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Ant-inspired metaheuristic algorithms known as ant colony optimization (ACO) offer an approach that has the ability to solve complex problems in both discrete and continuous domains. ACOs have gained significant attention in the field of water resources management, since many problems in this domain are non-linear, complex, challenging and also demand reliable solutions. The aim of this study is to critically review the applications of ACO algorithms specifically in the field of hydrology and hydrogeology, which include areas such as reservoir operations, water distribution systems, coastal aquifer management, long-term groundwater monitoring, hydraulic parameter estimation, and urban drainage and storm network design. Research articles, peer-reviewed journal papers and conference papers on ACO were critically analyzed to identify the arguments and research findings to delineate the scope for future research and to identify the drawbacks of ACO. Implementation of ACO variants is also discussed, as hybrid and modified ACO techniques prove to be more efficient over traditional ACO algorithms. These algorithms facilitate formulation of near-optimal solutions, and they also help improve cost efficiency. Although many studies are attempting to overcome the difficulties faced in the application of ACO, some parts of the mathematical analysis remain unsolved. It is also observed that despite its popularity, studies have not been successful in incorporating the uncertainty in ACOs and the problems of dimensionality, convergence and stability are yet to be resolved. Nevertheless, ACO is a potential area for further research as the studies on the applications of these techniques are few. [ABSTRACT FROM AUTHOR]

• Mathematical and physical analyses of the introduced problem. • Reporting a serious error in an important dimensionless parameter. • Indicating that the reported numerical results are completely erroneous. This is a comment on the paper [Optics and Laser Technology 128 (2020) 106233; https://doi.org/10.1016/j.optlastec.2020.106233 ] titled "Exact coupled solution for photothermal semiconducting beams using a refined multi-phase-lag theory". Herein, we report a serious error in an important dimensionless parameter employed in the problem, revealing that the defined parameter is dimensional and wrong. Accordingly, all given numerical results are based on this serious mistake, and are completely erroneous. [ABSTRACT FROM AUTHOR]

The article describes a study of the foodborne transmission mechanisms for norovirus. It was undertaken for the U.K. Food Standards Agency and received the System Dynamics Society's 2020 "System Dynamics Applications Award". The article opens with descriptions of norovirus, the organisational context and the aims of the study. The first phase involved the construction of a large, fully formulated SD simulation model which included person‐to‐person mechanisms and, newly built, food‐related mechanisms for norovirus transmission. The group modelling process and the model structure are described. The model's existence demonstrated that enough was known about foodborne mechanisms to create an explicit and carefully documented representation that specialists recognised, understood, and accepted. Additionally, a framework for analysing the model's parameters—some currently unknown—helped organise FSA thinking on future research and potential policy levers. A second phase used mathematical analysis of a simplified SD model to assess the relative scale of the foodborne effects. In terms of contributions, this generated insights into possible sources of seasonality and insights into whether the most effective leverage points in the system lay solely within the remit of the FSA or were also within the remits of other government departments. The article closes by summarising the findings and then exploring their policy implications and recording the client's reactions to them. © 2022 The Authors. System Dynamics Review published by John Wiley & Sons Ltd on behalf of System Dynamics Society. [ABSTRACT FROM AUTHOR]

We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we state that generalized convexity, invex sets, and the Fr'echet differentiability assumption associated with curvilinear integral type functionals represent some necessary and sufficient mathematical tools for establishing various connections between the solutions of some robust (weak) vector commanded variational inequalities and (weak, proper) robust efficient solutions of the corresponding multi-objective variational control problem. In addition, the physical motivation of the problem under investigation is formulated in the illustrative application given at the end of this paper. [ABSTRACT FROM AUTHOR]

