Let a,b,c be positive integers such that a²+b²=c², 2|b,gcd(a,b)=1. In 1956, Jesmanowicz conjectured that for any positive integer w, the only solution of (aw)^x+(bw)^y=(cw)^z in positive integers is (x, y, z) = (2, 2, 2). In this paper, based on Gaussian integer ring, we show that Je$\acute{s}$manowicz' conjecture is true for any positive integer

As an important support for power system with high penetration of renewable energy, energy storage system (ESS) has changed the traditional model of simultaneous implementation of electricity production and consumption, and its installed capacity under the source-grid-load scenario is rising year by year, but it faces the problems of insufficient utilization and benefits. This study analyzes the functional combination of ESS under the source-grid-load scenarios, and proposes a comprehensive benefit evaluation method of energy storage projects based on fuzzy decision-making trial and evaluation laboratory (DEMATEL) and super efficiency data envelopment analysis (DEA) model, which considers the perspective of economic and social environment. Firstly, the functional requirements of energy storage on the source-grid-load scenarios are explored respectively, and the characteristics of various functions are analyzed to form functional combination schemes. Secondly, index modeling is carried out from three aspects: the whole life cycle cost, functional combination benefit and social environmental benefit, and the comprehensive benefit evaluation index system of energy storage project is proposed, which includes both economic and social environment. Then, the intuitionistic trapezoidal fuzzy number is combined with DEMATEL to form an effective analysis method for the input-output relationship of the indexes, and the comprehensive evaluation is realized based on the super efficiency DEA model. Finally, the effectiveness of the proposed evaluation method and the rationality of the functional combination are verified under source-grid-load scenarios respectively.

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.

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

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

We presented a fractional order model to capture the transmission dynamics of Anthrax infection with a nonlinear force of infection and its long-term impacts. Analysis by the standard Fabrizio Caputo approach established the model is well-posed and investigation on the stability of the model, Anthrax-free equilibrium as connected to the basic reproduction number R0

SARS-CoV-2 Omicron variant spike RBD epitopes in complex with spike (S) -protein D614G mutations now predominate globally and increase infectivity by assembling more functional S proteins into the virion. On average, homeopathic medicine contains less than one molecule per dose on average. Single variable SphericalHarmonicY, LaguerreL, WhittakerM, SphericalBesselJ, LegendreP, LegendreQ, LaguerreL, ChebyshevT, and Hypergeometric1F1 Functions pFqarise in connection with the power series solution of the Schrodinger equation or in the summation of perturbation expansions in quantum mechanics. A quantum interpretation of the homeopathic method is presented here through a novel algebraic topology approach to supersymmetry and symmetry breaking in quantum fields and quantum gravity theory with the aim of developing a wide range of physical-based drug design applications in a Small Molecule Quantized Water Memory Network suggesting that the Hidden Black Hole Paradox of Information Loss might be solved under suitable conditions.

This paper presents a comprehensive analysis of the SEIRS COVID-19 pandemic model with saturated incidence rate. By modifying the existing model and proposing a new simplified version, we investigate the dynamics of disease transmission, including the impact of saturation terms on disease spread. Through stability analysis at disease-free and endemic equilibria, we aim to enhance understanding of the spread of COVID-19 and inform effective control strategies. Drawing on mathematical models and epidemiological insights, this study contributes to the ongoing efforts to combat the global pandemic.

We introduce a model of a passive optical cavity based on the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5, stable vortex-ring states (vortex pixels) are produced by a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump-strength and loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations which break the axial symmetry. The results suggest new possibilities for mode manipulations in nonlinear optical media.

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.

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

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

Molecular analysis of growing teratoma syndrome has not been extensively studied. Here, we report a 14-year-old boy with a growing mass during treatment for a mixed germ cell tumor of the pineal region. Tumor markers were negative; thus, growing teratoma syndrome was suspected. A radical resection via the occipital transtentorial approach was performed, and histopathological examination revealed a teratoma with malignant features. Methylation classifier analysis confirmed the diagnosis of teratoma, and DMRT1 loss and 12p gain were identified by copy number variation analysis, potentially elucidating the cause of growth and malignant transformation of the teratoma. The patient remains in remission after intense chemoradiation treatment as a high-risk germ cell tumor.

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

This paper provides a new discovery that adds to the contemporary theory of modelling of non-stationary queues, by capturing analytically the behavior of the root parameter, for the G1/M/1 PSFFA model of non-stationary Ek/M/1 queue. Additionally, it has been also revealed that the resulting root parameter reduces to the PSFFA model of non-stationary queue. Potential applications of PSFFA to Computer engineering are provided. Some challenging open problems are addressed combined with closing remarks and future research directions.

The Collatz conjecture is a well-known number theory puzzle that states that every positive integer would eventually converge to the trivial cycle of 1, 2, 1, 2,... when repeatedly exposed to a particular transformation. In this transformation, even numbers are divided in half, odd numbers are tripled, and one is added. In this study, we present a new method for creating a directed graph and using it to display and analyze Collatz sequences. Our technique creates what we call a Collatz directed graph by joining an endless number of simple directed graphs, each of which corresponds to a natural number. We show by careful mathematical analysis that all positive integers are included in this Collatz directed graph. Moreover, we give an evidence that verifies the Collatz conjecture by showing that the sole cycle in this graph is the trivial cycle of 1, 2, 1, 2,... We also prove that there is no sequence that diverges to infinity in this graph. Our results provide insights into the fundamental structure of Collatz sequences and further our knowledge of the Collatz conjecture .

Keywords: pelvic ultrasound, follicle number per ovary, FNPO, ovarian volume, PCOM, upper normal limits, referral population

This paper investigates the search for an exact analytic solution to a temporal first-order differential equation that represents the number of customers in a non-stationary or time-varying

The Collatz conjecture, a longstanding mathematical puzzle, posits that, regardless of the starting integer, iteratively applying a specific formula will eventually lead to the value 1. This paper introduces a novel approach to validate the Collatz conjecture by leveraging the binary representation of generated numbers. Each transition in the sequence is predetermined using the Collatz conjecture formula, yet the path of transitions is revealed to be intricate, involving alternating increases and decreases for each initial value. The study delves into the global flow of the sequence, investigating the behavior of the generated numbers as they progress toward the termination value of 1. The analysis utilizes the concept of probability to shed light on the complex dynamics of the Collatz conjecture. By incorporating probabilistic methods, this research aims to unravel the underlying patterns and tendencies that govern the convergence of the sequence. The findings contribute to a deeper understanding of the Collatz conjecture, offering insights into the inherent complexities of its trajectories. This work not only validates the conjecture through binary representation but also provides a probabilistic framework to elucidate the global flow of the sequence, enriching our comprehension of this enduring mathematical mystery.

I had previously developed an approach called Gocgen approach, which claimed to prove twin prime conjecture. In this paper, I processed the previously developed Gocgen approach with the zeta function and explained the relationship between the zeta function with some formulas to offer another perspective on the zeta function, and also created a new function that explains the Gocgen approach using the zeta function. Understanding the new function created will provide insight into the frequency of prime numbers.

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

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.

In my paper, a divisibility rule named the Queen function is de- scribed, which has been generalized for every integer and encompasses all pre- viously established divisibility rules. Subsequently, the paper discusses other areas where this function is instrumental. These include simplifying ratios, generating prime numbers, and more. Towards the end of the paper, a set of hypotheses is also presented. Among these, the most significant is the novel approach involving the application of the Queen function for prime number generation.

Chromosome analysis (CA) and chromosomal microarray analysis (CMA) have been successfully used to diagnose genetic disorders. However, many conditions remain undiagnosed due to limitations in resolution (CA) and detection of only unbalanced events (CMA). Optical genome mapping (OGM) has the potential to address these limitations by capturing both structural variants (SVs) resulting in copy number changes and balanced rearrangements with high resolution. In this study, we investigated OGM’s concordance using 87 SVs previously identified by CA, CMA, or Southern blot. Overall, OGM was 98% concordant with only three discordant cases: (1) uncalled translocation with one breakpoint in a centromere; (2) uncalled duplication with breakpoints in the pseudoautosomal region 1; and (3) uncalled mosaic triplication originating from a marker chromosome. OGM provided diagnosis for three previously unsolved cases: (1) disruption of the SON gene due to a balanced reciprocal translocation; (2) disruption of NBEA gene due to an inverted insertion; (3) disruption of the TSC2 gene due to a mosaic deletion. We show that OGM is a valid method for detection of many types of SVs in a single assay and is highly concordant with legacy cytogenomic methods; however, it has limited SV detection capabilities in centromeric and pseudoautosomal regions.

