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Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]

The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]

Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]

This special issue of the Journal of Optimization Theory & Applications focuses on the work of Professors Cornelis Roos and Florian A. Potra in the field of optimization. The issue includes a biographical sketch of both professors, highlighting their achievements. The papers in the special issue cover various topics such as conic optimization, interior point methods, proximal methods, convex optimization, and stochastic optimal control. The authors of the papers have close connections to Professors Roos and Potra, either as students, visitors, or co-authors. The document is a compilation of research papers on interior-point methods (IPMs) and their applications in optimization and conic programming. The papers cover theoretical developments of IPMs, algorithms for linear complementarity problems (LCPs), weighted LCPs, and sufficient linear complementarity problems. There are also papers on new computational approaches for IPMs, applications of IPMs in different fields such as mechanics and support vector machines, and the theory and application of conic optimization. The document also includes papers on proximal methods for convex and non-convex problems, as well as papers on convexity and convex optimization. The volume concludes with acknowledgments to the authors, reviewers, and editor-in-chief. [Extracted from the article]

Research paper recommenders emerged over the last decade to ease finding publications relating to researchers’ area of interest. The challenge was not just to provide researchers with very rich publications at any time, any place and in any form but to also offer the right publication to the right researcher in the right way. Several approaches exist in handling paper recommender systems. However, these approaches assumed the availability of the whole contents of the recommending papers to be freely accessible, which is not always true due to factors such as copyright restrictions. This paper presents a collaborative approach for research paper recommender system. By leveraging the advantages of collaborative filtering approach, we utilize the publicly available contextual metadata to infer the hidden associations that exist between research papers in order to personalize recommendations. The novelty of our proposed approach is that it provides personalized recommendations regardless of the research field and regardless of the user’s expertise. Using a publicly available dataset, our proposed approach has recorded a significant improvement over other baseline methods in measuring both the overall performance and the ability to return relevant and useful publications at the top of the recommendation list. [ABSTRACT FROM AUTHOR]

With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]

We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We discuss elliptic complexes and highlight the category theoretical background and its role as a unifying language between algebraic topology, differential geometry, and modelling software design. In particular, the ubiquitous concept of naturality is central. Natural differential operators have functorial analogues on the cochains of triangulated manifolds. In order to establish this correspondence, we derive formulas involving simplices and barycentric coordinates, defining discrete vector fields and a discrete Lie derivative as a result of a discrete analogue of Cartan’s magic formula. This theorem is the main mathematical result of the paper. [ABSTRACT FROM AUTHOR]

The aim of the 17th century philosophers, in general, was to show that, by taking as an example the success of the human mind embodied in science, definitive knowledge could be achieved in philosophy, just as in science. To this end, firstly, they described in detail the method to be followed in order to obtain the knowledge. In science, the efforts of scientists such as Kepler, Galileo, and Newton to explain the universe based on mathematics led mathematics to stand out as a way of thinking. In this period, while mathematical research methods enabled the examination of physical phenomena, philosophy, on the other hand, was seen as a model to reach exact knowledge. Rationalist philosophers such as Descartes, Spinoza, and Leibniz all agree that people should use their own minds, not authorities, and moving from this idea, mathematics is the method that will lead us to the truth. This paper aims to show how these three great philosophers applied mathematics to their own philosophies, based on their differences and similarities. [ABSTRACT FROM AUTHOR]

This paper describes the implementation and linearization of a coupled panel and vortex particle method in a state-variable form. More specifically, the coupled panel and vortex particle dynamics are formulated as a nonlinear system of ordinary differential equations in first-order form to be self-contained and inherently linearizable. Linearization of this coupled panel and vortex particle method is demonstrated via finite differencing and a novel analytical linearization technique to yield a linear time-invariant representation. The code is implemented in MATLAB® and validated against an open-source aerodynamic solver for a fixed wing in both stationary and unsteady conditions. The linearized models are verified against the nonlinear dynamics both in the time and frequency domains. Linearized models accurately represent the wake dynamics about the equilibrium condition for moderate amplitude inputs and for input frequencies covering the typical frequency range of flight dynamics and flight controls, i.e., 0.3-30 rad/s. Analytical linearization is shown to abate the cost of linearization over perturbation methods by O(n2), where n is the total number of states of the system. Linearized models of the coupled panel and vortex particle dynamics have applications in the flight dynamics of both fixed- and rotary-wing vehicles, where these dynamics can be used to augment the rigid-body dynamics. The coupled rigid-body and wake dynamics can be leveraged to assess the stability, response characteristics, and handling qualities of vehicles experiencing aerodynamic interactions between rotors, wings, and/or obstacles. [ABSTRACT FROM AUTHOR]

