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The article explores the conditions under which a specific type of variety, known as a trinomial variety, will have a finite number of automorphism group orbits. Trinomial varieties are defined as the spectrum of trinomial algebras, which are based on certain data. The authors provide examples of classes of varieties that have a finite number of orbits, such as algebraic groups, toric varieties, and spherical varieties. They also examine trinomial hypersurfaces and generalize previous results to prove a sufficient condition for the finiteness of the number of orbits on a trinomial variety. The authors discuss the connection between locally nilpotent derivations and automorphisms of the variety, and provide preliminary information on locally nilpotent derivations and trinomial varieties. The text is technical in nature and may be of interest to researchers studying algebraic geometry. [Extracted from the article]

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]

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nose tip, and the mechanisms underlying the low Mack's second-mode N-factor values at the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy-layer experience appreciable energy amplification for moderate to large nose-tip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the generalized minimal residual method (GMRES) iterative method with a preconditioner corresponding to a simplified Jacobian without the cross-derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over a blunt cone configuration with reduced transition N factor as measured in wind-tunnel experiments. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher-frequency Mack's second-mode instabilities farther downstream and hence can lead to a reduction in the transition N factor. [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]

A novel framework is proposed in this research based on multilevel method to solve the optimal control problem. In recent dacades, the mathematical theory of optimal control has rapidly developed into an important and separate field of applied mathematics. The solution of nonlinear partial differential equations is considerably difficult, and the theory of their optimal control is still an open field in many respects. These optimization problems have found diverse applications in various sciences including electrical engineering, mechanical engineering, and aerospace. Current methods for solving this class of optimal control problems usually fall into two classes: discrete-then-optimization or optimization-then-discrete approaches. The proposed approach, however, does not require discretization as it involves rewriting the optimal control problem as a multi-objective optimization problem followed by its solution with a feedforward single-layer artificial neural network based on learning through by the multi-level Levenberg–Marquardt method. Moreover, the convergence of the approach was discussed and some numerical results are presented. [ABSTRACT FROM AUTHOR]

Here attention is focused on the (1+1)-dimensional Sawada–Kotera (SK) model that is prominent in mathematical physics and engineering to analyze plasmas and coherent systems for communication. Our techniques offer fresh perspectives on the model’s attributes and structure, deepening our comprehension of the underlying dynamics. First, the SK model is reduced to ordinary differential equations by constructing the Lie symmetries and using the associated transformation. Graphs are used to build and display invariant solutions. This strategy has caused the revelation of novel constant solutions that have not been found in the previous works. We offer new understandings of nature and changes observed during the SK derivation by taking advantage of the Lie symmetries powerful tools. Next, the fluctuating layout of proposed framework is examined from several perspectives such as sensitivity and bifurcation analysis. We examined the bifurcation analysis of planar dynamical system by using bifurcation theory. We also include an external periodic perturbation term that breaks regular patterns in the perturbed dynamical system. Graphical structures are provided to display the invariant solutions. The sensitivity of the SK model is determined to be strong after sensitivity analysis under different initial conditions. These results are fascinating, fresh, and conceptually useful for understanding the suggested framework. In mathematics and the applied sciences, forecasting and learning about new technologies are greatly aided by the dynamic aspect of system processing. [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]

The Schrödinger–Korteweg–de Vries (SKdV) system can describe the nonlinear dynamics of phenomena such as Langmuir and ion acoustic waves, which are highly valuable for studying wave behavior and interactions. The SKdV system has wide-ranging applications in physics and applied mathematics. In this article, we investigate the local well-posedness of the SKdV system with Robin boundary conditions and polynomial terms in the Sobolev space. We want to enhance the applicability of this type of SKdV system. Our verification process is as follows: We estimate Fokas solutions for the Robin problem with external forces. Next, we define an iteration map in suitable solution space and prove the iteration map is a contraction mapping and onto some closed ball B (0 , r) . Finally, by the contraction mapping theorem, we obtain the uniqueness solution. Moreover, we show that the data-to-solution map is locally Lipschitz continuous and conclude with the well-posedness of the SKdV system. [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]