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

Traditional gene set enrichment analysis falters when applied to large genomic domains, where neighboring genes often share functions. This spatial dependency creates misleading enrichments, mistaking mere physical proximity for genuine biological connections. Here we present Spatial Adjusted Gene Ontology (SAGO), a novel cyclic permutation-based approach, to tackle this challenge. SAGO separates enrichments due to spatial proximity from genuine biological links by incorporating the genes' spatial arrangement into the analysis. We applied SAGO to various datasets in which the identified genomic intervals are large, including replication timing domains, H3K9me3 and H3K27me3 large domains, HiC compartments and lamina associated domains (LADs). Intriguingly, applying SAGO to prostate cancer samples with large copy number alteration (CNAs) domains eliminated most of the enriched GO terms, thus helping to accurately identify biologically relevant gene sets linked to oncogenic processes, free from spatial bias.

This review is a first attempt at bringing together various concepts from research on wall- and magnetically-bounded turbulent flows. Brief reviews of both fields are provided: The main similarities identified are coherent (turbulent) structures, flow generation and transport barriers. Examples are provided and discussed.

We developed some questions regarding twin prime conjecture by examining the bounded gaps between composite numbers and explained the relations between the formulas regarding composite numbers. Then we proved the twin prime conjecture to answer the new questions raised by proving the expression: \[ \liminf_{n\to\infty} (c_n_+_1 - c_n) \ge 10. \] In addition, we prove many different approaches have been and it has been proved that there must be a twin prime in the range $(p_k_2\cdot p_k_1, p^2_k_1)$, where $p \neq 2$.

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

This paper offers a novel geometric and visual approach to the renowned Four Color Map Theorem and K5 non-planarity problem while unveiling their profound connection to the "kissing number" problem in 2D. We represent planar graphs through circles and tangents, simplifying complex structures and shedding light on these classic problems. Our proofs by contradiction, rooted in the kissing number concept, reveal that both the Four Color Map Theorem and K5 non-planarity are fundamentally linked, as they pivot around the concept of coloring. This study bridges the realms of geometry and graph theory, providing fresh insights and emphasizing the significance of the kissing number problem in various fields.

It has been more than a century since Erlang published his paper in 1909. The classical queueing system for the M/D/c queue has been investigated by many authors. The key is to find the roots of an equation using explicit or numerical methods. We present an alternate form of explicit solution(s) of this/these root(s) using the Lambert-W function in this paper. In addition, the unsaturated probabilities of the number of customers in the system is derived explicitly in terms of this/these root(s). Finally, the mean number of customers in the system and the mean queueing delay are obtained from these probabilities. The exact queueing delay formula for the M/D/c queue is expressed in closed-form in terms of the root(s). Numerical results show that they are in excellent agreement with the numerical results published by Seelen, Tijms and Van Hoorn.

We study electrohydrodynamic (EHD) linear (in)stability of microfluidic channel flows, i.e. the stability of interface between two-shearing viscous (perfect) dielectrics exposed to an electric field in large aspect ratio microchannels. We then apply our results to particular microfluidic systems known as electroosmotic (EO) pumps. Our results are detailed analytical expressions for the growth rate of two-dimensional EHD modes in Couette-Poiseuille flows in the limit of small Reynolds number ($R$); the expansions to both zeroth- and first-order-$R$ are considered. The growth rates are complicated functions of viscosity-, height-, density- and dielectric-constant ratio, as well as of wavenumbers and voltages, and to our knowledge have not been presented before in literature. To make the results more useful, e.g., for voltage-control EO pump operations, we also derive equations for the impending voltages of the neutral stability curves that divide stable from unstable regions in voltage-wavenumber stability diagrams. The voltage equations and the stability diagrams are given for all wavenumbers. We finally outline the flow regimes in which our first-order-$R$ voltage corrections could potentially be experimentally measured. Our work gives the insight into the coupling mechanism between electric field and shear flow in parallel-planes channel flows, correcting an erroneous attempt from literature. Our general analysis enables us also to refine the renowned instability mechanism due to viscosity stratification, i.e., the case of pure shear instability, when the first-order-$R$ voltage correction equals zero.

On February 24, 2022 Russia started the full-scale invasion of Ukraine, which created an unprecedented number of refugees. To estimate the influence of this humanitarian disaster on the COVID-19 pandemic dynamics, the averaged daily numbers of cases and reproduction numbers in Ukraine, the UK, Poland, Germany, the Republic of Moldova, and in the whole world were calculated for the period February-April 2022. The registered numbers of cases were compared with ones calculated with the use of the generalized SIR-model and corresponding parameter identification procedure for the previous epidemic waves in Ukraine, Poland, Germany, and the world. Since before February 24, 2022 the estimation of the number of infectious persons per capita in Ukraine 3.6 times exceeded the global figure, the increase of the number the new cases and the pandemic duration was expected. In March 2022 the increase of the averaged number of new cases in the UK, Germany, and worldwide was visible. A simple formula to estimate the effective reproduction number based on the smoothed accumulated numbers of cases is proposed. The results of calculations agree with the figures presented by John Hopkins University and demonstrate a short-term growth of the reproduction number in the UK, Poland, Germany, Moldova, and worldwide in March 2022.

New insights into the causes and mechanisms of congenital heart disease (CHD) have been gained through the use of next-generation sequencing. Examination of the whole exome sequence detects detrimental gene variations modifying single or contiguous nucleotides, that are characterised as pathogenicity based on statistical assessments of families. and correlates with congenital heart disease, elevated expression during heart development, and reduction of harmful protein-coding mutations in the general population. Patients with CHD and extracardiac abnormalities enriched for gene classes meeting these criteria. CHDs and extracardiac defects, supporting a common set of pathways in the organogenesis of CHDs. Single-cell transcriptomics data reveal the expression of genes associated with CHD in specific cell lineages, and emerging evidence suggests that genetic variants disrupt multicellular genes essential for cardiogenesis. Metrics and units are being tracked in whole genome sequence studies.

In this paper, we examine a modified Friedmann model designed to explain cosmic structures and late-time accelerated expansion of the universe, grounded in the spatial distribution of luminous matter. Through comprehensive simulations of our universe, we observe a notable surge in the formation rate of galaxies at redshift z≈1, characterized by a peak expansion rate in cosmic structures formed at z ≈0.9, reaching its zenith at z ≈2. Subsequently, a transition occurs before the onset of dark matter-induced accelerated expansion. The acceleration of the universe stands as an entrenched and virtually model-independent theoretical tenet, resilient to the ongoing debate surrounding the enigma of dark energy. A distinctive redshift transition zone marks the shift from cosmic deceleration to accelerated expansion. The transition is proportional to matter density and contingent upon the geometry of the universe. The influence of the cosmological constant on the evolution of cosmic structures in the CDM paradigm appears insufficient in curtailing the efficiency of late-time structure formation compared to the observed values in the modified model

Unsupervised physics-informed deep learning can be used to solve computational physics problems by training neural networks to satisfy the underlying equations and boundary conditions without labeled data. Parameters such as network architecture and training method determine the training success. However, the best choice is unknown a priori as it is case specific. Here, we investigated network shapes, sizes, and types for unsupervised physics-informed deep learning of the two-dimensional Reynolds-averaged flow around cylinders. We trained mixed-variable networks and compared them to traditional models. Several network architectures with different shape factors and sizes were evaluated. The models were trained to solve the Reynolds-averaged Navier-Stokes equations incorporating Prandtl's mixing length turbulence model. No training data were deployed to train the models. The superiority of the mixed-variable approach was confirmed for the investigated high Reynolds number flow. The mixed-variable models were sensitive to the network shape. For the two cylinders, differently deep networks showed superior performance. The best fitting models were able to capture important flow phenomena such as stagnation regions, boundary layers, flow separation, and recirculation. We also encountered difficulties when predicting high Reynolds number flows without training data

This paper presents a novel approach to demonstrate the Collatz Conjecture, an unsolved problem in mathematics stating that all positive integers will eventually converge to 1 when subjected to a recursive sequence of operations. We introduce Algebraic Inverse Trees (AITs), innovative data structures that characterize relationships within the Collatz sequence by tracing inverse transformations back to the origin. Leveraging properties unveiled through this inverted representation, including absence of non-trivial cycles and guaranteed convergence of paths, we construct a topological framework to formally prove that all trajectories invariably lead to 1 under the Collatz iterative process. This modern technique provides not only the machinery to manifest a rigorous proof, but also grants intuitive insights into the deep complexity of this notorious yet elementary conjecture.

