Search

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]

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]

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]

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]

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]

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]

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]

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 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]

This document is an editorial on the special issue of Mathematical Methods in the Applied Sciences (MMAS) for the International Conference of Numerical Analysis and Applied Mathematics 2021 (ICNAAM 2021). The special issue includes the best papers presented at ICNAAM 2021, which were selected through an international peer-review process. The author expresses gratitude to the Editor-in-Chief of MMAS, the anonymous reviewers, and Wiley for their contributions to the special issue. The document concludes by inviting readers to enjoy reading the special issue and find inspiration for their own research. [Extracted from the article]

In this paper, we provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs in two different ways: (1) We represent spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper-Hafnians (orders and signs are not considered); (2) We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam (2004) [1] and Pfaffian matrix tree theorem by Masbaum and Vaintrob (2002) [15]. • We provide generating functions and counting formulas for spanning trees and spanning forests in hypergraphs through Berezin-Grassmann integrals on Zeon algebra and hyper- Hafnians when orders and signs are not considered. • We establish a Hyper-Pfaffian-Cactus Spanning Forest Theorem through Berezin-Grassmann integrals on Grassmann algebra (orders and signs are considered), which generalizes the Hyper-Pfaffian-Cactus Theorem by Abdesselam [Advances in Applied Mathematics (2004) Vol. 33: 51-70] and Pfaffian matrix tree theorem by Masbaum and Vaintrob [Internat. Math. Res. Notices (2002) Vol. 27: 1397-1426]. [ABSTRACT FROM AUTHOR]