Na and K contents of the meals served at the cafeteria and estimated changes in the intakes when suitable low-Na/K seasonings were used. We also considered using milk as a good source of K. We used an ingredient list of a company cafeteria and calculated Na and K contents in each dish. The average amounts of NaCl and K per use were 5.04 g and 718 mg, respectively. Seasonings contributed 70.9% of the NaCl. With the use of low-Na/K seasonings, an estimated reduction in NaCl of 0.8 g/day and an estimated increase in K of 308 mg/day was achieved. An additional serving (200 mL) of milk, NaCl was reduced by 0.57 g/day and K was increased by 610 mg/day, with an overall decrease in the dietary Na/K ratio from 3.20 to 2.40. The use of low-Na/K seasonings and dairy may improve the dietary Na/K ratio among cafeteria users and help prevent hypertension.

Cardiovascular disease is the number one cause of death in the world and Quoting from WHO, around 31% of deaths in the world are caused by cardiovascular diseases and more than 75% of deaths occur in developing countries. The results of patients with cardiovascular disease produce many medical records that can be used for further patient management. This study aims to develop a method of data mining by grouping patients with cardiovascular disease to determine the level of patient complications in the two clusters. The method applied is principal component analysis (PCA) which aims to reduce the dimensions of the large data available and the techniques of data mining in the form of cluster analysis which implements the K-Medoids algorithm. The results of data reduction with PCA resulted in five new components with a cumulative proportion variance of 0.8311. The five new components are implemented for cluster formation using the K-Medoids algorithm which results in the form of two clusters with a silhouette coefficient of 0.35. Combination of techniques of Data reduction by PCA and the application of the K-Medoids clustering algorithm are new ways for grouping data of patients with cardiovascular disease based on the level of patient complications in each cluster of data generated.

In this paper, we define and investigate modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo sequences as special cases of the generalized Leonardo sequence. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences. Furthermore, we show that there are close relations between modified p-Leonardo, p-Leonardo-Lucas, p-Leonardo numbers and Fibonacci, Lucas numbers.

Abstract The aim of the present review is to discuss the roles of vitamin K and vitamin K-dependent proteins, and the combined action of the vitamins K and D, for maintenance of bone health. The most relevant vitamin K-dependent proteins in this respect are osteocalcin and matrix Gla-protein (MGP). When carboxylated these proteins appear to have the ability to chelate and import calcium from the blood to the bone, thereby reducing the risk of osteoporosis. Carboxylated osteocalcin appears to contribute directly to bone quality and strength. Adequate vitamin K status is required for carboxylation of MGP and osteocalcin. In addition, vitamin K acts on bone metabolism by other mechanism, such as a ligand for the nuclear steroid and xenobiotic receptor (SXR). In this narrative review, we examine the evidence for increased bone mineralization through dietary adequacy of vitamin K (phylloquinone or menaquinone). Summarizing the evidence for a synergistic effect of vitamin K and vitamin D3 we find that an adequate supply of vitamin K on top of an optimal vitamin D status seems to add to the benefit for maintaining bone health. More research related to synergism and possible mechanisms of vitamins D3 and K interaction in bone health is needed.

The African continent has the highest prevalence of hypertension globally, with South Africa reporting the highest prevalence in Southern Africa. While the influence of genetic variability in the pathogenesis of hypertension is well described internationally, limited reports are available for African populations. This study aimed to assess the association of genetic variants and essential hypertension in a cohort of two ethnic South African population groups. Two hundred and seventy-seven hypertensive and one hundred and seventy-six normotensive individuals were genotyped for 79 variants. Genotyping was performed using the Illumina GoldenGate Assay and allele-specific polymerase chain reaction. The association of variants was assessed using the Fisher Exact test under the additive and allelic genetic models, while multivariate logistic regression was used to predict the development of hypertension. Five variants (CYP11B2 rs179998, AGT rs5051 and rs699, AGTR1 rs5186 and ACE rs4646994) were significantly associated with essential hypertension in the cohort under study. Furthermore, AGTR1 rs5186 and AGT rs699 were identified as risk factors for the development of hypertension in both ethnic groups. In two ethnic South African populations an association was observed between Renin-Angiotensin-Aldosterone System (RAAS) related genes and the development of hypertension.

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 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.