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X‐ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid‐state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state‐of‐the‐art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction‐/density matrix‐based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies. [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of the steady-state transmission problem between two Herschel-Bulkley fluids in thin layers with different viscosities, yield limits and power law index. [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]

In this article I argue that i is a quantity associated with the two-dimensional real number plane, whether as a vector, a bi-vector, a point or a transformation (rotation). This position provides a foundation for the complex numbers and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold. [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]

The new types of exact solitons of the space–time fractional nonlinear (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) model are achieved by applying the unified technique and modified extended tanh-expansion function technique. A novel definition of the fractional derivative known as the truncated M-fractional derivative is also used. This model describes both the non-elastic and elastic interactions between internal waves. This model is used to represent intricate nonlinear phenomena like shallow-water waves, plasma physics, and others. The obtained results are in the form of kink, singular, bright, periodic, and dark solitons. The observed results are verified and represented by 2D and 3D graphs. The observed results are not present in the literature due to the use of fractional derivatives. The impact of the truncated M-fractional derivative on the observed results is also represented by graphs. Hence, our observed results are fruitful for the future study of these models. The applied techniques are simple, fruitful, and reliable in solving the other models in applied mathematics. [ABSTRACT FROM AUTHOR]

Long live the vis-viva equation. There is sometimes more than one way of telling a story with the same ending, and this is particularly true in the field of applied mathematics where there are often different ways of obtaining the same result to a given problem, so that what might be lost or not appreciated in one approach can be found and appreciated in another. It is the purpose here to illustrate this by presenting a well-known example drawn from the field of orbital dynamics, namely the development of what is called the Vis-viva equation. This equation is simply an expression relating the square of the velocity of an orbiting object, for example a planet orbiting a sun, to orbit parameters and scientific constants. It is a standard workhorse equation that is used extensively today by orbit control specialists wishing to determine and affect velocities of spacecraft orbiting significantly larger masses, and it was developed from work carried out centuries ago by Gottfried Leibniz (1646 – 1716). The first story will simply acknowledge the equation and how it arose. The second story will present an alternative approach based on calculus, trigonometry, algebra and computations set against the backdrop of an ellipse geometry. This second story leads to the vis-viva equation in disguise, so to speak, and examples of the speeds of two planets, Earth and Mercury, orbiting the Sun will be discussed. Where relevant, the nomenclature of orbit dynamics will be acknowledged. The discussion will involve primarily a planet's orbit velocity of translation and detailed considerations will not be given to effects due to its speed of rotation. [ABSTRACT FROM AUTHOR]

This paper introduces the contents of the second of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue. [ABSTRACT FROM AUTHOR]

In this academic investigation, an innovative mapping approach is applied to complex three coupled Maccari's system to unveil novel soliton solutions. This is achieved through the utilization of M-Truncated fractional derivative with employing the new mapping method and computer algebraic syatem (CAS) such as Maple. The derived solutions in the form of hyperbolic and trigonometric functions. Our study elucidates a variety of soliton solutions such as periodic, singular, dark, kink, bright, dark-bright solitons solutions. To facilitate comprehension, with certain solutions being visually depicted through 2-dimensional, contour, 3- dimensional, and phase plots depicting bifurcation characteristics utilizing Maple software. Furthermore, the incorporation of M-Truncated derivative enables a more extensive exploration of solution patterns. Our study establishes a connection between computer science and soliton physics, emphasizing the pivotal role of soliton phenomena in advancing simulations and computational modelling. Analytical solutions are subsequently generated through the application of the new mapping method. Following this, a thorough examination of the dynamic nature of the equation is conducted from various perspectives. In essence, understanding the dynamic characteristics of systems is of great importance for predicting outcomes and advancing new technologies. This research significantly contributes to the convergence of theoretical mathematics and applied computer science, emphasizing the crucial role of solitons in scientific disciplines. [ABSTRACT FROM AUTHOR]