Agriculture was and remains the support of human existence, representing the backbone of the Romanian rural economy. The gross domestic product represents a macroeconomic indicator of results, being the consequence of the efficient use of resources. In this context, the authors analyze the place that agriculture holds in achieving the gross domestic product in Romania compared to the European Union, as well as its dynamics. In this sense, the share of resources in the formation of the gross domestic product in the period 2000-2022 is presented. The main research methods used for this work are: analysis, synthesis, comparison and mathematical analysis. From the analysis carried out, conclusive ideas emerge, and the article becomes even more suggestive, in that it is accompanied by tables synthesized by the authors and relevant graphics that highlight and support the assessments that the authors make in the content of this article. At the end of the paper, the authors emphasize the fact that the GDP is the most complex indicator that reflects the transformations that the Romanian economy has gone through in recent years. From the point of view of the use of resources, it can be seen that the share of the agricultural sector has registered a downward evolution, which can be largely explained by the increase in the importance of industry and the service sector in the overall national economy. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for the nonlinear Schrodinger system {idtu1(x,t)== ∆u1(x, t)− |u1(x, t)| p−1u1(x, t)− |u2(x, t)| p−1u1(x, t), idtu2(x, t) = ∆u2(x, t) − |u2(x, t)| p−1u2(x, t) − |u1(x, t)| p−1u2(x, t), was investigated in d space dimensions. For 1 < p ≤ 1 + 2/d, the nonexistence of asymptotically free solutions for the nonlinear Schrödinger system was proved based on mathematical analysis and scattering theory methods. The novelty of this paper was to give the proof of pseudo-conformal identity on the nonlinear Schrödinger system. The present results improved and complemented these of Bisognin, Sepúlveda, and Vera(Appl. Numer. Math. 59(9)(2009): 2285–2302), in which they only proved the nonexistence of asymptotically free solutions when d = 1, p = 3. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) is the underlying technology that has enabled connecting daily apparatus to the Internet and enjoying the facilities of smart services. IoT marketing is experiencing an impressive 16.7% growth rate and is a nearly USD 300.3 billion market. These eye-catching figures have made it an attractive playground for cybercriminals. IoT devices are built using resource-constrained architecture to offer compact sizes and competitive prices. As a result, integrating sophisticated cybersecurity features is beyond the scope of the computational capabilities of IoT. All of these have contributed to a surge in IoT intrusion. This paper presents an LSTM-based Intrusion Detection System (IDS) with a Dynamic Access Control (DAC) algorithm that not only detects but also defends against intrusion. This novel approach has achieved an impressive 97.16% validation accuracy. Unlike most of the IDSs, the model of the proposed IDS has been selected and optimized through mathematical analysis. Additionally, it boasts the ability to identify a wider range of threats (14 to be exact) compared to other IDS solutions, translating to enhanced security. Furthermore, it has been fine-tuned to strike a balance between accurately flagging threats and minimizing false alarms. Its impressive performance metrics (precision, recall, and F1 score all hovering around 97%) showcase the potential of this innovative IDS to elevate IoT security. The proposed IDS boasts an impressive detection rate, exceeding 98%. This high accuracy instills confidence in its reliability. Furthermore, its lightning-fast response time, averaging under 1.2 s, positions it among the fastest intrusion detection systems available. [ABSTRACT FROM AUTHOR]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

In our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input Multiple-Output (MIMO) channels with high-level Additive White Gaussian Noise (AWGN). It can handle various destructive phenomena without restricting the number of antenna arrays in the transmitter/receiver. Importantly, it does not rely on closed-loop MIMO feedback or the need for Channel-State Information Transmission (CSIT). We have demonstrated the effectiveness of our approach and provided a Bit Error Rate (BER) analysis for 16-, 32-, and 64-QAM modulation systems. Real-time simulations showcase the differences and advantages of our proposed algorithm compared to the Multi-Group Space-Time Coding (MGSTC) decoding algorithm and the Lagrange Multipliers Hard Successive Interference Cancellation (LM-HSIC) algorithm, which we have also developed here. Additionally, our paper includes a mathematical analysis of the LM-HSIC algorithm. The AP-HSIC algorithm is not only effective and fast in decoding, including interference cancellation computational feedback, but it can also be integrated with any Linear Processing Complex Orthogonal Design (LPCOD) technique, including Complex Orthogonal Design (COD) schemes such as high-order Orthogonal Space–Time Block Code (OSTBC) with high-order QAM symbols. [ABSTRACT FROM AUTHOR]

The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems. [ABSTRACT FROM AUTHOR]