The $k$-means problem is to compute a set of $k$ centers (points) that minimizes the sum of squared distances to a given set of $n$ points in a metric space. Arguably, the most common algorithm to solve it is $k$-means++ which is easy to implement, and provides a provably small approximation factor in time that is linear in $n$. We generalize $k$-means++ to support: (i) non-metric spaces and any pseudo-distance function. In particular, it supports M-estimators functions that handle outliers, e.g. where the distance $\mathrm{dist}(p,x)$ between a pair of points is replaced by $\min {\mathrm{dist}(p,x),1}$. (ii) $k$-means clustering with $m\geq 1$ outliers, i.e., where the $m$ farthest points from the $k$ centers are excluded from the total sum of distances. This is the first algorithm whose running time is linear in $n$ and polynomial in $k$ and $m$.

Nanoporous membranes promise energy-efficient water desalination. Hexagonal boron nitride (h-BN), like graphene, exhibits outstanding physical and chemical properties, making it a promising candidate for water treatment. We employed Car–Parrinello molecular dynamics simulations to establish accurate modeling of Na+ and Cl- permeation through hydrogen passivated nanopores in graphene and h-BN membranes. In these complex systems the classical potentials cannot properly account for the physics at play. We demonstrate that ion separation works well for the h-BN by imposing a barrier of 0.13 eV and 0.24 eV for Na+ and Cl- permeation respectively, compared to the graphene where the Cl- ion faces a negative barrier of 0.68 eV and is prone toward blockade and Na+ permeation is associated with a slightly negative barrier of 0.03 eV. From the change in the solvation shell, we get the following trend: Na/h-BN > Na/G > Cl/G > Cl/h-BN. We argue that the trend in the permeation barrier changes to Cl-h-BN > Na-h-BN > Na-G > Cl-G due to a combination of several interactions, including the distortion of the water network induced by the ions, the ion-water interaction, and the ion-nanopore interaction. Overall, the desalination performance of h-BN surpasses that of their graphene counterparts.

Graphene hybrid-filler polymer composites have emerged as prominent materials that revolutionize heavy industries. This study encapsulates the in-depth analysis of different influential factors such as filler/graphene type, aspect ratios, dispersion methods, filler-matrix compatibility, fiber orientation, synergistic effects, different processing techniques, and post-curing conditions that affect the processing, properties and determine the resultant applications of graphene hybrid polymer composites. Additionally, it discusses the substantial role of graphene collaboration with other fillers such as carbon nanotubes, silica, nano-clays and metal oxides to produce functionalized hybrid polymer composites with synergistically enhanced tailored properties to offer solutions for heavy industries like aerospace, automotive, electronics, and energy harvesting. The review concludes with some suggestions and outlook on the future of these composite materials by emphasizing the need for continued research to fully optimize their potential.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

Number is based in special edges, is introduced. The kind of natural extension from edges toward vertex and the set of vertices in the way that, the final notion is number, is studied. The result is obtained which is about the study on the classes of graphs in the matter of new notions. There is the extended notion about having edge amid two vertices toward having some edges in the word of neighbor and in another stage going into the atmosphere of having consecutive edges in the terminology of path and in the upper vision going on the notion about path with jargon and buzzword of distance as if the minimal vertices has concluded the new notions with the word, number.

The key links of face recognition are digital image preprocessing, facial feature extraction and pattern recognition, this article aimed at the current problem of slow speed and low recognition accuracy of face recognition , from the above three key links, on the basic of analyzing the therories of Fractional Differential Masks Operator (FDMO), Principal Component Analysis (PCA) and Support Vector Machine (SVM), design a kind of FDMO+PVA+SVM coupling algorithm that applies to face recognition to improve the speed and accuracy of it. To realize FDMO+PCA+SVM coupling algorithm, first, we should apply FDMO to face image processing binary marginalization, the purpose is getting face contour; Then, we apply PCA to get the feature of face image which is disposed by binary marainalization. At last, we can apply One-Against All of the SVM classifier and LibSVM software package to realize face recognition. Beside, the article with nine different coupling algorithm design four groups of experimental reaults on the ORL face database verified by comparative analysic FDMO+PCA+SVM coupling algorithm in the superiority of face recognition accuracy and speed.