Gastric mixing relies both on enzymatic reactions and mechanical solicitations through antral contraction waves (ACWs). This work aims at discussing the influence of ACWs frequency and digesta viscosity on human gastric mixing efficiency by comparison with that of a soft elastic reactor (SER), that induces mixing by vibration of its wall in a similar way as ACWs promote stomach motility. The SER mixing curve was considered in order to determine the flow regime reached during gastric mixing. The number of contractions required to achieve homogenization was found to depend on the viscosity of the stomach content and the ACWs amplitude. Moreover, it was deduced from the same range of SER and ACWs operating points that the mechanical solicitation provided by human peristalsis was low and that gastric mixing was confined in laminar regime. Further efforts are needed to investigate the role of other physiological processes such as gastric secretions and emptying in overall gastric mixing performance.

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

Broadly speaking, binominal and biverbal lexical constructions have been studied independently in different research traditions and frameworks. It is true that the two do not necessarily have overlapping areal distributions, but the fundamental question remains whether Indo-European NN compounds and Transeurasian VV compounds have nothing in common. From a purely theoretical perspective also, the cross-categorial parallelism is worthy of serious investigation because a theory of the process of compounding that inherits the spirit of X-bar theory strives to capture commonalities among various compounding patterns and category-specific constraints observed within and across languages. Against this background, a cross-categorial comparison, not within but across languages, is made of coordinative binominal and biverbal constructions. NN and VV coordinate compounds from English and Japanese are examined in detail using the methodology of contrastive morphology and decompositional lexical semantics. It is shown that dvandva is possible not only in NN but also in VV coordinate compounds and furthermore that the dvandva-appositive distinction in NN coordinate compounds recurs in VV coordinate compounds.

Prime numbers are the atoms of mathematics and mathematics is needed to make sense of the real world. Finding the Prime number structure and eventually being able to crack their code is the ultimate goal in what is called Number Theory. From the evolution of species to cryptography, Nature finds help in Prime numbers. One of the most important advances in the study of Prime numbers was the paper by Bernhard Riemann in November 1859 called “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (On the number of primes less than a given quantity). In that paper, Riemann gave a formula for the number of primes less than x in terms the integral of 1/log(x) and the roots (zeros) of the zeta function defined by: Where ζ(z) is a function of a complex variable z that analytically continues the Dirichlet series. Riemann also formulated a conjecture about the location of the zeros of RZF, which fall into two classes: the "trivial zeros" -2, -4, -6, etc., and those whose real part lies between 0 and 1. Riemann's conjecture Riemann hypothesis [RH] was formulated as this: [RH] The real part of every nontrivial zero z* of the RZF is 1/2. Proving the RH is, as of today, one of the most important problems in mathematics. In this paper we will provide a proof of the RH. The proof of the RH will be built following these five parts: PART 1: Description of the RZF PART 2: The C-transformation PART 3: Application of the C-transformation to in Re(z) 0 to obtain ζ(z)=X(z)-Y(z) PART 4: Analysis of the values of z such that X(z)=Y(z), and |X(z)|=|Y(z)|, that equates to ζ(z)=0 Proof that |X(z)|=|Y(z)| only if Re(z)=1/2 Conclude that ζ(z)=0 only if Re(z)=1/2 for Re(z) 0 PART 5: We will also prove that all non-trivial zeros of ζ(z) in the critical line of the form are not distributed randomly. There is a relationship between the values of those zeros and the Harmonic function that leads to an algebraic relationship between any two zeros.

Cognitive linguistics is founded on the assumption that language is a reflection of universal cognitive principles, implying that all cognitive processes share a common origin. This assumption is known as the 'Cognitive Commitment.' The present article examines the sensory schema hypothesis, which traces all forms of expression back to sensations. This theoretical framework integrates the physicality of the body with sensations that underlie human experiences and their linguistic and non-linguistic expressions. By challenging the traditional dichotomy between mind and body, it provides a more integrated understanding.

Here, we describe the bicomplex (p,q)- Fibonacci numbers and the bicomplex (p,q)- Fibonacci quaternions that are based on these numbers and give some of their equations, including the Binet formula, generating function, Catalan, Cassini, d’Ocagne’s identities, and some summation formulas for both of them. Finally, we create a matrix for bicomplex (p,q)- Fibonacci quaternions, and we obtain a determinant of a special matrix that gives the terms of that quaternion.

This study considers the values of the credit payments that are made at random values for both payment size and number. The simultaneous existence of the two random variables increases the total value of the volatility of the payment process. The dependence for the simultaneous influence of the two random variables is derived by applying conditional probabilistic formulations. Formal relations apply to animal husbandry credit payments. The credit policy was analyzed for the cases of regular payments and with a stochastic number of payments. A recommendation for the upper level of credit payments is proposed based on a model predictive approach using historical payment data. A credit management algorithm is derived, in which decision-making for credit payments is formally derived and numerically discussed. The application of derived quantitative relations is empirically applied to real data on animal husbandry. The recommendations from the dependencies obtained allow a reduction in the mean values of credit payments, which correspond to a reduction in the credits used for business management, without a change in business policy.

The present work provides continuity with studies where currently the industrial market is characterized by a highly variable demand in terms of quantities and flexibility of manufacturing or mass customization, which translates into a more demanding production context in terms of the continuous changes required to the production systems, the effect of which results in an increase in the fatigue subjected to the machines that make up the production systems. On the other hand, current production systems tend to use highly communicative and sensorized cyber-physical systems; these characteristics can be used to integrate them into decision-assisted systems in order to improve the availability of the industrial plant. The assisted system developed focuses on collecting and taking advantage of historical knowledge of industrial plant failures and breakdowns. By ideally integrating the Reliability Centered Maintenance (RCM) methodology and Case-Based Reasoning (CBR) algorithms implemented in a Java application, it is possible to design maintenance plans adjusted to a real and changing operational context of any industrial plant. As a result, faster and more accurate decisions are made, as they are based on data. This article focuses on improving certain aspects of the developed assisted system by adding more value to it by incorporating Fuzzy Logic (FL) techniques. The aim is to improve the way of entering information about risk factors and their relative importance, by incorporating natural language, instead of a numerical score, resulting in increased precision in the calculation of the Risk Priority Number (RPN) of the new cases incorporated into the assisted system.

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

In the literature, the question of the amount of data necessary and sufficient to validate different models of the occurrence of risk of adverse events for patients or the classification of the presence or absence of pathological features has been repeatedly raised. In the presented study, we propose a new approach to determine the necessary and enough studies for validation of medical software based on artificial intelligence technology, whose main task is to classify medical X-rays according to the presence of normality and pathology. It is shown that for several studies in a dataset, when AUC ROC has maximum heterogeneity, it varies depending on the balance of "norm"/"pathology" classes. Thus, for a balance of "normal"/"abnormality", where 90% is "normal" and 10% is "abnormality", maximum heterogeneity is achieved for 190 studies, for a balance of 80% ("normal")/20% ("abnormality") for 80 studies, for a balance of 70% ("norm")/30% ("abnormality") - 120 trials, for a balance of 60% ("norm")/40% ("abnormality") the maximum heterogeneity is reached at 110 trials, and for a balance of 50% ("norm")/50% ("abnormality") - at 70 trials. The obtained data are in good agreement with the previous results. They allow us to determine a sufficient (necessary) number of studies in the dataset to perform an unbiased assessment of AUC ROC.

A new approach for predicting the geometrical characteristics of the mixing behavior of an inclined dense jet for angles ranging from 15° to 85° is proposed in this study. This approach is called group method of data handling (GMDH) which is based on the artificial neural network (ANN) technique. The proposed model was trained and tested using existing experimental data reported in literature. The model was then evaluated using statistical indices as well as compared with analytical models from previous studies. The results of the coefficient of determination (R2) indicate a high accuracy of the proposed model with values of 0.9719 and 0.9513 for training and testing for the dimensionless of the distance from the nozzle to the return point xr/D, and 0.9454 and 0.9565 for training and testing for the dimensionless of the terminal rise height yt/D . Moreover, four previous analytical models were used to evaluate the GMDH model. The results showed the superiority of the proposed model in predicting the geometrical characteristics of the inclined dense jet for all tested angles. Finally, the standard error of estimate (SEE) was applied to demonstrate which model performed the best in terms of getting closer to the actual data. The results illustrate that all fitting lines of the GMDH model performed very well for all geometrical parameter predictions and was the best model with approximately 10% error, which was the lowest value of error among the models. Therefore, this study confirms that the GMDH model can be used to predict the geometrical properties of the inclined negatively buoyant jet with high performance and accuracy.