This paper is dedicated to defining and studying for the first time the concept of fuzzy metric spaces based on two-fold fuzzy algebras, where the elementary properties of this new concept will be studied and presented by many theorems and related examples that explain the validity of our work. Also, many different types of open and closed balls will be discussed, as well as the relationships between these metric substructures. Keywords: fuzzy metric space, two-fold algebra, open ball, closed ball, torus Introduction and basic concepts The applications of neutrosophic sets and fuzzy sets are very wide and open research areas. In the literature, we can find many neutrosophic and fuzzy algebraic structures with deep connection with applied mathematics and number theory [5-11]. The concept of two-fold algebra was presented by Smarandache in [4], where many suggestions for the algebraic structure related to this algebra were defined and presented. This new idea has been used in [1] to study the two-fold algebra based on the standard fuzzy number theoretical system [3]. In [2], Hatip et.al. proposed the two-fold vector space and two-fold algebraic module based on fuzzy mappings, where they have studied the elementary properties of these new generalizations with many interesting examples. This work is motivated by the modern idea of two-fold algebra, and metric spaces, where we can combine those to different structures in one algebraic structure called two-fold. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to solve Fredholm integral equations (IEs) that involve Sfunction, generalized extended Mittag-Leffler function (GEMLF), and incomplete ℵ-function as the kernel. These types of integral equations appear frequently in applied mathematics, particularly in mathematical physics, engineering, and finance. To solve these integral equations, we employ two powerful mathematical tools, namely fractional calculus (FC) and integral transforms. Specifically, we use the Weyl operator and Mellin transform to solve the integral equation associated with S-functions, GEMLF, and incomplete ℵ-functions. These techniques allow us to express the solution in a closed form, which is essential for practical applications. Moreover, we present several special cases of the solutions obtained, which provide additional insights into the behavior of the solutions. These results are significant for the study of integral equations, as they can be used to derive several known results. Furthermore, the techniques used in this study can be applied to other integral equations that involve different types of functions. [ABSTRACT FROM AUTHOR]

Inequalities play a main role in pure and applied mathematics. In this paper, we prove a generalization of Milne inequality for any measure space. The argument in the proof of this inequality allows us to obtain other Milne-type inequalities. Also, we improve the discrete version of Milne inequality, which holds for any positive value of the parameter p. Finally, we present a Milne-type inequality in the fractional context. [ABSTRACT FROM AUTHOR]

This study delves into special class of generalized p-trigonometric functions, examining their connection to the established counterparts like p-cosine and p-sine functions. We here explore the new class of functions called the p-versine, p-coversine, p-haversine, and p-hacovercosine, by providing comprehensive definitions and properties. Grounded in the characteristics of p-cosine and p-sine functions, the newly proposed functions offer unique mathematical insights. Our work contributes towards a thorough understanding of these new special functions, showcasing their potential applications in diverse scientific domains, from mathematical analysis to physics and engineering. This paper contributes as a valuable resource for future applied mathematics researchers, engaging with these new mathematical functions, enhancing the ability to model complex patterns from diverse real-world applications. [ABSTRACT FROM AUTHOR]

This special issue of Studies in Applied Mathematics is dedicated to the 70th birthday of Professor Thanasis Fokas. It contains a selection of papers that all use in some ways the ground‐breaking mathematical ideas and techniques introduced by Thanasis over his long and exceptionally prolific career. [ABSTRACT FROM AUTHOR]