New setting is introduced to study “closing numbers” and “super-closing numbers” as optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. In this way, some approaches are applied to get some sets from (Neutrosophic)n-SuperHyperGraph and after that, some ideas are applied to get different types of super-closing numbers which are called by optimal-super-resolving number, optimal-super-coloring number and optimal-super-dominating number. The notion of dual is another new idea which is covered by these notions and results. In the setting of dual, the set of super-vertices is exchanged with the set of super-edges. Thus these results and definitions hold in the setting of dual. Setting of neutrosophic n-SuperHyperGraph is used to get some examples and solutions for two applications which are proposed. Both setting of SuperHyperGraph and neutrosophic n-SuperHyperGraph are simultaneously studied but the results are about the setting of n-SuperHyperGraphs. Setting of neutrosophic n-SuperHyperGraph get some examples where neutrosophic hypergraphs as special case of neutrosophic n-SuperHyperGraph are used. The clarifications use neutrosophic n-SuperHyperGraph and theoretical study is to use n-SuperHyperGraph but these results are also applicable into neutrosophic n-SuperHyperGraph. Special usage from different attributes of neutrosophic n-SuperHyperGraph are appropriate to have open ways to pursue this study. Different types of procedures including optimal-super-set, and optimal-super-number alongside study on the family of (neutrosophic)n-SuperHyperGraph are proposed in this way, some results are obtained. General classes of (neutrosophic)n-SuperHyperGraph are used to obtains these closing numbers and super-closing numbers and the representatives of the optimal-super-coloring sets, optimal-super-dominating sets and optimal-super-resolving sets. Using colors to assign to the super-vertices of n-SuperHyperGraph and characterizing optimal-super-resolving sets and optimal-super-dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on n-SuperHyperGraph to get new results about closing numbers and super-closing numbers alongside sets in the way that some closing numbers super-closing numbers get understandable perspective. Family of n-SuperHyperGraph are studied to investigate about the notions, super-resolving and super-coloring alongside super-dominating in n-SuperHyperGraph. In this way, sets of representatives of optimal-super-colors, optimal-super-resolving sets and optimal-super-dominating sets have key role. Optimal-super sets and optimal-super numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal-super ones. Simultaneously, three notions are applied into (neutrosophic)n-SuperHyperGraph to get sensible results about their structures. Basic familiarities with n-SuperHyperGraph theory and neutrosophic n-SuperHyperGraph theory are proposed for this article.

In the paper, by virtue of the Faá di Bruno formula and two identities for the Bell polynomial of the second kind, the authors find a closed form for the Stirling polynomials in terms of the Stirling numbers of the first and second kinds.

China's cotton production has shown a concentration to the advantageous regions in recent years. Based on the relevant data of cotton production in China, the study measures the cotton production agglomeration levels of 16 major cotton-producing provinces from 1978 to 2020, summarizes the spatiotemporal evolution characteristics of cotton production agglomeration, and analyzes the factors influencing cotton production agglomeration using spatial econometric models. The results indicate that: Firstly, since the opening-up and reform, China's cotton production agglomeration levels have shown an overall upward trend, exhibiting periodic dynamic changes over time, and the spatial pattern reveals a dynamic regional gradient. Secondly, there is spatial correlation among the production scales of cotton in different provinces, with a trend resembling a "U" shape, and the agglomeration form shows a low-level convergence. Thirdly, technological level, policies, substitute industrial products and foreign trade are identified as important factors. The cotton production in each province is spatially correlated through these factors, and there is also a presence of spillover effects. In conclusion, the government should prioritize considerations of various influencing factors to formulate tailored support policies, promote large-scale production to enhance technological levels, and focus on policies aimed at improving the quality of cotton.

In this paper, we first discuss the research status and application progress of the finite element method and the smoothed particle method. By analyzing the advantages of the smoothed particle method and the finite element method, a new coupling algorithm, namely FEM-SPH algorithm, is proposed. By the method of comparison, it shows that finite element method and SPH method in the simulation of large deformation problems each have advantages and disadvantages, the finite element method smoothed particle coupling algorithm is effective to achieve the performance of high computational efficiency and can naturally simulate large deformation problems across. In the process of calculation, the large deformation unit can be freely into an algorithm to facilitate the calculation accuracy and efficiency of three methods of numerical simulation. Through the study found, FEM-SPH algorithm not only overcome the defect of smooth particle tensile instability, but also overcomes the problem of low efficiency of finite element computation. To further test the FEM-SPH algorithm has advantages in the practical engineering, we have carried out the actual test to the example of the super high speed collision, concluded that, since the target of most of the computational domain is always finite element, smoothed particle focused only in contact with the projectile and target of local area, particle number is not much, the whole calculation process just ten minutes, computational efficiency has been greatly improved, at the same time in the simulation of large deformation, the advantage is very obvious .This provides a criterion for the actual project, depending on the specific material deformation mode and choose a more appropriate conversion algorithm.