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

Here we analyze three well-known conjectures: (i) the existence of infinitely-many twin primes, (ii) Goldbach’s strong conjecture, and (iii) Polignac’s conjecture. We show that the three conjectures are related to each other. In particular, we see that in analysing the validity of the Goldbach’s strong conjecture, one must consider also the existence of an infinite number of twin primes. As a consequence of how we approach this analysis, we also observe that if this conjecture is true, then so is Polignac’s conjecture. Our first step is an analysis of the existence of infinitely-many twin primes numbers. For this, using the formula 4((n−1)!+1) ≡ −n (mod n(n + 2)) – satisfied if and only if (n, n + 2) are twin primes –, together with Wilson’s theorem, we obtain conditions that must be met for two numbers to be twin primes. Our results, obtained from an analytic and functional study, lead us to conclude that there may exist infinitely-many twin primes. Next, we consider the validity of the Goldbach’s strong conjecture. After showing that the conjecture is true for the first even numbers, we notice a pattern that we analyze for any even number, reducing it to three cases: (i) when the even number 2n is two times a prime number n; (ii) when the even number 2n is such that n = 2m, with 2m − 1 and 2m + 1 twin primes; (iii) all other cases, i.e., for any 2n even number ∀n ∈ N with n > 1, n prime or not, with independence of n = 2m being 2m−1 and 2m+1 twin primes or not. In this last case we show that one can always find a certain r ∈ N such that 1 < r < n satisfying that n−r and n+r are primes, so that their sum is 2n. In this case we use the reduction to absurd method, and our results lead us to conclude that Goldbach’s strong conjecture is true to the best of our calculations, as well as the Polignac’s conjecture.

Experimental measurement of porous polypropylene (PP) using the DTC-25 TA laboratory equipment and hot box test has been compared. The thermal conductivity of materials indicates the insulation capability of building materials. Excellent building materials will have a lower thermal conductivities value as well as other building insulator performance metrics. While results show that increasing the volume fraction of fluid in the porous PP has an inverse association with the thermal conductivity of the material as predicted by porous media theories, there is a marked difference in the measured values of the thermal conductivity using the two methods. The thermal conductivity values of porous from DTC-25 and hot box test were 0.21 and 0.0033 W/mK, respectively. The difference in the thermal conductivity values was due to the misapplication of the Fourier’s guarded heat flow model in the DTC-25 device to a convective fluid porous medium material.

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

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

Study of differential equation theory has come a long way with applications in the various fields. In 1961, Zygmund and Calderón introduced the notion of derivatives on metric Lr which proved to be better in applications than approximate derivatives. But most of the studies involved are on fuzzy set theory, so it seems likely that intuitionistic fuzzy Lr - norm - based derivatives deserve study. In the study, the fuzzy derivative is extended to intuitionistic fuzzy derivatives with respect.to Lr - norm - based derivatives using intuitionistic fuzzy number valued functions. The efficacy of the proposed method is established by proving the associated theorems along with numerical examples. Further, the Cauchy problem is also studied with respect to intuitionistic fuzzy setting.

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy graphs and intuitionistic fuzzy graphs (IFGs) and it is an important part of making decisions. However, one or two membership degrees are not always sufficient for making decisions on real-world problems that need an answer of types “yes, neutral, and no". Consequently, in previous work, we generalized the concept into picture fuzzy graphs (PFGs) where each element in the PFG has membership, neutral, and non-membership degrees. Moreover, we constructed the notion of the coloring of PFGs based on strong and weak adjacencies between vertices. In this paper, we investigate some properties of the chromatic number of PFGs based on the concept of strong and weak adjacencies between vertices. According to the properties, we construct an algorithm to find the chromatic number of PFGs. The algorithm is usefull when we work with large PFGs. Further, we improve the method to implement the PFG’s coloring for determining traffic signal phasing at an intersection. A case study has also been done to evaluate the method.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

Bounded number theory says that number is not infinite; that is, the number is limited. To come to a conclusion about limited number, one needs to understand the meaning of math and varying spaces, so one needs to understand that math and spaces interact. A matemática tem a função de descrever com precisão o mundo, onde os números representam elementos ou fatos que racionalmente elementos ou fatos pertencem ao espaço, e os espaços têm propriedades que os diferenciem de outros espaços; portanto, não há nenhum elemento ou fato infinito devido a diferenças nas propriedades dos espaços não permite o elemento ou fato em todos os espaços.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Background: Cervical cancer prevention in regions with limited access to screening and HPV vaccination necessitates innovative approaches. This study explored the potential of a test-and-treat strategy using mRNA HPV tests to impact cervical cancer prevention in a high-prevalence HIV population. Methods: A cervical screening study was conducted at three South African hospitals involving 710 under-screened, non-pregnant women (25 to 65 years) without known cervical diseases. Cytology, HPV testing, colposcopy, and biopsies were performed concurrently. Histopathologists determined final histological diagnoses based on biopsy and LLETZ histology. mRNA-HPV-genotyping for 3 (16, 18, 45) to 8 (16, 18, 31, 33, 35, 45, 52, 58) high-risk types was performed on leftover liquid-based cytology material. The preventive potential of the test-and-treat approach was estimated based on published data, reporting the causative HPV types in cervical cancer tissue from South African women. Treatment was provided as needed. Results: HPV positivity rate more than doubled from 3-type (15.2%; 95% CI: 12.6-17.8) to 8-type mRNA (31.5%; 95% CI: 28.8-34.9) combinations, significantly higher among HIV-positive women. CIN3+ prevalence among HIV-positive women (26.4%) was double that of HIV-negative women (12.9%) (p&lt;0.01). The 6-type combination showed the best balance of sensitivity, specificity and treatment group size, and effectiveness to prevent cervical cancer. A 4-type combination (16, 18, 35, 45) could potentially prevent 77.6% (95% CI: 71.2-84.0) of cervical cancer burden by treating 20% and detecting 41.1% of CIN3 cases in the study group. Similarly, a 6-type combination (16, 18, 31, 33, 35, 45), treating 25% and including 62% of CIN3 cases, might prevent 85% of cervical cancer cases (95% CI: 79.6-90.6) among HIV-positive and negative women. Conclusion: Employing mRNA HPV tests within a test-and-treat approach holds huge promise for targeted cervical cancer prevention in under-screened populations. Testing for mRNA of the 6 highest-risk HPV types in this population and treating them all is projected to effectively prevent progression from CIN3 to invasive cervical cancer while reducing overtreatment in resource-constrained settings.

The success rate of extracorporeal shock wave lithotripsy (ESWL) is influenced by various factors, including stone density, which is determined through computed tomography scans in Hounsfield Units (HU). Materials and method: This retrospective single-center study was conducted in King Fahad hospital. Sixty-seven adult patients with renal and ureteric stones were selected randomly and enrolled in the study. Their age ranged from 20 to 69 years. The patients were examined with non-contrast enhancement (NCCT) to assess the HU of stones, consequently, treated with ESWL. Results: of the 67 patients, 37.3% of the stones were completely fragmented, while 62.7% were partially fragmented. HU, location of the stone, a multiplicity of the stone, and patient age were significant factors contributing to stone fragility (p-values&lt; 0.05). The HU has a positive significant linear correlation with serum calcium (r= .28, p-value=.036), while serum acid has a negative correlation (r=-.55, p-value= &lt; .001). Thus, the probability of calcium-containing stones formation increased with increased HU. In contrast, uric acid stone formation is likely to develop with decreasing HU with serum uric acid. Renal stones in patients with diabetes mellitus and hypertension were not completely fragmented compared to those without clinical history. Conclusion: Mean HU, location of the stone, laterality, status of stone, and the number of ESWL sessions were the most significant factors affecting stone fragility. CT attenuation values can predict the composition of stones from serum calcium and uric acid examinations. Hypertension and Diabetes mellitus are risk factors for renal stone fragmentation.

In this study, we first discover some new concept coordinated UD-convex mappings with fuzzy-number values. After that, we look into Hermite-Hadamard type inequalities via fuzzy-number-valued coordinated UD-convex fuzzy-number-valued mapping (coordinated UD-convex FNVM). In the case of coordinated UD-convex FNVM, novel conclusions are derived by making particular decisions in recently proven inequalities. Additionally, it is demonstrated that the recently discovered inequalities are expansions of comparable findings in the literature. It is important to note that the main outcomes are validated by nontrivial examples.

Mouse wild-derived strains (WDS) combine the advantages of classical laboratory stocks and wild animals, and thus appear as promising tools for diverse biomedical and evolutionary studies. We employed 18 WDS representing three non-synanthropic species (Mus spretus, M. spicilegus, and M. macedonicus) and three house mouse subspecies (M. musculus musculus, M. m. domesticus, M. m. castaneus) which are all important human commensals to explore whether the number of major urinary protein (MUP) genes and their final protein levels in the urine are correlated with the level of commensalism. Contrary to expectations, MUP copy number (CN) and protein excretion in the strains derived from M. m. castaneus, which is supposed to be the strongest commensal, were not significantly different from the non-commensal species. Regardless of an overall tendency for higher MUP amounts in taxa with higher CN, there is no significant correlation at the strain level. Our study thus suggests that the expansion of the Mup cluster, which appeared before the house mouse diversification, is unlikely to facilitate commensalism with humans in the three house mouse subspecies. Finally, we found considerable variation among con(sub)specific WDS, warning against generalisations of results based on a few strains.