The main contribution of this paper is to present a simple algorithm that theoretically and numerically assesses the switching angles of an inverter operated with the SPWM technique. This technique is the most widely used for eliminating harmonics in DC-AC converters for powering motors, renewable energy applications, household appliances, etc. Unlike conventional implementations of the SPWM technique based on the analog or digital comparison of a sinusoidal signal with a triangular signal, this paper mathematically performs this comparison. It proposes a simple solution to solve the transcendental equations arising from the mathematical analysis numerically. The technique is validated by calculating the total harmonic distortion (THD) of the generated signal theoretically and numerically, and the results indicate that the calculated angles produce the same distribution of harmonics calculated analytically and numerically. The algorithm is limited to single-phase inverters with unipolar SPWM. [ABSTRACT FROM AUTHOR]

This paper explores the Apéry-like series and demonstrates the derivation of closed-form expressions using fractional calculus. We consider a variety of Apéry-like functions, which were categorized by their functional forms and coefficients by applying the Riemann–Liouville fractional integral and derivative to examine their properties across various domains. The study focuses on establishing rigorous mathematical frameworks that unveil new insights into the behaviors of these series, contributing to a deeper understanding of number theory and mathematical analysis. Key results include proofs of convergence and divergence within specified intervals and the derivation of closed-form solutions through fractional integration and differentiation. This paper also introduces a method aimed at conjecturing mathematical constants through continued fractions as an application of our results. Finally, we provide the proof of validation for three unproven conjectures of continued fractions obtained from the Ramanujan Machine. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study existence results for a singular problem involving the p-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, the multiplicity of solutions is proved. An example is also given to illustrate the importance of these results. [ABSTRACT FROM AUTHOR]

In this paper, we consider homogeneous quasideviation means generated by real functions (defined on (0, ∞)) which are concave around the point 1 and possess certain upper estimates near 0 and ∞. It turns out that their concave envelopes can be completely determined. Using this description, we establish su˚cient conditions for the Hardy property of the homogeneous quasideviation mean and we also furnish an upper estimates for its Hardy constant. [ABSTRACT FROM AUTHOR]

Calculus of Variations In the paper I On a Non-Newtonian Calculus of Variations i , Delfim F. M. Torres presents, for the first time in the literature, a non-Newtonian calculus of variations that involves the minimization of a function defined by a non-Newtonian integral with a Lagrangian depending on the non-Newtonian derivative. This publication is an editorial for the Special Issue of Axioms "Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th birthday". This Special Issue is dedicated to Professor Delfim F. M. Torres on the occasion of his 50th birthday, as recognition of his significant contributions to Mathematics, in particular in the calculus of variations, optimal control, and mathematical biology. [Extracted from the article]

Climate change has become a critical global issue and challenge, with significant implications for financial enterprises as an integral part of economic activities. A thorough analysis of the impact of climate change on the high-quality development of financial enterprises is of great importance for financial sustainability. This paper first conducts an indepth mathematical analysis of the intrinsic mechanisms through which climate change affects the high-quality development of financial enterprises by establishing a game theory model. Secondly, using data from listed companies for the years 2000-2020, an econometric model is constructed to empirically examine the relationship between climate change and the high-quality development of financial enterprises. The research findings demonstrate that climate change significantly inhibits the highquality development of financial enterprises, as evidenced by robust results obtained through various methods such as data truncation, variable substitution, and changes in sample periods. Furthermore, this study addresses the endogeneity of the regression model using propensity score matching (PSM), instrumental variable methods, and system generalized method of moments (GMM). Additionally, climate change impacts the high-quality development of financial enterprises through technological innovation. Given the backdrop of climate change, understanding the relationship and logic between climate change and the high-quality development of financial enterprises and discerning the channels and mechanisms through which climate change affects their development are crucial. This research provides a new perspective and expands the research frontier on the high-quality development of financial enterprises, enriching the theoretical foundations in this field. [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