Let g be a strictly increasing function on $\left(a,b\right),$ having a continuous derivative g′ on $\left(a,b\right).$ For the Lebesgue integrable function $f:\left(a,b\right)\to \mathbb{C}$ , we define the k-g-left-sided fractional integral of f by $S_{k,g,a+}f\left(x\right)={\int }_a^{x}k\left(g\left(x\right)-g\left(t\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in \left(a,b\right]$ and the k-g-right-sided fractional integral of f by $S_{k,g,b-}f\left(x\right)={\int }_x^{b}k\left(g\left(t\right)-g\left(x\right)\right)g^{\prime }\left(t\right)f\left(t\right)dt,x\in [a,b),$ where the kernel k is defined either on $\left(0,\infty \right)$ or on $\left[0,\infty \right)$ with complex values and integrable on any finite subinterval. In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

The aim of the article is to verify differences in the perception of selected factors of sustainability among small and medium-sized enterprises (SMEs) in Central Europe. The subjects of analysis are factors such as corporate social responsibility (CSR), business risk sources (market, financial, personnel, and operational), reputation and social media, national support, social changes, and crisis events in business. The questionnaire was completed by 1,090 SMEs from the business environments of Visegrad Group countries. Statistical hypotheses were verified using Z-scores for two population properties. The most negatively perceived factors among owners and managers in the SME segment are national support and legislative changes. The most positively perceived factor is reputation and social media. The country of doing business is a significant factor. The perception of crisis events in business is most negative among Czech SMEs. More than 80% of Hungarian SMEs perceive their companies as sustainable. In comparison with Slovak and Polish SMEs, Hungarian perceptions are more positive in the context of sustainability. The country of doing business is the strongest factor in evaluating CSR indicators. The positive perception of CSR in Czech SMEs (43.9%) is lower than in other countries.

The natural product elaiophylin is a macrodiolide with broad biological activities. However, no direct target of elaiophylin in eukaryotes has been described so far, which hinders a systematic explanation of its astonishing activity range. We recently showed that the related conglobatin A, a protein-protein interface inhibitor of the interaction between the N-terminus of Hsp90 and its cochaperone Cdc37, blocks cancer stem cell properties by selectively inhibiting K-Ras4B but not H-Ras. Here we elaborate that elaiophylin likewise disrupts the Hsp90/ Cdc37 interaction, without affecting the ATP-pocket of Hsp90. Similar to conglobatin A, elaiophylin decreased expression levels of the Hsp90 client HIF1⍺, a transcription factor with various downstream targets, including galectin-3. Galectin-3 is a nanocluster scaffold of K-Ras, which explains the K-Ras selectivity of Hsp90 inhibitors. In agreement with this K-Ras targeting and the potent effect on other Hsp90 clients, we observed with elaiophylin treatment a submicromolar IC50 for MDA-MB-231 3D spheroid formation. Finally, a strong inhibition of the same cells grown in the chorioallantoic membrane (CAM) microtumor model was determined. These results suggest that several other macrodiolides may have the Hsp90/ Cdc37 interface as a target site.