Cardiomyopathies are major causes of heart failure. Chagas disease (CD) is caused by the parasite Trypanosoma cruzi, and it is endemic in Central, South America. Thirty percent of the cases evolve into chronic cardiomyopathy (CCC) with worse prognosis as compared with other cardiomyopathies. In vivo bioenergetic analysis and ex vivo proteomic analysis of myocardial tissues highlighted worse mitochondrial dysfunction in CCC, and previous studies identified nuclear-encoded mitochondrial gene variants segregating with CCC. Here, we assessed the role of the mitochondrial genome through mtDNA copy number variations and mtDNA haplotyping and sequencing from heart or blood tissues of severe, moderate CCC and asymptomatic/indeterminate Chagas disease as well as healthy controls as an attempt to help decipher mitochondrial-intrinsic genetic involvement in Chagas disease development. We have found that mtDNA copy number was significantly lower in CCC than in heart tissue from healthy individuals, while blood mtDNA content was similar among asymptomatic Chagas disease, moderate and severe CCC patients. MtDNA haplogrouping study has indicated that African haplogroups were over represented in the Chagas subject groups in comparison with Brazilian healthy individuals. The European lineage is associated to protection against cardiomyopathy and the macro haplogroup H is associated with increased risk towards CCC. By mitochondria DNA sequencing, 84 mtDNA-encoded protein sequence pathogenic variants were associated with CCC. Among them, two variants were associated to left ventricular non-compaction and two to hypertrophic cardiomyopathy. The finding that mitochondrial protein-coding SNPs and mitochondrial haplogroups associate with risk of evolving to CCC is consistent with a key role of mitochondrial DNA in the development of Chronic Chagas disease Cardiomyopathy.

Adenoviruses are associated with respiratory tract, gastrointestinal or, less frequently, other involvement. Epidemics of adenovirus infections occur globally, in communities and in closed or crowded settings. In our institution, an outbreak of Adenovirus infection in infants and children was recently observed. Two main patterns of clinical presentation were observed: 68 patients had mainly respiratory symptoms (pharyngitis n=67, cough n=44; tonsillar exudate n=17; other respiratory signs n=4) while 26 patients showed prevalent gastrointestinal involvement (diarrhea n=26, vomiting n=8). Patients with respiratory symptoms had a significantly higher count of WBC, PMN and platelets, while CRP level approached statistical significance (p=0.07) for higher values in the patients with diarrhea. In order to explore the impact of selected presenting features, possible association between level of CRP and presence of pharyngeal exudate, cough, vomiting, diarrhea, duration of fever, number of neutrophils, and administration of antibiotics was analyzed. Patients falling in the tertile with more elevated CRP values had significantly more often tonsillar exudate and diarrhea, while those in the lower tertile had a 4.4 days duration of fever, vs. ≥5.0 days in the remaining patients. Antibiotic therapy was administered more frequently to patients with higher values of CRP (p=0.006). Duration of hospitalization was not associated with the CRP level. The median time from the receipt of positive adenovirus PCR test result to patient discharge was 1 day in 73% of cases. The number of copies of adenovirus detected by PCR ranged between 47 million and 15/L. Falling in the highest terzile of copy number was significantly associated with pharyngitis. The 24 patients with evidence of viral coinfection had no difference in the demographics or presenting features, with the only exception of a significantly higher leukocyte count. Rapid turn-around of results of molecular testing of adenovirus genome on pharyngeal swab allowed us to rapidly diagnose adenovirus infection, allowing stopping antibiotic therapy and immediate discharge, with reduced discomfort for the families and more appropriate use of hospital beds. A high copy number of adenovirus from pharyngeal swab should not be taken as an indicator of worse prognosis, thus allowing preferential use of qualitative rather than quantitaive assay.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained a large number of results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry.

Typhoid fever is an infectious disease that affects humanity worldwide particularly in the lower socio-economic communities where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in the different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and results obtained indicates that the overall combination of the control measures eradicates Typhoid fever in the population but the controls are more optimal in the higher socio-economic communities.

The amount of heat transfer in gas turbine blades depends on cooling techniques and various flow phenomena. The effect of eddies, passing shock waves and free flow turbulence has been noticed by many researchers since the beginning. The focus of the upcoming work is on the numerical investigation of the effects of turbulence intensity and Reynolds number on the amount of heat transfer from the blade surface with internal cooling. The SST model has been used to solve this problem, which has been compared with the experimental work to ensure the correctness of the numerical simulation. In this regard, by changing the free flow turbulence intensity with values of 1, 5, 7, and 10% and at three Reynolds numbers of 150,000, 350,000, and 750,000, the changes in heat transfer coefficients have been investigated. The results show that with the increase of the turbulence intensity at different Reynolds numbers, due to the positive effect of the flow turbulence on the suppression of separation and promotion of the boundary layer transition, the blade surface heat transferincreases and this increase is more evident at higher Reynolds numbers.

A (2,6)-fullerene F is a 2-connected cubic planar graph whose faces are only 2-length and 6-length. Furthermore, it consists of exactly three 2-length faces by Euler's formula. The (2,6)-fullerene comes from Do\v{s}li\'{c}'s (k,6)-fullerene, a 2-connected 3-regular plane graph with only k-length faces and hexagons. Do\v{s}li\'{c} showed that the (k,6)-fullerenes only exist for k = 2, 3, 4 or 5, and some of the structural properties of (k,6)-fullerene for k = 3, 4 or 5 are studied. In this paper, we study the properties of (2,6)-fullerene. We obtain that the edge-connectivity of (2,6)-fullerenes is 2. Every (2,6)-fullerene is 1-extendable, but not 2-extendable. F is said to be k- resonant (k>0) if the deleting of any i (0=< i<= k) disjoint even faces of F results in a graph with at least one perfect matching. We have that every (2,6)-fullerene is 1-resonant. An edge set S of F is called an anti-Kekule set if F-S is connected and has no perfect matchings, where F-S denotes the subgraph obtained by deleting all edges in S from F. The anti-Kekule number of F, denoted by ak(F), is the cardinality of a smallest anti-Kekule set of F. We have that every (2,6)-fullerene F with |V(F)|>6 has anti-Kekule number 4. Further we mainly prove that there exists a (2,6)-fullerene F having f_{F} hexagonal faces, where f_{F} is related to the two parameters n, m.

In 1937,German mathematician L.Collatz proposed the following conjeture:for any positive integer,if it is even,divide it by 2,if it is odd,multiply it by 3 and add 1 to get an even number.Continuing with the above rule, the final result will be 1.This paper gives a proof of this conjecture.

We present results of the detected voltage distribution of a quantum random number generator based on the photonic integration of semiconductor laser, delay interferometer and photodetector. We find that the integrated system behaves as expected for random number generation from gain-switched laser sources. The biggest advantage is that only electrical connections are needed to operate the system without the need for tricky and expensive optical alignment to external circuitry. We supply results showing that random bit stream created from the random numbers passes the NISTS statistical test suite tests; thus demonstrating the feasibility to generate random number via quantum means at gigabit/s rates from a single photonic integrated circuit. The results are backed by numerical simulations.

Aspergillus fumigatus is a ubiquitous, critical priority human fungal pathogen. Despite its clinical importance, there is limited knowledge regarding the variations of the genome within mitochondria, the powerhouse organelle within eukaryotic cells. In this study, we leveraged publicly available raw, whole genome sequence data from 1939 isolates to investigate the variations in the mitochondrial genomes of A. fumigatus. These isolates were isolated from 22 countries on six continents, as well as from outer space and from within the International Space Station. In total, our analysis revealed 39 mitochondrial single nucleotide polymorphisms (mtSNPs) within this global sample and together, these 39 mtSNPs grouped the 1939 isolates into 79 mitochondrial multilocus genotypes (MLGs). Among the 79 MLGs, 39 were each distributed in at least two countries and 30 were each shared by at least two continents. The two most frequent MLGs were also broadly distributed: MLG11 represented 420 isolates from 11 countries and four continents and while MLG79 represented 418 isolates from 18 countries and five continents, consistent with long-distance dispersals of mitogenomes. Our population genetic analyses of the mtSNPs revealed limited differentiation among continental populations but highly variable genetic differences among national populations, largely due to localized clonal expansions of different MLGs. Phylogenetic analysis and Discriminant Analysis of Principal Components of mtSNPs suggested the presence of at least three mitogenome clusters. Linkage disequilibrium, Index of Association, and phylogenetic incompatibility analyses collectively suggested evidence for mitogenome recombination in natural populations of A. fumigatus. In addition, sequence read depth analyses revealed an average ratio of ~20 mitogenomes per nuclear genome in this global population but the ratios varied among strains within and between certain geographic populations. Together, our results suggest evidence for organelle dynamics, genetic differentiation, recombination, and both widespread and localized clonal expansion of the mitogenomes in the global A. fumigatus population.