The class of generalized S D D 1 (G S D D 1 ) matrices is a new subclass of H -matrices. In this paper, we focus on the subdirect sum of G S D D 1 matrices, and some sufficient conditions to ensure that the subdirect sum of G S D D 1 matrices with strictly diagonally dominant (S D D) matrices is in the class of G S D D 1 matrices are given. Moreover, corresponding examples are given to illustrate our results. The class of generalized matrices is a new subclass of -matrices. In this paper, we focus on the subdirect sum of matrices, and some sufficient conditions to ensure that the subdirect sum of matrices with strictly diagonally dominant matrices is in the class of matrices are given. Moreover, corresponding examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Today, because infectious diseases have a large impact on people, control methods for all infectious diseases are crucial. In this paper, we propose a SIQR model with Crowley-Martin type incidence rate and saturated treatment. We have incorporated precautionary measures taken by the population through the saturated incidence rate. Screening of individuals who have come into contact with infected individuals is modelled. Thus, we explore a four-dimensional mathematical model to study the dynamics of the infectious diseases and their management. Stability and bifurcation analysis ofthe system is done. The Mensitivity analysis of all parameters in relation to the basic reproduction number has been performed and the theoretical results have been validated using numerical simulation. Mathematical results in this paper suggest that both government interventions and individual efforts must be incorporated to achieve better control of emerging infectious diseases in the population. [ABSTRACT FROM AUTHOR]

This paper focuses on the projective Riemann quadratic (PR-quadratic) Finsler metrics, which are variant of the Finsler metrics in Finsler geometry. The paper introduces a special class of PR-quadratic Finsler metrics, called SPR-quadratic Finsler metrics, which is closed under projective changes with respect to a fixed volume form on M. This class contains the class of Douglas-Weyl metrics and is a subset of the class of Weyl metrics. The paper shows that any SPR-quadratic Finsler metric has a scalar flag curvature and a PR-quadratic Finsler metric has a scalar curvature if and only if it is of SPR-quadratic type. The results presented in this paper contribute to a deeper understanding of the behavior of PR-quadratic Finsler metrics and provide insights into the geometric properties of these metrics. [ABSTRACT FROM AUTHOR]

In this paper the generalization of the converse of Baer's theorem for two-nilpotent variety of class row (n,m) is carried out. Baer proved that finiteness of G/Zn(G) implies that γn+1(G) is finite. Hekster proved the converse of the Baer's theorem with the assumption that G can be finitely generated. The Baer's theorem can be considered as a result of a classical theorem by Schur denoting that finiteness of G/Z(G) leads to the finiteness of G ′. The converse of the Baer's theorem has been proved conditionally by Taghavi et al. (2019), as well. In the Main Theorem, we prove that, if γm,n(G) ∩ Zn,m(G) = 1 and γm,n+i(G) is finite for some n, i,m ≥ 0. Then G/Zn,m(G) is finite in which γm,n(G) and Zn,m(G) denote verbal and marginal subgroups with respect to two-nilpotent variety of class row (n,m). Thus the generalization of the converse of Baer's theorem for two-nilpotent variety of groups valids by considering i = 0. In this article some other results are attained by the converse of the Baer's theorem. It is also concluded that when n = m = 1. Similar results are obtained for variety of the soluble groups. In addition, the converse of the Schur's theorem which proved by Halasi and Podoski is concluded in this paper, for two-nilpotent variety. We have also obtained some similar results of Chakaneh et al. (2019) for (n,m)-isoclinic family of groups and (1,m)-stem groups. [ABSTRACT FROM AUTHOR]

The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the 'forcing term'. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The 'forcing term' does not express a 'classical' force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problems moves the mathematical analysis of the effects of different kinds of forcing terms on solutions to equations governing the collective (that is statistical) behaviour of such nonconservative many-particle systems. In the present paper, we offer a study of the basic mathematical properties of such solutions, along with some numerical simulations to show the effects of forcing terms for a classical prey–predator model in ecology. [ABSTRACT FROM AUTHOR]