Extracting the useful information has been used almost everywhere in many fields of mathematics and applied mathematics. It is a classical ill-posed problem due to the unstable dependence of approximations on small perturbation of the data. The traditional regularization methods depend on the choice of the regularization parameter, which are closely related to an available accurate upper bound of noise level; thus it is not appropriate for the randomly distributed noise with big or unknown variance. In this paper, a purely data driven statistical regularization method is proposed, effectively extracting the information from randomly noisy observations. The rigorous upper bound estimation of confidence interval of the error in L 2 norm is established, and some numerical examples are provided to illustrate the effectiveness and computational performance of the method. [ABSTRACT FROM AUTHOR]

Let $ \mathcal {O} $ O denote the ring of integers of a quadratic field $ \mathbb {Q}(\sqrt {-7}) $ Q (− 7). In 2022, Murtuza and Garge [Murtuza N, Garge A. Universality of certain diagonal quadratic forms for matrices over a ring of integers, Indian Journal of Pure and Applied Mathematics, Published online; December 2022.] gave a necessary and sufficient condition for a diagonal quadratic form $ a_1X_1^2+a_2X_2^2+a_3X_3^2 $ a 1 X 1 2 + a 2 X 2 2 + a 3 X 3 2 where $ a_i\in \mathbb {\mathcal {O}} $ a i ∈ O for $ 1\leq i \leq ~3 $ 1 ≤ i ≤ 3 for representing all $ 2\times 2 $ 2 × 2 matrices over $ \mathcal {O} $ O . Let K denote a quadratic field such that its ring of integers $ \mathcal {O}_K $ O K is a principal ideal domain and 2 is a product of two distinct primes. It is a well-known fact that $ \mathbb {Q}(\sqrt {-7}) $ Q (− 7) is the only imaginary quadratic field with the above properties. Let $ D_K $ D K denote the discriminant of K. We have $ D_K\equiv 1(\text{mod }8) $ D K ≡ 1 (mod 8) if and only if 2 is a product of two distinct primes in $ \mathcal {O}_K $ O K . With $ \mathcal {O}_K $ O K as above, in this paper we generalize our earlier result. We give a necessary and sufficient condition for a diagonal quadratic form $ {\sum _{i=1}^{m}a_iX_i^2} $ ∑ i = 1 m a i X i 2 where $ a_i\in \mathcal {O}_K $ a i ∈ O K , $ 1\leq i \leq m $ 1 ≤ i ≤ m to represent all $ 2\times 2 $ 2 × 2 matrices over $ \mathcal {O}_K $ O K . This result is a conjecture stated in [Murtuza N, Garge A. Universality of certain diagonal quadratic forms for matrices over a ring of integers, Indian Journal of Pure and Applied Mathematics, Published online; December 2022]. [ABSTRACT FROM AUTHOR]

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field. [ABSTRACT FROM AUTHOR]

Nowadays, there has been a rapidly increasing number of scientific submissions in multiple research domains. A large number of journals have various acceptance rates, impact factors, and rankings in different publishers. It becomes time-consuming for many researchers to select the most suitable journal to submit their work with the highest acceptance rate. A paper submission recommendation system is more critical for the research community and publishers as it gives scientists another support to complete their submission conveniently. This paper investigates the submission recommendation system for two main research topics: computer science and applied mathematics. Unlike the previous works (Wang et al., 2018; Son et al., 2020) that extract TF–IDF and statistical features as well as utilize numerous machine learning algorithms (logistics regression and multiple perceptrons) for building the recommendation engine, we present an efficient paper submission recommendation algorithm by using different bidirectional transformer encoders and the Mixture of Transformer Encoders technique. We compare the performance between our methodology and other approaches by one dataset from Wang et al. (2018) with 14012 papers in computer science and another dataset collected by us with 223,782 articles in 178 Springer applied mathematics journals in terms of top K accuracy (K = 1 , 3 , 5 , 10). The experimental results show that our proposed method extensively outperforms other state-of-the-art techniques with a significant margin in all top K accuracy for both two datasets. We publish all datasets collected and our implementation codes for further references. 1 1 https://github.com/BinhMisfit/PSRMTE. • Bidirectional transformer encoders can improve the performance of the paper submission recommendation system. • The Mixture of Transformer Encoders framework shows the efficiency in the paper submission recommendation problem. • Proposed techniques can surpass other recent techniques on two datasets related. [ABSTRACT FROM AUTHOR]