Rivers, as water resources, are considered an origin of supply for many requirements of urban communities. River networks consist of many branches that connect at river confluences. Because pollutants usually enter the river in different situations from the upstream branches of river intersections, it is essential to investigate the mixing process through the river network. For this purpose, precise analytical and numerical models should be used to evaluate this phenomenon quantitatively. Based on the cell concept and separation of advection and dispersion operations, this study developed a new analytical relationship through the confluences of rivers. A physical model of the Y-shaped junction was created in the laboratory, and four inlet flow discharges 25, 21, 12, and 9 l/s and three initial concentrations of sodium chloride solution 80, 160, and 200 g/L were selected as study parameters. Then, the concentration-time curves along the sub-branches, the intersection, and the downstream of the river's main channel were taken at 2-second intervals. In order to evaluate the efficiency of the analytical model, the parameters of the model were first calculated by coding based on its framework and using the least squares method. Then the analytical curves were outlined versus the experimental results. It was observed that the presented model could produce double-peaked curves and also cover experimental data series precisely. The dispersion coefficients and the related time parameter in the presented model (T) were found to increase by moving downstream of the river junction. It was also observed that the Peclet numbers (Pe = xu/D ) are increased like dispersion coefficients by increasing the distance downstream of the confluence. In addition, the research results showed that increasing the residence time parameter in dispersion cells (T) causes growth in the dispersion coefficient, despite increasing the residence time in advection cells (β), compelling the movement of the pollutant breakthrough curves. [ABSTRACT FROM AUTHOR]

Aviation is one of the most global industries, and if we can model and predict a country’s air transportation flow and indicators ahead of time, we may be able to use it as a key decision-making tool for the management and operation process. This study proposes a new modeling, and prediction method that employs both fractional calculus and Multi Deep Assessment Methodology (MDAM) techniques. For the application, air passengers carried, air freight, available seat kilometers, number of flights, destination points, international travelers, international destination points, and international flight data between 2011 and 2019 for eight countries with the busiest airports were chosen. As a result, the highest modeling error was discovered to be Germany’s air transport freight factor expressed as a percentage of 1,59E-02. The percentage of predictions with errors less than 10% was 90.278. We also compared the performance of two different MDAM methodologies. The novel MDAM wd methodology proposed in this paper has a higher accuracy in aviation factors prediction and modeling.

Traditional finite element analysis methods have the problem of expensive and unstable band structure diagram calculation when generating phononic crystals. Therefore, this study combines back propagation neural networks with ocean predator algorithms to optimize the geometric structure of phononic crystals. The results show that the coefficient of determination for the predicted bandgap width and lower bound of Model 3 is 1.00, which is better than the comparison model. However, Models 2 and 5 have poor predictive performance for bandgap width due to overfitting during actual training. Therefore, after using the ocean predator algorithm for hyperparameter adjustment, it is found that the maximum number of failures in the validation set of Model 5 is 30, the number of hidden layer nodes is 30, and after 500 experiments, the average error of the bandgap width is 5.26%, and the average error of the lower bound of the bandgap is 1.33%. The average error of the bandgap width after hyperparameter adjustment is 4.89%, and the average error of the lower bound of the bandgap is 1.21%, both of which are effectively reduced and better than the comparison model. Overall, the combination model has high computational efficiency and stability in phononic crystal optimization and can be practically applied in the design and optimization of phononic crystal geometric structures. [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]

This document is a foreword to a special issue of the journal "Mathematics & Mechanics of Solids" dedicated to Professor Alain Goriely. The foreword highlights Professor Goriely's achievements and contributions to the field of mathematics and mechanics, particularly in the areas of nonlinear elasticity and biological growth. It also mentions his involvement in scientific dissemination and his support for junior researchers and graduate students. The special issue includes articles on various topics related to Professor Goriely's research interests, such as theories of rods and shells, materials modeling, energy, biomechanics, and mathematical foundations of mechanics. The foreword expresses the hope that Professor Goriely will find the collection inspiring and wishes him many more successful years of research. [Extracted from the article]