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

In the framework of mean field approximation, we consider a spin system consisting of two interacting sub-ensembles: spins interactions with in each sub-ensemble are ferromagnetic, while the inter-ensemble interactions are antiferromagnetic. We define the effective number of the nearest neighbors, and show that if the two sub-ensembles have the same effective number of the nearest neighbors, the classical form of critical exponents (, , , ) gives way to the non-classical form (, , , ), and the scaling function changes simultaneously. We demonstrate that this system allows for two second-order phase transitions and two first-order phase transitions. We observe that an external magnetic field does not destroy the phase transitions, but only shifts their critical points, allowing for control of the system’s parameters. We discuss the regime when the magnetization as a function of the magnetic field develops a low-magnetization plateau, and show that the height of this plateau abruptly rises to the value of one when the magnetic field reaches a critical value. Our analytical results are supported by a Monte Carlo simulation of a three-dimensional layered model.

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

Climate change-induced temperature fluctuations pose a significant threat to crop production, particularly in the Southern Hemisphere. This study investigates the transcriptome and physiological responses of rapeseed to post-flowering temperature increases, providing valuable insights into the molecular mechanisms underlying rapeseed tolerance to heat stress. Two rapeseed genotypes, Lumen and Solar, were assessed under control and heat stress conditions in field experiments conducted in Valdivia, Chile. Results showed that seed yield and seed number were negatively affected by heat stress, with genotype-specific responses. Lumen exhibited a 9.3% average seed yield reduction, while Solar showed a 28.7% reduction. RNA-seq analysis of siliques and seeds revealed tissue-specific responses to heat stress, with siliques being more sensitive to temperature stress. Hierarchical clustering analysis identified distinct gene clusters reflecting different aspects of heat stress adaptation in siliques, with a role for protein folding in maintaining silique development and seed quality under high temperature conditions. In seeds, three distinct patterns of heat-responsive gene expression were observed, with genes involved in protein folding and response to heat showing genotype-specific expression. Gene coexpression network analysis revealed major modules for rapeseed yield and quality, as well as the trade-off between seed number and seed weight. Overall, this study contributes to understanding the molecular mechanisms underlying rapeseed tolerance to heat stress and can inform crop improvement strategies targeting yield optimization under changing environmental conditions.

Abstract: In this study, a computational fluid dynamics (CFD) simulation was conducted to validate the CFD model with experimental data from Zimparov et.al (2012), which investigates the heat transfer performance in a spirally corrugated tube that has a twisted tape inserted. The heat transfer was then compared to a simple corrugated tube without the twisted tape and to a smooth tube with no corrugations and no twisted tape. This simulation is compared with a previous experimental study conducted by (Zimparov et al. 2012), which focuses on tubes with a height-to-diameter ratio e/Di > 0.04 and small relative pitches of the twisted tape, H/Di. The largest improvement was noticed in the tube with e/Di= 0.057 and ridge pitch-to-height ratio p/e=6.77 with a twisted tape of H/Di= 4.7. This tube is labeled 5035. Tube 5035 was found to have the most significant enhancement, hence the focus of the CFD simulation will be on this tube, and the simulation will range for Reynolds numbers, 3.5 x 103 < Re < 5.0 x 104. The focus of this simulation is the evaluation of heat transfer and friction factors; a metric was used to obtain an empirical representation of the tube’s performance. Keywords: Spirally corrugated tube; Twisted tape; Heat transfer enhancement; Friction factor; Nusselt number; Computational fluid dynamics (CFD); Star CCM+

Spinors are used for the computation of probability in quantum mechanics. They are treated as elements of a complex vector space in contrast to a real vector space. Spinor theory is abstract mathematics with an ambiguous interpretation. The overall phase of spinors does not affect the computation of probability in quantum mechanics. If two spinors have an overall phase of imaginary number i, then they can be treated like vectors in a real vector space. The square of the magnitude of the number, which is the sum of dot product and the term having basis vector i of cross product of two such vectors, is equal to the probability computed using the corresponding spinors. Therefore, the geometry of such spinors can be easily depicted in a three-dimensional space like vectors in a real vector space. Spinors are not isotropic vectors in Hilbert space. The sum of dot product and cross product of two complex numbers is equivalent to the quotient of the division of one complex number by another. Similarly, the sum of dot product and cross product of two vectors is the quotient of the division of one vector by another. Using the rules of division of vectors, we can find the rules of multiplication of vectors. The rules of multiplication and division of basis vector i match the rules of multiplication and division of imaginary number i. Therefore, basis vector i is nothing but imaginary number i. Multiplication of dot and cross product of two vectors to the second vector will give us the components of the first vector that are parallel and orthogonal to the second vector. Vectors are also made up of complex numbers like spinors. The reason for finding dot product of complex numbers in the process of computing the probability is to ignore the overall phase in contrast to the phase difference. This is misconstrued as complex vector space in quantum mechanics. 3-D number which is nothing but a spinor with new notation is an extension of vector algebra. It can have a real number as a term in addition to the terms i, j and k. In all other respects, it is a vector. 3-D numbers are part of the number system like real numbers and complex numbers. The real numbers are one dimensional numbers, the complex numbers are two-dimensional numbers and the 3-D numbers as well as vectors and spinors are three-dimensional numbers. As polarisation and spin are one and the same, we can straight away apply 3-D numbers to polarisation of light. 3-D numbers will greatly simplify the study of areas of science where three-dimensional space is involved.

To assess the impact of tourism on the incidence of HIV and AIDS using Malaysian epidemiological data over the period of 1986-2011 with additional consideration for newborns infected with HIV. A population-level mathematical model was used to investigate: i) the role of tourism in the spread of HIV and measures used to reduce HIV spread in Malaysia; ii) whether the stability of infectious disease transmission is dependent on the flow of visiting tourists. We first derived an equation for the reproduction number (R0) threshold to quantify the contagiousness of HIV in Malaysia. Sensitivity analyses were used to determine the effect of various parameters on HIV transmission with respect to the increase in tourism. Our findings suggest that a stable disease-free state is sustainable based on the low value of R0 was 0.0017. This result is encouraging from a public health perspective. Approximately 14% of outbound tourists who leave the country return infected with HIV and the difference between the rate at which tourists move to the susceptible category and the rate at which tourists leave the susceptible is category is 12%. Estimated parameters for the influx of tourist rates, δ=1.1540x10-3[1.1477x10-3 - 1.15954x10-3], δ1=7.7901x10-4[7.7867x10-4 - 7.79418x10-4], and δ2=1.4030x10-8[-7.2287x10-7-7.5096x10-7], significantly impacted the spread of HIV in Malaysia. Some significant adjustments were made to the expected parameters. The methods used are helpful to public health analyses and provide a framework for epidemiological modeling of HIV spread among tourists. The trend and magnitude of tourist inflows may be determinants in the incidence of HIV and AIDS in Malaysia.

The divination function of China's Yijing has led to its circulation for thousands of years. In our exploration of Yijing's characteristics using big data, we have discovered variations in results between the coin toss method and the ancient yarrow-stalk method of divination, known as "the number for the great expansion method of divination(大衍之数)". The yarrow-stalk method serves as the fundamental method of divination in Yijing and continues to hold significance in studying the essential characteristics of Yijing. Despite the complexity of yarrow calculations, advancements in computer technology and big data have simplified its application. By employing the yarrow-stalk method, we simulated changes in the 64 hexagrams, calculated probabilities and proportions of hexagram alterations, and derived fundamental characteristics and patterns of hexagrams. Additionally, we constructed the spatial representation of lines and hexagrams. Through a binary system rearrangement, we created a 64x64 matrix illustrating hexagram transformations. Subsequently, we generated 100 million random hexagrams and analyzed line and hexagram changes accordingly. Our findings indicate the following:(1) Big data analysis reveals evident asymmetry in the hexagrams obtained through the yarrow-stalk method, with a triangular fractal characteristic forming the background.(2) Each of the 64 hexagrams exhibits a distinct probability distribution when transforming into other hexagrams, which can be categorized into five types.(3)The occurrence probabilities of Laoyang, Laoyin, Shaoyang, and Shaoyin are 18.61%, 6.387%, 31.38%, and 43.62% respectively. The probabilities of Yin and Yang occurrences are nearly equal, each close to 50%. However, the probability of Laoyang is approximately three times higher than that of Laoyin.(4) Visualized and analyzed the characteristics of hexagram changes greater than 100000 times using 3D statistical maps and Sankey diagram.These results demonstrate that the yarrow-stalk method effectively unveils the characteristics and underlying patterns of the 64 hexagrams. This study provides a novel approach for scientifically exploring the internal laws governing the 64 hexagrams in Yijing.