This document is a preface to a special issue of the journal Mathematics titled "State-of-the-Art Mathematical Applications in Europe." The special issue features twelve original research papers and one review paper from European researchers and their collaborators in various fields of mathematics. The papers cover topics such as mathematical physics, applied mathematics, algebra, navigation algorithms, decision-making models, Lagrange interpolation polynomials, and nonlinear fractional differential equations. The preface provides a brief overview of each paper and expresses gratitude to the authors and reviewers. The special issue has received significant interest and demonstrates the importance of open access research in applied mathematics. [Extracted from the article]

In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of proximal (α , F) -contractions in F -metric spaces. We establish novel results concerning the existence and uniqueness of best proximity points for such mappings. The validity of our findings is corroborated through a non-trivial example. Furthermore, we demonstrate the applicability of these results by proving the existence of solutions for Volterra integral equations related to population growth models. This approach not only extends best proximity theory, but also paves the way for further research in applied mathematics and beyond. [ABSTRACT FROM AUTHOR]

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann's integral theory, the Hermite–Hadamard's type inequalities are introduced for a newly defined class of nonconvex functions, which is known as  U · D preinvex fuzzy number-valued mappings ( U · D preinvex  F · N · V · M s) on coordinates. Some Pachpatte-type inequalities are also established for the product of two  U · D preinvex  F · N · V · M s, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann's integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. [ABSTRACT FROM AUTHOR]

In this paper, we present the general Bernstein functions for the first time. The properties of generalized Bernstein basis functions are given and demonstrated. The classical Bernstein polynomial bases are merely a subset of the general Bernstein functions. Based on the new Bernstein base functions and the collocation method, we present a numerical method for solving linear and nonlinear χ-fractional differential equations (χ-FDEs) with variable coefficients. The fractional derivative used in this work is the χ-Caputo fractional derivative sense (χ-CFD). Combining the Bernstein functions basis and the collocation methods yields the approximation solution of nonlinear differential equations. These base functions can be used to solve many problems in applied mathematics, including calculus of variations, differential equations, optimal control, and integral equations. Furthermore, the convergence of the method is rigorously justified and supported by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering. [ABSTRACT FROM AUTHOR]

This paper investigates a recently introduced (2 + 1) -dimensional extended Calogero–Bogoyavlenskii–Schiff equation. The considered model is widely used in fluid dynamics, nonlinear optics and plasma physics. The study of the governing equation has provided insights into the dynamical behaviors of wave systems, which is an important area of research in applied mathematics and theoretical physics. Firstly, the description of the generalized Kudryashov and the two variable ( G ′ G , 1 G) -expansion methods is presented. The governing model is converted into a nonlinear ordinary differential equation by utilizing the traveling wave hypothesis. A family of exact traveling wave solutions such as solitons and solitary waves are extracted using the two proposed methods for the governing model. The graphical demonstrations are presented to examine the physical behavior of the constructed solutions. Kink solitary wave, singular kink, W-shape soliton, dark-bright soliton and periodic wave solutions are successfully retrieved. The proposed techniques are utilized to examine the governing model for the first time in this work to the best of our knowledge. The acquired results will help in guiding future investigations of the wave phenomena represented by the considered equation. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a STEM scholarship program which utilized a holistic approach to providing a multi-dimensional student support system. The program has been successful in encouraging and supporting women in Applied Mathematics and Computer Science by offering a diverse suite of extracurricular opportunities, actively engaging them in organized events, research projects, and participation in STEM communities, and helping them achieve higher GPAs and shorter times to graduation. The supported women also benefitted from close mentoring relationships with the faculty mentors. The program emphasized the development of empowering settings for women's engagement and achievement, which act to sustain and expand interest in mathematics and computing, and thereby help them to see themselves as future professionals in the field. [ABSTRACT FROM AUTHOR]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. Cozad and Sahinidis propose a nonconvex mixed-integer nonlinear program (MINLP), in which binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators, such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program–based method and a neural network–based method from the literature. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Applied Mathematics activity within the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Grant DE-AC02-06CH11357]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0050) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0050). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]