This study delves into the structure and properties of left inverse zero divisor bands within semigroups, identifying their maximal forms and broadening the theoretical landscape of semigroup analysis. A significant focus is placed on the automorphisms of a semigroup S of centralizers of idempotent transformations with restricted range, revealing that these automorphisms are inner ones and induced by the units of S. Additionally, we establish that the automorphism group Aut (S) is isomorphic to U S , the group of units of S. These findings extend previous results on semigroups of transformations, enhancing their applicability and providing a more unified theory. The practical implications of this work span multiple fields, including automata theory, coding theory, cryptography, and graph theory, offering tools for more efficient algorithms and models. By simplifying complex concepts and providing a solid foundation for future research, this study makes significant contributions to both theoretical and applied mathematics. [ABSTRACT FROM AUTHOR]

This paper studies the analytical solution to the Fractional Differential Equations (FDEs) under uncertainty. Fuzzy differential equations are one of the emerging topics in the present era of research, where we have found an effective combination of FDEs with fuzziness. The Homotopy Analysis Transform Method (HATM) with the Caputo fractional derivative is applied in this work to find the analytical fuzzy solution of two fuzzy FDEs. One of the interesting parts of this study is that we have found upper and lower fuzzy solutions for both fuzzy FDEs. The different graphical representations that have been presented for both examples show that there is a symmetry relation between the upper and lower-cut fuzzy solutions. In this method, the region and rate of convergence of the solution series are controlled by the auxiliary parameter r-cut. This paper shows that the proposed method is reliable and efficient in determining the fuzzy solutions of the FDEs in applied mathematics and engineering [ABSTRACT FROM AUTHOR]

We consider semilinear elliptic equations of the form Δu+f(|x|,u)=0 on RN with f(|x|,u)=q(|x|)g(u). These type of equations arise in various problems in applied mathematics, and particularly in the study of population dynamics, solitary waves, diffusion processes, and phase transitions. We show that under suitable assumptions on the nonlinearity f, there exists an oscillating radial solution converging to a zero of the function g. We also study the oscillating and limiting behavior of this solution. [ABSTRACT FROM AUTHOR]

This article tells the story of the first international topological conference in Moscow (1935), an outstanding event that, for the first time, brought together the most notable American, European, and Soviet mathematicians, including those who would later play decisive roles in the mathematization of economics: John von Neumann, Leonid Kantorovich, and Albert W. Tucker. The fact that Kantorovich was in contact with von Neumann and his closest colleagues, Solomon Lefschetz and Garrett Birkhoff, is hardly appreciated in the histories of mathematics and mathematical economics. Their brief academic exchange was interrupted by the increasing international isolation of Soviet mathematics and by the wars that ensued. The article provides a historical account of the conference and traces the intellectual and personal affinities of Soviet and non-Soviet mathematicians, as well as their conceptual innovations. It argues that the conference, as a singular event linking several research communities, mattered for the development of various formal frameworks and their dissemination, contributing to the intellectual landscape in which postwar mathematical economics could emerge. The article calls for a deeper analysis of conceptual affinities and motivations in applying mathematics to economics and for a more nuanced narrative linking these motivations to social and political contexts of economic modeling. [ABSTRACT FROM AUTHOR]

This article studies the entanglements of mathematical economics in Brazil by delving into the emergence of a scientific community identified with the subject at the Instituto de Matemática Pura e Aplicada (IMPA). It traces how networks built since IMPA's early years in the 1950s made economics a viable alternative to applied mathematics in an institute mostly dedicated to research in pure mathematics. The article examines how interests in mathematical economics remained active during IMPA's expansion beginning in the late 1960s. This process culminated with the creation of the mathematical economics graduate program at IMPA in 1980 by Aloisio Araujo. The article follows how the program could build strong connections to the Escola de Pós-Graduação em Economia (EPGE), an important department of economics in Brazil, helping to shape recent developments in the center. The article thus aims to reveal how historical connections and entwinements of economics and mathematics groomed at IMPA have affected recent developments in the Brazilian economics community. [ABSTRACT FROM AUTHOR]