This research paper is devoted to including new methods of approximation in Theory Of Approximation using Chebyshev Polynomials. The research focuses on creating a potential model for approximation using Neural Networks. This work enables mathematical analysis of the Chebyshev polynomials and activation functions. One of the goals of this paper was to minimize the time spent on the learning process. However, implementing every term of Chebyshev Polynomial could only be realized in some frameworks. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to examine the impact of moisture and temperature changes on the behavior of a semi-infinite solid cylinder made of T300/5208 composite material. This study aims to provide analytical solutions for temperature, moisture and thermal stress through the de-coupling technique and the method of integral transforms. Both coupled and uncoupled cases are considered. Design/methodology/approach: This study investigates the hygrothermo-elastic response of a semi-infinite solid circular cylinder using an integral transform technique that includes Hankel and Fourier transforms. The cylinder is subjected to prescribed sources, and a numerical algorithm is developed for the numerical computation of the results. The goal is to understand how the cylinder responds to changes in temperature and moisture. Findings: The paper presents an analytical solution for temperature, moisture and thermal stress in a semi-infinite solid cylinder obtained through the use of an integral transform technique. The study focuses on a graphite fiber-reinforced epoxy matrix composite material (T300/5208) and discusses the coupled and uncoupled effects of temperature, moisture and thermal stress on the material. The results of the transient response hygrothermo-elastic field are presented graphically to provide a visual representation of the findings. Research limitations/implications: The research presented in this article is primarily hypothetical and focused on the analysis of mathematical models. Originality/value: To the authors' best knowledge, this study is the first to investigate the hygrothermal effect in a semi-infinite circular cylinder. Additionally, the material properties used in the analysis are both homogenous and isotropic and independent of both temperature and moisture. These unique aspects of the study make it a novel contribution to the field. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove the existence, uniqueness and strong consistency (i.e. almost sure convergence to the true unknown value) of the maximum likelihood estimator (MLE) of the vector parameter for a statistical model used in statistics applied to road safety. In the general case, the strong consistency of the MLE may be established by using the well-known result by Abraham Wald (in 1949) or its variants under a set of conditions. However, for the model considered in this paper, all these conditions are very difficult to verify because of the great dimension of the parameter space and the rather complex expression of the log-likelihood function. To circumvent these difficulties, we first demonstrate that the MLE exists and is unique afterwards we demonstrate the strong consistency of the MLE using the properties of the model and some theorems of mathematical analysis. [ABSTRACT FROM AUTHOR]

In the article 'How long is my toilet roll-a simple exercise in mathematical modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a laboratory is an important part of the experiment. The calculation of the absolute errors in indirect measurements provides us with information about the confidence that we must have in our experimental results. For that reason, the error calculation for all approximations has been made. [ABSTRACT FROM AUTHOR]

The global stress distribution and state parameter analysis of the building's main structure is an urgent problem to be solved in the online state assessment technology of building structure health. In this paper, a stress curve clustering algorithm of fiber Bragg grating stress sensor based on density clustering algorithm is proposed. To solve the problem of large dimension and sparse sample space of sensor stress curve, the distance between samples is measured based on improved cosine similarity. Aiming at the problem of low efficiency and poor effect of traditional clustering algorithm, density clustering algorithm based on mutual nearest neighbor is used to cluster. Finally, the classification of the daily stress load characteristics of the sensor is realized, which provides a basis for constructing the mathematical analysis model of building health. The experimental results show that the stress curve clustering method proposed in this paper is better than the latest clustering algorithms such as HDBSCAN, CBKM, K-mean++,FINCH and NPIR, and is suitable for the feature classification of stress curves of fiber Bragg grating sensors. [ABSTRACT FROM AUTHOR]

This paper provides another proof of Fermat's theorem. As in the previous work, a geometric approach is used, namely: instead of integers a, b, c, a triangle with side lengths a, b, c is considered. To preserve the completeness of the proof of the theorem in this work, the proof is repeated for the cases of right and obtuse triangles. In this case, the Fermat equation ap+bp = cp has no solutions for any natural number p > 2 and arbitrary numbers a, b, c. When considering the case when the numbers a, b, c are sides of an acute triangle, it is proven that Fermat's equation has no solutions for any natural number p > 2 and non-zero integer numbers a, b, c. Numbers a = k, b = k+m, c = k+n, where k, m, n are natural numbers that satisfy the inequalities n > m, n < k+m, exhaust all possible variants of natural numbers a, b, c, which are the sides of the triangle. In an acute triangle, the following condition is additionally satisfied: k > n -m + √2n(n - m). To study the Fermat equation, an auxiliary function f(k,p) = kp+(k+m)p-(k+n)p, is introduced, which is a polynomial of natural degree p in the variable k. The equation f(k, p) = 0 has a single positive root for any natural p = 2. A recurrent formula connecting the functions f(k,p+1) and f(k,p) has been proven: f(k,p+1) = kf(k, p)-[n(k+n)p-m(k+m)p]. The proof of the main proposition 2 is based on considering all possible relationships between the assumed integer solution of the equation f(k, p+1) = 0 and the number (ñ -m) corresponding to this solution k. The proof was carried out using the mathematical apparatus of number theory, elements of higher algebra and the foundations of mathematical analysis. These studies are a continuation of the author's works, in which some special cases of Fermat's theorem were proved. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the isoperimetric-type inequalities for the closed convex curve in the Euclidean plane R². The main result of this paper is that we establish a family of parametric inequalities. By adjusting the parameters, we can derive some well-known isoperimetric inequalities and some new improved isoperimetric-type inequalities. Furthermore, we investigate the stability property of the main inequality. [ABSTRACT FROM AUTHOR]