It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu's lemma and Maingé's fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations. [ABSTRACT FROM AUTHOR]

This paper addresses discontinuities in the solutions of mathematical physics that describe actual processes and are not observed in experiments. The appearance of discontinuities is associated in this paper with the classical differential calculus based on the analysis of infinitesimal quantities. Nonlocal functions and nonlocal derivatives, which are not specified, in contrast to the traditional approach to a point, but are the results of averaging over small but finite intervals of the independent variable are introduced. Classical equations of mathematical physics preserve the traditional form but include nonlocal functions. These equations are supplemented with additional equations that link nonlocal and traditional functions. The proposed approach results in continuous solutions of the classical singular problems of mathematical physics. The problems of a string and a circular membrane loaded with concentrated forces are used to demonstrate the procedure. Analytical results are supported with experimental data. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Nonlinear Studies, featuring interdisciplinary perspectives in applied mathematics. It includes articles on consumer behavior, diffusion of innovation, numerical methods, game theory, and optimization, covering domains such as engineering, management, and physics. The papers have undergone peer review and offer original and high-quality research. The document compiles research contributions on reliability analysis, mathematical modeling, differential equations, and optimization problems, with references for further exploration. The authors express gratitude to the contributors and reviewers for their valuable contributions. [Extracted from the article]

A porous material that has been contaminated with a hazardous chemical agent is typically decontaminated by applying a cleanser solution to the surface and allowing the cleanser to react into the porous material, neutralising the agent. The agent and cleanser are often immiscible fluids and so, if the porous material is initially saturated with agent, a reaction front develops with the decontamination reaction occurring at this interface between the fluids. We investigate the effect of different initial agent configurations within the pore space on the decontamination process. Specifically, we compare the decontamination of a material initially saturated by the agent with the situation when, initially, the agent only coats the walls of the pores (referred to as the 'agent-on-walls' case). In previous work (Luckins et al., European Journal of Applied Mathematics, 31(5):782–805, 2020), we derived homogenised models for both of these decontamination scenarios, and in this paper we explore the solutions of these two models. We find that, for an identical initial volume of agent, the decontamination time is generally much faster for the agent-on-walls case compared with the initially saturated case, since the surface area on which the reaction can occur is greater. However for sufficiently deep spills of contaminant, or sufficiently slow reaction rates, decontamination in the agent-on-walls scenario can be slower. We also show that, in the limit of a dilute cleanser with a deep initial agent spill, the agent-on-walls model exhibits behaviour akin to a Stefan problem of the same form as that arising in the initially saturated model. The decontamination time is shown to decrease with both the applied cleanser concentration and the rate of the chemical reaction. However, increasing the cleanser concentration is also shown to result in lower decontamination efficiency, with an increase in the amount of cleanser chemical that is wasted. [ABSTRACT FROM AUTHOR]

Invasive‐invaded species problems are of relevance in mathematics applied to population dynamics. In this paper, the mentioned dynamics is introduced based on a fourth‐order parabolic operator, together with coupled non‐linear reaction terms. The fourth‐order operator allows us to model a heterogeneous diffusion, as introduced by the Landau–Ginzburg free energy approach. The reaction terms are given by a coupled non‐linear effect in the invasive species, to account for the action of the invaded species and limited resources, and by a non‐Lipschitz term in the invaded species, to account for possible sprouts, once the invasion occurs. The analysis starts by the proof of existence and uniqueness of solutions, making use of the semi‐group theory and a fixed point argument. Asymptotic solutions to the invasive species are explored with an exponential scaling. Afterward, the problem is analyzed with traveling wave profiles, for which a region of positive solutions is explored. [ABSTRACT FROM AUTHOR]