Myocarditis is the form of an inflammation of the middle layer of the heart wall which is caused by a viral infection and can affect the heart muscle and its electrical system. It has remained as one of the most challenging diagnoses in cardiology. Myocardial is the prime cause of unexpected death in approximately 20% of adults less than 40 years of age. Cardiac MRI (CMR) has been considered as a noninvasive and golden standard diagnostic tool for suspected myocarditis and plays an indispensable role in diagnosing various cardiac diseases. However, the performance of CMR is heavily dependent on the clinical presentation and non-specific features such as chest pain, arrhythmia, and heart failure. Besides, other imaging factors like artifacts, technical errors, pulse sequence, acquisition parameters, contrast agent dose, and more importantly qualitatively visual interpretation can affect the result of the diagnosis. This paper introduces a new deep learning-based model called Convolutional Neural Network-Clustering (CNN-KCL) to diagnose the Myocarditis. The hybrid CNN-KCL method performs the early and accurate diagnosis of Myocarditis. To the best-of-our-knowledge, a Convolutional neural network has never been used before for the diagnosis of Myocarditis. In this study, we used 47 subjects to diagnose myocarditis patients from Tehran's Omid Hospital. The total number of data examined is 10425. Our results demonstrate that CNN-KCL achieves 92.3% in terms of diagnosis myocarditis prediction accuracy which is significantly better than those reported in previous studies.

Acanthamoeba keratitis (AK) is a severe, rare protozoal infection of the cornea. Acanthamoeba can survive in diverse habitats and at extreme temperatures. AK is mostly seen in contact lens wearers, whose lenses have become contaminated, or a history of water exposure, and in those without contact lens wear, who have experienced recent eye trauma involving contaminated soil or water. Infection usually results in severe eye pain, photophobia, inflammation, and corneal epithelial defects. The pathophysiology of this infection is multifactorial, including the production of cytotoxic proteases by Acanthamoeba that degrades the corneal epithelial basement membrane and induce the death of ocular surface cells, resulting in degradation of the collagen-rich corneal stroma. AK can be prevented by avoiding the risk factors, which include avoiding water contact such as swimming or showering in contact lenses, and wearing protective goggles when working on the land. AK is mostly treated with an antimicrobial therapy of biguanides alone or in combination with diaminidines, although the commercial availability of these medicines is variable. Other than anti-amoeba therapies, targeting host immune pathways in Acanthamoeba disease may lead to the development of vaccines or antibody therapeutics which could transform the management of AK.

In this study, the motion characteristics of soft alginate microrobots were investigated with wireless magnetic fields in complex fluidic environments. Our aim is to explore the various motion modes that arise as a result of shear forces in viscoelastic fluids. Polyacrylamide (PAA), a water-soluble polymer, was characterized to produce a dynamic environment with a non-Newtonian fluid. The robots were fabricated by an extrusion-based microcentrifugal droplet method. We successfully demonstrated the feasibility of both wiggling and tumbling motions using snowman-shaped microbots. It is found that wiggling motion is primarily influenced by the interaction between the viscoelastic fluid environment and the non-uniform magnetization of the microbots. Additionally, it is discovered that modifying the viscoelasticity properties of the fluid can affect the motion behavior of the microbots. Furthermore, we observed that swarms of microbots exhibit non-uniform behavior within complex environments. Our velocity analysis has provided valuable insights into the relationship between applied magnetic fields and motion characteristics, enabling a more realistic understanding of surface locomotion in the context of targeted drug delivery.

Background and Objectives: The aim of this study was to determine the job-related and individual features that influence BS and depression levels among dentists working in faculties, oral and dental health centres (ODHC) and private clinics. Materials and Methods: This prospective, cross sectional study was carried out on dentists working in different regions of Turkey. Data were collected using an on-line questionnaire created using Google Forms. The questionnaire consisted of demographic data, Maslach BS Inventory (MBI) and Beck Depression Inventory (BDI) sections. Demographics were age, height, weight, marital status, blood type, gender, monthly income, income satisfaction and having enough free time. The dentists were divided into 3 groups as faculty, private clinic and ODHC according to the institutions in which they worked. Results: Of the total 290 dentists enrolled in the study, there were 172 males and 118 females with a mean age of 36.98±5.6 years. 128 of the dentists worked in faculties, 72 in private clinics and 90 in ODHCs. It was observed that women's EE scores were higher than men's (P<0.05). No statistically significant difference was found between the groups when comparing BS and depression scores according to marital status and blood group (P>0.05). There was no significant relationship between emotional exhaustion (EE), depersonalisation (DP), personal accomplishment (PA) and depression scores according to age, BMI and work experience, age, work experience and BMI (P<0.05). It was found that the EE scores of the dentists working in the faculty and private clinic were lower than those of the dentists working in the ODHC (P<0.05). Monthly income was associated with depression (r = -0.35). Conclusions: This study showed that dentists working in ODHCs had more EE. These findings suggest that there is a need for improvement in the working conditions of dentists, particularly in ODHCs.