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

We show that the compound samarium hexaboride is a strong topological insulator using the eigenvalues of the space inversion operator in the low-energy limit of the periodic Anderson model. Additionally, we assume the presence of the ferromagnetic exchange interaction (M). A Dirac cone like feature in the surface state energy spectra is observed for M equals zero in a certain parameter range. For M not equal to zero, there is no Kramers degeneracy. We have been able to show that this phase corresponds to the quantum anomalous Hall state by calculating Berry curvature and the Chern number. Using Floquet theory, we further show that the access to a novel state with broken time reversal symmetry is possible due to the normal incidence of circularly polarized optical field on the surface of the compound despite M being absent.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

The accurate identification of the primary tumor origin in metastatic cancer cases is crucial for guiding treatment decisions and improving patient outcomes. Copy Number Alterations (CNA) have emerged as valuable genomic markers for predicting the origin of metastases. This research article presents a comprehensive analysis of CNA-based prediction models in metastatic cancer. The study utilizes a dataset comprising CNA profiles from twenty different cancer types and employs advanced AI-based techniques for prediction. The research workflow consists of two models. The first is convolution network-based, while the other is a multi-stage model. In the first stage, a RELU model is developed to differentiate between 16 cancer types, considering their CNA, chromosome location, strand, and overall location. The second stage involves building specialized models to detect differences between cancer types within the same location or organs, such as brain lower-grade glioma and glioblastoma multiforme. Both generalized models achieve an overall accuracy of over 90%, while the specialized models achieve an accuracy of approximately 95% with minimal loss values. The results demonstrate the potential of AI-based approaches utilizing CNA data for improved diagnosis and personalized treatment strategies in metastatic cancer. This research establishes a solid foundation for future advancements in the field, paving the way for more effective and targeted approaches in metastatic cancer management.

In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a vertex-clique incidence matrix for a graph and produce new lower bounds for the negative eigenvalues and negative inertia of a graph. Moreover, utilizing these vertex-clique incidence matrices, we generalize several notions such as the signless Laplacian matrix, and develop bounds on the incidence energy and the signless Laplacian energy of the graph. %The tight upper bounds for the energies of a graph and its line graph are given. More generally, we also consider the set $S(G)$ of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent. An important parameter in this setting is $q(G)$, and is defined to be the minimum number of distinct eigenvalues over all matrices in $S(G)$. For a given graph $G$ the concept of a vertex-clique incidence matrix associated with an edge clique cover is applied to establish several classes of graphs with $q(G)=2$.

Investment management is a common process and practice used for achieving a desirable investment goal or outcome. Investment assessment should be carried out at various stages of project realization in accordance with capital investment volume. Investment risk management implies the effective control of all procedures and monitoring of risks in all phases of the investment project. Because of the reason that a single indicator in probability calculation of achieving optimal return from the investment does not exist, performing sufficiently reliable estimates of the quality of investments becomes a tedious task. There are many indicators, factors, and criteria required for consideration to reach the effective solution of the investment problem. Unfortunately, the systematic variation of economic situations in the marketplace stipulates the continuous and frequent changes of investment conditions and environment in which the investor should act and operate. Hence, the rules required for providing a reasonable quality of investment projects can be based only on investor’s management strategy and rely on investor’s intuition and practice. The importance of classification in investment management and decision making process is undeniable. The objects to be classified are described using assessments in accordance with various criteria which can be both quantitative and qualitative. With a competent formulation of the investment process, both methods are used in parallel. There exist various decision making approaches for the investment management, and simple additive weighting (SAW) is one of the well-known multi-criteria decision making (MCDM) methods aiming to provide an optimal decision for decision maker when solving various real-life problems, and particularly, investment problem. In this paper, fuzzy simple additive weighting (FSAW) method in group decision making is applied to undertake the capital investment expenditure for purchasing cars with the purpose of renting them to the public. The development of existing FSAW method is accomplished and this process involves the sensibility of outcomes to changes in the rate of fuzziness represented with decisions taken. Eventually, the degree of fuzziness involved in an analysis that directly attempts to model the immanent vagueness and imperfectness in particular precedency judgments made, is determined. A numerical example illustrates the importance and effectiveness of the suggested approach with the aim of ranking alternatives and hence, determining the most preferred alternative in MCDM problem.

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: explaining the waveform pattern of DNI, predicting the occurrence of the second wave of infection, and understanding the competitive spread of two viruses in a region. The findings demonstrate that these significant challenges can be comprehensively tackled using a simple mathematical framework. The theoretical insights derived from this model hold potential in guiding the estimation of the severity of an infection wave and formulating effective strategies for the control and mitigation of epidemic outbreaks.

This study presents the numerical investigation of bioconvective nanofluid (NF) flow compris-ing gyrotactic microorganisms through convective boundary conditions (CBC) enclosing heat and mass transmission analysis above an inclined extending cylinder. Via appropriate transfor-mation, the set of Partial Differential Equations is transformed into a scheme of nonlinear ODEs. A new set of variables are presented in the directive to get the first-order convectional equations and, then solved numerically by using bvp4c. The influence of several factors on velocity, ener-gy, concentration, and the density of motile microorganisms (DMM) is investigated and exam-ined. The analysis describes and addresses all physical measures of concentration such as Skin Friction (SF), Sherwood number (SN), DMM, and Nusselt number (NN). The present conse-quences display a validation with published. For confirmation of bvp4c, the ND-solve approach is also applied. Error analysis is also examined for the confirmation of the mathematical model.

This paper proposes the optimization method for the minimum mass of permanent magnet (PM) excited homopolar inductor alternator (HIA) with air-gap winding used for high-speed driving system. The calculation results show that there is an optimal value for shell diameter and unit number of HIA to make the mass to be smallest. A 1 MW at 22000 rpm PM excited HIA is designed. The analytical results are verified by the FEM simulations. The losses, temperature rise, rotor stress and modal of the PM excited HIA are also analyzed. The calculation results show that the solid rotor eddy-current losses and the temperature rise of PM excited HIA are acceptable. Also the rotor strength is adequate, and the rotor system is a stiffness rotor, and it can safely operate. Finally, the comparison between PM excited HIA and permanent magnet rotor machine is discussed.

Low-Level Virtual Machine (LLVM) compiler infrastructure is a useful tool for building Just-in-time (JIT) compilers, besides its reliable front-end represented by clang compiler and its elaborated middle-end containing different optimizations that improve the runtime performance. This paper addresses specifically the part of building a JIT compiler using LLVM with the scope of getting the hardware architecture details of the underlying machine such as the number of cores and the number of logical cores per processing unit and providing them to NUMA-BTLP static thread classification algorithm and to NUMA-BTDM static thread mapping algorithm. Afterwards, the hardware-aware algorithms are run by the JIT compiler within an optimization pass. JIT compiler in this paper is designed to run on a parallel C/C++ application (which creates threads using Pthreads), before the first time the application is executed on a machine. To do that, the JIT compiler takes the native code of the application, gets the corresponding LLVM IR (Intermediate Representation) for the native code and executes the hardware-aware thread classification and the thread mapping algorithms on the IR. The NUMA-Balanced Task and Loop Parallelism (NUMA-BTLP) and NUMA-Balanced Thread and Data Mapping (NUMA-BTDM) are expected to optimize the energy consumption up to 15%, on NUMA systems.

(1)Background:The purpose of the study was conducted to investigate the recovery of heart rate according to the performance level and rest interval conditions during 65%1RM bench press exercise;(2)Methods:The subjects of this study were eight healthy male college studentsin their 20 (years) attending University C. 1RM was measured before theexperiment, and the exercise sequence of six rest intervals (30sec, 1, 2, 3, 4,5min) was randomly selected and cross-distribution experiment. The experimental measurement was conducted a total of six times according to the rest interval condition (six conditions) once every 3 days to minimize the learning effect. The data was verified with repeated measures Two-way ANOVA and Contrast's repeated method was applied for post-comparison;(3)Results: First, the amount of exercise and the number of repetitions statistically substantially dropped (p&lt;.001) as the number of sets rose, and a greater decline was shown when the rest periods got shorter. Second, the heart rate after exercise was increased significantly (p&lt;.01) as the set progressed in the long rest interval conditions (4, 5min), and the heart rate after rest was increased statistically significantly (p&lt;,05) as the set progressed in the short rest interval conditions (30sec, 1min). Third, the heart rate recovery rate (%) was able to perform more repetitions than in the short rest interval condition due to the relatively high physiological recovery of the neuromuscular and circulatory system under the long rest interval condition;(4)Conclusions: Therefore, according to the rest conditionduring the 65%1RM bench press exercise conducted in this study, the restinterval condition of 2~3min may be effective in improving muscular endurance,and the rest interval condition of 4~5min may be effective in improving muscular hypertrophy. As a result of this study, there was a significant difference in exercise performance (repetition) and physiological recovery depending on the rest interval condition according to the set progress during the same intensity resistance exercise. Through this, it is judged that it is possible to adjust the amount of exercise appropriate for the purpose of training by adjusting not only the intensity during resistance exercise but also the rest interval between sets.