Let G be a graph and R = {r1, r2, ..., rk} be an ordered subset of vertices of G, if every two vertices of G have different representation r (v|R) = (d (v, r1) , d (v, r2) , ..., d (v, rk)) with respect to R, then R is said to be a metric-based resolving parameter or resolving set of G and its minimum cardinality is called the metric dimension of graph G. Metric dimension is considered as an important applied concept of graph theory especially in the localization of a network and also in the chemical graph theoretical study of molecular compounds. Therefore, it is hot topic to study for different families of graphs as well. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. In this paper, we determine the metric-based resolving parameter of line graph of a convex polytope Sn, and conclude that it has constant metric dimension but vary with the parity of n. This article presents a measurement of the line graph of a convex polytope, denoted as ( S n). The subsequent section provides the metric dimension of the resulting graph. There are two scenarios pertaining to the metric dimension of a selected graph with respect to the metric dimension. The metric dimension of even cycle-based convex polytopes is three, whereas for other values, the metric dimension is four. [ABSTRACT FROM AUTHOR]

The processing of dielectric materials in the radio frequency field continues to be a concern in engineering. This procedure involves a rigorous analysis of the electromagnetic field based on specific numerical methods. This paper presents an original method for analysing the process of drying wooden boards in a radio frequency (RF) installation. The electromagnetic field and thermal field are calculated using the finite element method (FEM). The load capacity of the installation is also calculated, since the material being heated in the radio frequency heating installations is placed in a capacitor-type applicator. A specific method is created in order to solve the problem related to mass, a quantity which tends to change during the drying of the dielectric. In addition, special consideration is given to issues regarding the coupling of the electromagnetic field and the thermal field, along with aspects pertaining to mass. These are implemented numerically using a program written in the Fortran language, which takes the distribution of finite elements from the Flux2D program, the dielectric thermal module, intended only for the study of RF heating. The results obtained after running the program are satisfactory and they represent a support for future studies, especially if the movement of the dielectric is taken into account. [ABSTRACT FROM AUTHOR]

Adequate mathematical description of magnetization curves is indispensable in engineering. The accuracy of the description has a significant impact on the design of electric machines and devices. The aim of this paper was to analyze the capability of Bézier curves systematically, to describe the nonlinear static magnetic properties of non-oriented electrical steels, and to compare this approach versus the established mathematical descriptions. First, analytic functions versus measurements were analyzed. The Bézier curves were then compared systematically with the most adequate analytic functions. Next, the most suitable orders of Bézier curves were determined for the approximation of nonlinear magnetic properties, where the influence of the range of the input measurement dataset on the approximation process was analyzed. Last, the extrapolation capabilities of the Bézier curves and analytic functions were evaluated. The general conclusion is that Bézier curves have adequate flexibility and significant potential for the approximation and extrapolation of nonlinear properties of non-oriented electrical steels. [ABSTRACT FROM AUTHOR]

Let C k + 1 be a cycle of length k + 1 and C t + 1 be a cycle of length t + 1. A polygon flower with two centers, denoted by F = F (C k + 1 ; P 1 , ... , P k ; C t + 1 ; P k + 1 , ... , P k + t) is obtained by identifying the i th edge of C k + 1 with an edge ei that belongs to an end-polygon of Pi for i = 1 , ... , k , and identifying the j th edge of C t + 1 with an edge ej that belongs to an end-polygon of Pj for j = k + 1 , ... , k + t , where C k + 1 and C t + 1 have a common edge h. In this paper, we determine the order of sandpile group S(F) of F, which can be viewed as generalized of results in paper (Haiyan Chen, Bojan Mohar. The sandpile group of a polygon flower. Discrete Applied Mathematics, 2019). Moreover, the formula and structure for sandpile group of polygon flower can be obtained. Finally, as application of our result, we also present the sandpile group of cata-condensed system with two branched hexagons. [ABSTRACT FROM AUTHOR]