In the paper, by virtue of the Fa`a di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers.

Introduction: Cleft lip with or without cleft palate (CL/P) is the most common congenital face anomaly in the world of multifactorial etiology. Objective: To determine the prevalence and characteristics of cleft palate. To identify associated risk factors to guide prevention and/or prenatal detection for early intervention and better health outcomes. To assess the rehabilitation protocols after operations in cleft palate. Design: Retrospective descriptive and clinical study. Patients: One hundred and three children with cleft palate treated in the Department of Head and Neck Surgery Clinic for Children and Young Adults, Department of Clinical Pediatrics, University of Warmia and Mazury, were included in the study. Methods: Records evaluation was conducted regarding sex, cleft type, mother occupation, parents education, histories of cleft in any of parents. The data were analyzed using R (R core team 2021) and the ordinal logistic regression analyses. Results: Children of stressed mothers during pregnancy had 9.4 times higher odds of having bilateral cleft. While there was no evidence that children sex, order of birth, and body mass as well as risk of maternal toxicity at work or reporting infections or drugs toxicity had a significant effect on the dependent variable. Conclusions: Children of parents with cleft history and having low educated mothers had higher probability of bilateral cleft palate. Children of stressed mothers during pregnancy had higher odds of having bilateral cleft. In literature, there is a lack of reports about rehabilitation in different operations methods in children with cleft palates.

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.

In the context of sustainable development, integrating the work aspect into health promotion systems is essential, ensuring that employees maintain a healthy balance between their professional and personal lives, which respects and amplifies the potential of every individual. Lately, there has been a noticeable shift of medical professionals from the public to the private sector. This trend paints a bleak picture, highlighting the vulnerabilities of a system teetering on the brink of failure, with significant impacts on patient care. Among the myriad reasons behind this shift, burnout stands out prominently. Medical professionals face increasing pressures due to understaffing, limited organizational support, and insufficient resources, leading to feelings of cynicism, exhaustion, and detachment from their roles. Utilizing the Maslach et al. questionnaire, we assessed the risk of burnout among physicians in public hospitals to identify and underscore preventive measures and improvements, correlating our findings with key aspects of organizational empowerment. Our research indicates that enhancing interpersonal relationships and resources—both within teams and between the organization and its physicians—is crucial for the revival of the healthcare system. This approach aims at improving the delivery of healthcare services and offering appropriate recognition to healthcare professionals, aligning with the principles of sustainable employment.

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to currently not provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed `quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

Vitamin K occupies a unique and often obscured place among its fellow fat-soluble vitamins. Evidence is mounting however, that vitamin K (VK) may play an important role in the visual system apart from the hepatic carboxylation of hemostatic related proteins. However, to our knowledge, no review covering the topic has appeared in the medical literature. Recent studies have confirmed that matrix Gla protein (MGP), a vitamin K-dependent protein (VKDP), is essential for the regulation of intraocular pressure in the mouse. The PREDIMED (Prevención con Dieta Mediterránea) study, a randomized trial involving 5860 adults at risk for cardiovascular disease, demonstrated a 29% reduction in the risk of cataract surgery in participants with the highest tertile of dietary vitamin K1 (PK) intake compared with the lowest tertile. However, the specific requirements of the eye and visual system (EVS) for VK, and what might constitute an optimized VK status, is currently unknown and largely unexplored. It is the intention therefore of this narrative review to provide an introduction concerning VK and the visual system, review ocular VK biology, and to provide some historical context to recent discoveries. Potential opportunities and gaps in current research efforts will be touched upon, in the hope of raising awareness, and encouraging continued VK related investigations in this important and highly specialized sensory system.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

Systems genetics is key for integrating a large number of variants associated with diseases. Vitamin K (VK) is one of the scarcely studied conditions in lieu of ascertaining either the differentially expressed genes (DEGs) or variants in an individual subpopulation of diseased phenotypes associated with VK, viz. myocardial infarction, renal failure, prostate cancer, thrombosis, thrombocytopenia, coagulation related diseases to name a few. In this work, we have screened characteristic DEGs common to three VK-related diseases, viz. myocardial infarction, renal failure and prostate cancer and asked whether or not any DEGs in addition to pathogenic variants are common to these conditions. We attempt to bridge the gap in finding characteristic biomarkers and discuss the role of long noncoding RNAs (lncRNAs) in the biogenesis of VK deficiencies.