This paper examines in a mathematically simplified form the incentive system of publication activity adopted by Bulgarian universities. The methodology of the study is a mathematical analysis of a competitive game between multiple players. All proofs are made in the generalised case. It is shown that in this (and similar) mathematical form of the basic formula for calculating players’ rewards, there exists an optimal number of publications at which each player reaches his maximum profit. It is shown that if individual players do not cooperate but follow competitive behavior, they will realise their maximum profits in a Nash equilibrium. It is shown that in this equilibrium some players will prefer to have zero publication activity, which depends on the costs they incur for their publications. Easy done and cheap publications will be more competitive and more numerous. It has been shown that it is more profitable for players to cooperate and minimise the amount of publications rather than compete. Potential problems and distortions in the implementation of incentives are commented. [ABSTRACT FROM AUTHOR]

The Sombor index (SO) is a recently invented vertex-degreebased molecular structure-descriptor. LetM1 be the first Zagreb index. The fact that SO is bounded from below by M1/√2 and from above by M1 is well-known and easy to prove. In this paper, we improve these bounds. [ABSTRACT FROM AUTHOR]

Let p(z) be a polynomial of degree n with zero of multiplicity s at the origin and the remaining zeros be 0. In this paper, we investigate the relative growth of a polynomial p(z) with respect to two circles z=r and z = R and obtain inequalities about the dependence of p(rz) on p(Rz), where z = 1, for 0 while taking into account the placement of the zeros of the underlying polynomial. Our results improve as well as generalize certain well-known polynomial inequalities. Some numerical examples are also given in order to illustrate and compare graphically the obtained inequalities with some recent results. [ABSTRACT FROM AUTHOR]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

In this paper, we investigate mathematical models of meteorological forecasting based on the work of neural networks, which allow us to calculate presumptive meteorological parameters of the desired location on the basis of previous meteorological data. A new method of grouping neural networks to obtain a more accurate output result is proposed. An algorithm is presented, based on which the most accurate meteorological forecast was obtained based on the results of the study. This algorithm can be used in a wide range of situations, such as obtaining data for the operation of equipment in a given location and studying meteorological parameters of the location. To build this model, we used data obtained from personal weather stations of the Weather Underground company and the US National Digital Forecast Database (NDFD). Also, a Google remote learning machine was used to compare the results with existing products on the market. The algorithm for building the forecast model covered several locations across the US in order to compare its performance in different weather zones. Different methods of training the machine to produce the most effective weather forecast result were also considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a Quasi B-algebra, building upon the foundational work on Post algebras by G. Epstein and the investigation of semi B-algebras. We systematically explore the properties of Quasi B-algebras, establishing equivalent conditions for the transition from a semi B-algebra to a Quasi B-algebra. [ABSTRACT FROM AUTHOR]

The k-deck of a graph is the multiset of its subgraphs induced by k vertices which is denoted by Dk(G). A graph or graph property is l-reconstructible if it is determined by the deck of subgraphs obtained by deleting l vertices. Manvel proved that from the (n−l)-deck of a graph and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−1, the degree list of the graph is determined. In this paper, we extend this result and prove that if G is a graph with n vertices, then from the (n−l)-deck of G and the numbers of vertices with degree i for all i, n−l ≤ i ≤ n−3, where l ≥ 4 and n ≥ l + 6, the degree list of the graph is determined. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for T -contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered. [ABSTRACT FROM AUTHOR]

The paper is using the nonlocal field equations for modelling a nanocontact made from the thin films. The theory describes long-range interactions among the particles. An elastic layer loaded by a rigid indenter is considered. We show that the stress field is finite for all points and have a maximum value that does not occur at the boundary of the contact domain. [ABSTRACT FROM AUTHOR]