Clustering is an important tool in statistics, machine learning and applied mathematics. This paper considers the clustering model Y=μlT+Z∈ℝp×n, where the noise matrix Z consists of independent sub‐Gaussian entries Zij and the variance Var(Zij)=σij2 may vary across different coordinates. Our aim is to estimate the error between the label vector l and its defined estimator l^. We provide upper bound estimations for the misclassification rate in the sense of expectation and probability, respectively. Finally, some simulations have been carried out to support our theoretical results and illustrate the advantage of our proposed estimator. [ABSTRACT FROM AUTHOR]

We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated Π 1 1 -comprehension and the existence of admissible sets, over weak base theories. Our work extends a previous result on the non-iterated case, which had been conjectured in Montalbán's "Open questions in reverse mathematics" (Bull Symb Log 17(3):431–454, 2011). This previous result has already been applied to the reverse mathematics of combinatorial and set theoretic principles. The present paper is a significant contribution to a general approach that connects these fields. [ABSTRACT FROM AUTHOR]

Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [[1]], economics [[3]], medicine [[5]], ecology [[7]], education [[9]], etc. Conclusions The purpose of this Special Issue was to attract high-quality new papers in the field of applied and computational mathematics for digital environments, offering original solutions to various problems that are relevant and in demand in various fields of human activity. 10.3390/math10224297 21 Demidova L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. I hope that these selected research papers are recognized as important and meaningful by the international scientific community and can form the basis for further research in the field of applied and computational mathematics for digital environments, solving complex problems in various disciplines and application areas. [Extracted from the article]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

This paper deals with a fourth‐order parabolic equation involving variable exponents, subject to Navier boundary conditions. We firstly give an optimal classification on the initial energy for blow‐up or global solutions, which is characterized by the sign of the Nehari energy and the difference between the initial energy and the depth of the potential well. Then, large time estimates of solutions are obtained. The results of the paper extend and complete the ones in "Applied Mathematics Letters 78(2018)141–146." [ABSTRACT FROM AUTHOR]

Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]

The generalized hypergeometric functions in one and several variables and their natural generalizations appear in many mathematical problems and their applications. The theory of generalized hypergeometric functions in several variables comes from the fact that the solutions of the partial differential equations appearing in a large number of applied problems of mathematical physics have been expressed in terms of such generalized hypergeometric functions. In particular, the Kampé de Fériet function (in two variables) has proved its practical utility in representing solutions to a wide range of problems in pure and applied mathematics, statistics, and mathematical physics. In this context, in a very recent paper, Progri successfully calculated the 2 F 2 generalized hypergeometric function for a particular set of parameters and expressed the result in terms of the difference between two Kampé de Fériet functions. Inspired by his work, in the present paper, we obtain three results for a terminating 3 F 2 series of arguments 1 and 2, together with a transformation formula of a 3 F 2 (z) generalized hypergeometric function in terms of the difference between two Kampé de Fériet functions. One application of this result is also provided. The paper concludes with six reduction formulas for the Kampé de Fériet function. Of note, symmetry occurs naturally in the generalized hypergeometric functions p F q and the Kampé de Fériet function involving two variables, which are the two most important functions discussed in this paper. [ABSTRACT FROM AUTHOR]

The enumerative problem of spanning trees of graphs is one of the fundamental problems in the field of graph theory, which has attracted the attention of mathematicians and physicists. For a connected graph G , let T be a spanning tree of G. In this paper, we call T to be a pm - t r e e of G if T contains a perfect matching. Recently, Li and Yan (Applied Mathematics and Computation, 456 (2023), 128125.) gave an explicit expression for the number of pm-trees in linear hexagonal chains on the plane, cylinder and Möbius strip, respectively. In this paper, we extend the results above and obtain the explicit formula for the number of pm-trees in linear polygonal chains with n polygons of 4 k + 2 vertices on the plane, cylinder and Möbius strip, respectively. [ABSTRACT FROM AUTHOR]