In the particular configuration of the scalar field K-essence in the Wheeler-DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. The order of the fractional differential equation is $\beta=\frac{2\alpha}{2\alpha - 1}$. This fractional equation belongs to different intervals, depending on the value of the barotropic parameter; when $\omega_{X} \in [0,1]$, the order belongs to the interval $1\leq \beta \leq 2$, and when $\omega_{X}\in[-1,0)$, the order belongs to the interval $0<\beta \leq 1$. In the quantum scheme, we introduce the factor ordering problem in the variables $(\Omega,\phi)$ and its corresponding momenta $(\Pi_\Omega, \Pi_\phi)$, obtaining a linear fractional differential equation with variable coefficients in the scalar field equation, then the solution is found using a fractional power series expansion. The corresponding quantum solutions are also given. We found the classical solution in the usual gauge N obtained in the Hamiltonian formalism and without a gauge. In the last case, the general solution is presented in a transformed time $T(\tau)$, however in the dust era we found a closed solution in the gauge time $\tau$.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

The supply chain has incorporated products by putting them into hair scarfs. This study introduces the use of mini chips in health and beauty products and can reduce fatigue through enhanced sleep patterns. The mini chip could be placed in the scarf and used as a prototype. RFID technology provides the supply chain with specific information that is used to identify products and make communication easier. (Muhammad, et. al. 2013) This paper presents a new tool herein referred to as a scarf prototype which is developed to analyse EMG (electromyogram), ECG (electrocardiography), EEG (electroencephalogram), and EOG (electro-oculogram) signals that focuses in the area of sleep disorders. The mini chips used can be used to determine a solution for sleep disruption by using automated analytics. This could lead to improvement in our understanding of sleep disruption and overall sleep physiology. Automated technology allows repeated measurements, evaluation of sleep patterns, and provide suggestions to improve a person’s quality of sleep. This analysis compares the use of polysomnography and the scarf prototype. The analytics provide models and shows correlation between variables, such as EMG, ECG, EEG, and EOG. This study shows that the results from the scarf prototype is just as reliable as the original method, polysomnography.

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

In this paper, we introduce the partially degenerate Changhee-Genocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear dierential equations.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

The process of establishing secure communication between devices in the Internet of Things (IoT) can be approached by using a One-time-Pad (OTP) protocol. We propose using a known secure multiparty sum protocol for generating a One-time-Pad key using true (physical) random numbers in each device (party). We implemented the proposal using ZeroC-Ice, a middleware for distributed computing. The protocol security properties were analyzed under the assumptions of the Dolev-Yao threat model.

Introduction: Rotavirus-induced acute diarrhoea continues to pose a significant health threat to children under 5 years old worldwide, despite the availability of effective vaccines. This study aimed to assess the prevalence, associated risk factors, and circulating genotypes of rotavirus among children under 5 admitted to Ikom Medical Centre due to diarrhea. Methodology: Stool samples were collected from 294 children under 5 with diarrhoea at Ikom Medical Centre. Rotavirus antigen detection was performed using rapid chromatographic immunoassay. Molecular techniques such as polyacrylamide gel electrophoresis (PAGE), RT-PCR, and semi-nested multiplex RT-PCR were used to analyze rotavirus strains. Data were obtained through questionnaires, and statistical significance was assessed using the chi-square test (P < 0.05). Results: Among the 294 samples, 20.4% (60/294) tested positive for rotavirus. Significant risk factors influencing rotavirus prevalence included feeding status, toilet system, and duration of diarrhoea. The most prevalent genotype for VP7 was G4 (26.7%), and for VP4, it was genotype P[4] (23.3%). Predominant genotype combinations were G4P [4] (11.6%) and G12P[4] (6.7%), while non-typeable P[NT] was observed in 41.7% of cases. Conclusion: This study highlights the circulation of rotavirus in Ikom, Cross River State, emphasizing its neglected status despite its significant global impact on child mortality. Urgent attention is needed to address rotavirus as a serious public health concern, particularly in low-resource settings.