The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. Typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function based entropy accumulation has slow speed in general. For a practical perspective we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover we examine our theoretical results by applying to the quantum random number generator that uses dark noise arising from image sensor pixels as its entropy source.

Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV), which affects the liver. Every year, about 390,000 people die from HBV-related diseases in China, about 86 million people are carriers of HBV, accounting for about 6% of the total population, and 30 million people are chronically infected. From 2002 to 2007, though China government launched “The Global Alliance for Vaccines and Immunization (GAVI)” program to reduce HBV infection in children, but the number of hepatitis B cases in China remains high. Reasonable estimation of potential HBV carriers is crucial to prevention and control the spread hepatitis B virus. This study is based on the case data from the National Bureau of Statistics of China from 2003 to 2021. We build a dynamic model that includes potential hepatitis B virus carriers, use nonlinear least squares and genetic algorithms to fit the parameters in the model, and calculate the reproduction number of hepatitis B virus transmission in the population and obtain R_c=1.741. The number of potential hepatitis B virus carriers is estimated to be 449,535 (95%CI [415651 to 483420]) based on our model, which is 30.49% of the total number of hepatitis B cases, and the simulation results show the number of chronic hepatitis B incidence decreases as the vaccination rate α increases, increasing α by 20%, the number of chronic hepatitis B incidence decreases by 169,469 on average.

This work presents a design and model of the thermo-hydrodynamic behavior applying CFD for pin-fin heat sink with square shape (rectangular fin profile), through a novel pin arrangement that improves heat removal in the system. The novelty consist in the insertion of a deflector row that will help to direct the flow, so it hits the rectangular cross-sectional fins the presents in the system. The heat sink model is placed in channel designed in which air flows as suitable medium, and its overall performance is investigated. In addition, a constant heat flux is applied to the bottom wall of the heat sink model, equal values and amounts that​ correspond to the heat fluxes generated by current electronic equipment and devices. The numerical results of the global thermal resistance, the pressure drop and the Nusselt number are reported. The results allow determining best arrangement or geometry configuration, location and functionality of the fin-deflectors were collocated for evaluate thermal-hydraulic efficiency of system.

The DNS of film boiling requires strong computational resources that are difficult to obtain for a daily CFD use by the practitioners of the industrial R&amp;D experts. On the other hand, the film boiling experiments are associated with the usage of the expensive and highly sophisticated apparatus, and the research to this end is found to be relatively difficult due to high heat flow rates that are present in the process itself. When combined with a transient heat conduction in a solid, the problem becomes significantly difficult. Therefore, a novel method in computation of conjugate heat transfer during film boiling in a quiescent liquid has been proposed in this paper. The method relies on the solution of mass, momentum and energy conservation equations in a two-fluid framework, supplemented with the appropriate closures. Furthermore, the turbulent flow has been found as an important parameter in obtaining the accurate solution of the temperature field evolution in a solid specimen, via the proper modeling of turbulent kinetic energy (TKE) value, that has been imposed as a constant value, i.e., the frozen turbulence approach. It was found, in addition, that the appropriate TKE value can be obtained by use of Kelvin-Helmholtz instability theory in conjunction with the boundary layer theory. The obtained results show excellent agreement with the experimental data within the first 15 s of the experiment, i.e., the first ca. 10 % of the total duration of the film boiling mode of heat transfer. Furthermore, the heat transfer coefficient has matched the error bands prescribed by the authors of the paper that has presented the correlations, whilst the averaged values are far beyond this band, i.e., are slightly more than 30 % higher. The further inspection has revealed a measure of similarity between the computational result of the volume fraction field distribution and the experiment, thus confirming the capability of the method to obtain realistic interface evolution in time. The method has shown full capability for further pursuing the industrial-scale film boiling problems that involve turbulent flow and the conjugate heat transfer approach.

Next Generation Sequencing (NGS), now widely used in the clinical setting, offers an efficient and comprehensive molecular approach for patients with Familial hypercholesterolemia (FH). Although the dominant form of disease is mostly due to low-density lipoprotein receptor (LDLR) small-scale pathogenic variants, approximately 10% of molecularly defined FH cases are due to Copy Number Variations (CNVs). Here, we report a novel large deletion of the LDLR gene involving exons 4–18, identified by bioinformatic analysis of NGS data in an Italian family. A long PCR strategy was employed for breakpoint region analysis where an insertion of 6 nucleotides (TTCACT) was found. Two Alu sequences, identified within intron 3 and exon 18, could underlie the identified rearrangement by a Nonallelic Homologous Recombination (NAHR) mechanism. NGS proves to be a powerful tool used to precisely identify CNVs, in addition to small-scale variants in FH-related genes. At this purpose, the use and implementation of this cost-effective, efficient molecular approach meets the clinical need for personalized diagnosis in FH cases.

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

Firstly, we present a more explicit formulation of the complete system $D(N)$ of representatives of Manin's symbols over $\mathbb{Q}$, which was initially given by Shimura. Then we establish a bijection between $D(M)\times D(N)$ and $D(MN)$ for $(M,N)=1$, which reveals a recursive structure between Manin's symbols of different levels. Based on Manin's complete system $\Pi (N)$ of representatives of cusps on $X_0(N)$ and Cremona's characterization of the equivalence between cusps, we establish a bijection between a subset $C(N)$ of $D(N)$ and $\Pi (N)$, and then establish a bijection between $C(M)\times C(N)$ and $C(MN)$ for $(M,N)=1$. We also provide a recursive structure for elliptical points on $X_0(N)$. Based on these recursive structures, we obtain recursive algorithms for constructing Manin symbols over $\mathbb{Q}$, cusps and elliptical points on $X_0(N)$. This gives rise to a more efficient algorithms for modular elliptic curve. As direct corollaries of these recursive structures, we present a recursive version of the genus formula and an elementary proof of formulas of the numbers of $D(N)$, cusps and elliptical points on $X_0(N)$.

The mathematical modelling of reverse logistics inventory systems ignores that returned items may arrive out of sequence, i.e. with different number of remanufacturing times. Moreover, such modelling assumes that the retuned items may retain the same quality upon recovery regardless of how many times they have been previously remanufactured. This paper develops a new mathematical expression of the percentage of retuned items that can be remanufactured a finite number of times. The proposed expression is modelled as a function of the expected number of times an item can be remanufactured on its life cycle and the number of times an item can be technologically (or optimally) remanufactured based on its quality upon recovery. The model developed in this paper considers joint production and remanufacturing options. The return rate is a varying demand dependent rate, which is a decision variable with demand, product deterioration, manufacturing and remanufacturing rates being arbitrary functions of time. The model considers the initial inventory of returned items in the mathematical formulation, which enables decision makers to adjust all functions and input parameters for subsequent cycles. Illustrative examples indicate that dependent purchasing price of recovery items and the incorporation of remanufacturing investment cost significantly impact on the optimal remanufacturing policy.

Commercial banks usually classify customers according to their credit reports when making loans. In this study, we put our focus on classifying customers based on their credit reports from the People's Bank of China (PBC). Since there are no target labels of users in the credit report of the People's Bank of China, we put forward the fuzzy clustering method for the initial label, and then Construct ant colony search to optimize intelligent recognition. Finally, this study uses SVM, BP neural network, and random forest to classify users and compare their results. The research re-sults indicate that using ant colony clustering algorithm and random forest for classification is the most effective method with the PBC credit reports.

Infectious diseases continue to be a significant threat to human health and civilization, and finding effective methods to combat them is crucial. In this research, we investigate the impact of awareness campaigns and optimal control techniques on infectious diseases without proper vaccines. Specifically, we develop an SIRS type mathematical model that incorporates awareness campaigns through media and treatment for disease transmission dynamics and control. The model displays two equilibria, a disease-free equilibrium and an endemic equilibrium, and exhibits Hopf bifurcation when the bifurcation parameter exceeds its critical value, causing a switch in the stability of the system. We also propose an optimal control problem that minimizes the cost of control measures while achieving a desired level of disease control. By applying the minimum principle to the optimal control problem, we obtain analytical and numerical results that show how the infection rate of the disease affects the stability of the system and how awareness campaigns and treatment can maintain system stability. This study highlights the importance of awareness campaigns in controlling infectious diseases and demonstrates the effectiveness of optimal control theory in achieving disease control with minimal cost.