Frank Ramsey is a towering figure in economics. His two papers published in the 1920s are responsible for his reputation as a pioneer in mathematical economics. Economists and historians of economics disagree on how to read Ramsey. One point of contention is whether he introduced the use of a representative agent or instead employed a social welfare function. We intend to clarify this question by further complicating it. It is clear from archival materials, including a previously undiscovered paper ('Mathematical Economics'), that he was not a trailblazer in mathematical analyses of economic questions. Ramsey was a socialist who was inclined to theories of value and psychology that went beyond utility. He struggled with the tension between what is good for the individual and what is good for society. He was sure that utilitarian psychology was not an accurate basis for economics and he was sceptical of its idealizations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of the fractional (p, q)-difference initial value problem with the fractional (p, q)-integral boundary conditions with the aid of the method of successive approximations(Picard method) and fractional (p, q)-Gronwall inequality, obtaining sufficient conditions for the existence, uniqueness and continuous dependence results of solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a novel topology for a non‐isolated bidirectional multiphase single inductor (BMPSIC) DC–DC converter. The proposed BMPSIC requires only a single inductor, irrespective of the number of arms, and features reduced volume and weight compared to the total magnetics needed for a conventional converter with similar ratings. The proposed BMPSIC advantages include a high DC voltage gain without operating on a large duty cycle, voltage stress on the power switches equal to that at the high‐voltage port, easy implementation, and a lower cost for application at high‐power densities. Furthermore, this topology requires only one current and voltage control loop. This paper thoroughly details the steady‐state operating principles of the inductor current continuous mode. It provides theoretical and mathematical analysis, including a comparative analysis of the proposed BMPSIC against earlier DC–DC converters, highlighting the superior performance and efficiency of the BMPSIC. An 8‐kW laboratory prototype, designed as a proof of concept, has been meticulously developed and tested, showcasing the performance of the converter across a broad range of load variations. The efficiency measured for the rated load exceeded 98.2% at the low‐voltage port of 250 V and the high‐voltage port of 400 V. Additionally, the article features Video S1, which illustrates the functioning of the converter. [ABSTRACT FROM AUTHOR]

Summary: Multilevel inverters are known as essential converters in renewable sources. First, in this paper, a new submodule is presented, and based on it, a new sub‐multilevel inverter is presented. The proposed sub‐multilevel inverter consists of several unidirectional and bidirectional switches and DC voltage sources. Then, the generalized topology, developed in two modular and cascaded modes, is presented to increase production levels. The proposed submodules are connected in series in the modular topology, increasing production levels. The proposed topology to produce the maximum output levels has the minimum number of IGBTs, drivers, DC voltage sources, etc. Mathematical analyses for conduction and switching losses are provided, and mathematical analyses for the number of devices and voltage across the switches are also presented. In addition to the mathematical analysis of losses, the simulation results are also presented. A general comparison of proposed topology components is presented to demonstrate their advantages. This comparison shows that the proposed topology has the minimum number of power electronic devices. In this paper, nearest level modulation is used to control the proposed topology. The simulation and experimental results of the proposed sub‐multilevel verify the performance of the proposed topology. [ABSTRACT FROM AUTHOR]

The Randić matrix R = [rij] of a graph G = (V;E) was defined as...j if vertices vi and vj are adjacent and rij = 0 otherwise, where di is the degree of the vertex vi 2 V. In this paper, we define the Randić matrix of a uniform hypergraph and study some its spectral properties. We also define the Randić energy of a uniform hypergraph and determine some upper and lower bound for it. [ABSTRACT FROM AUTHOR]

A significant development in the field of gyrogroups was the introduction of the space of all relativistically admissible velocities, which brought gyrogroups into the mainstream. A group has various generalizations, one of which is the notion of gyrogroups. Moreover, for any pair (a; b) in this structure, there exists an automorphism gyr[a; b] that fulfills left associativity and left loop property. The motivation behind this study is to generalize gyrogroups and semigroups, which has led to the introduction of gyrosemigroups. Accordingly, in this paper, some classes of gyrosemigroups are presented. Also, all gyrosemigroups of order 2 are characterized. Furthermore, the gyrosemigroups with an identity or a zero are studied. [ABSTRACT FROM AUTHOR]