This article serves as a preface to a special issue of the International Game Theory Review, dedicated to game theory and optimization in honor of Pierre Bernhard. It highlights Pierre's significant contributions to the scientific community, particularly in applied mathematics and game theory. The special issue contains 10 contributions from friends and collaborators of Pierre, covering a range of topics such as evolutionary economic models, dynamic game-theoretic frameworks, and mathematical biology. The article also includes testimonials from colleagues and friends, providing insight into Pierre's impact on their careers and his role in the development of INRIA-Sophia Antipolis. [Extracted from the article]

Recently, the problem of multitasking scheduling has raised a lot of interest in the service industries. Hall et al. (Discrete Applied Mathematics, 2016) proposed a shared processing multitasking scheduling model which allows a team to continue to work on the primary tasks while processing the routinely scheduled activities as they occur. With a team being modeled as a single machine, the processing sharing of the machine is achieved by allocating a fraction of the processing capacity to routine jobs and the remaining fraction, which we denote as sharing ratio, to the primary jobs. In this paper, we generalize this model to parallel machines and allow the fraction of the processing capacity assigned to routine jobs to vary from one to another. The objectives are minimizing makespan and minimizing the total completion time of primary jobs. We show that for both objectives, there is no polynomial time approximation algorithm unless P=NP if the sharing ratios are arbitrary for all machines. Then we consider the problems where the sharing ratios on some machines have a constant lower bound. For each objective, we analyze the performance of the classical scheduling algorithms and their variations and then develop a polynomial time approximation scheme when the number of machines is a constant. [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]

Both mathematics and science exhibit a reciprocally advantageous and close relationship. The undeniable significance of mathematics in diverse scientific fields, including electrical engineering, physics, biology, and medicine, is beyond dispute. Due to the multitude of applications of mathematical biology in the present era, scholars have demonstrated a marked intrigue in this specific realm. In the past few years, there has been a discernible rise in the application of different fractional operators as a method of expressing the given problem. The utilization of this approach has gained significant acceptance as a customary technique for examining the propagation of epidemics. The current investigation explores innovative fractional operators in the framework of a model for an infectious disease. The mechanical characteristics of the model with fractional orders are established by employing diverse numerical methods and adjusting parameters related to time fractional components. To substantiate the theoretical discoveries, computational simulations are implemented for the suggested approach over a variety of fractional orders, displaying the outcomes of both fractional and fractal orders. We employed a highly efficient numerical methodology to obtain solutions for both the model and simulations. Additionally, we provide the criteria for the existence of a solution to the proposed epidemic model, and we determine the reproductive number under specific state conditions of the analyzed dynamic system. A fractional-order model of infectious disease is proposed to be analyzed through simulations, aiming to ascertain the possible efficacy of disease transmission within the community. These aspects are tackled through the application of the Banach contraction principle. Moreover, we have proposed future research directions incorporating the utilization of a novel hybrid fractional operator. Fractional calculus emerges as a significant area of investigation within applied mathematics, offering valuable tools for problem-solving across diverse fields such as medicine, science, and engineering. Recent scholars have emphasized the importance of mathematical techniques, especially those related to fractional and integer calculus modeling, as extremely advantageous when examining the dynamics of different disease models. The utilization of the fractional operator allows for the investigation of the dynamic impact of diseases on society, providing valuable insights for analysis, decision-making, and disease control. [ABSTRACT FROM AUTHOR]

This article aims to discuss the mathematical knowledge and practices carried out by bricklayers in the municipality of Amapá, State of Amapá, Brazil, aiming to reinforce that applied mathematics is highly effective in building empirical knowledge. The work also aims to describe how this mathematical knowledge and practices are transmitted and passed on by these families. The research has a qualitative, exploratory, and descriptive nature. To this end, direct observation was carried out through in place visits to works being carried out in the municipality. The research data were obtained through informal conversations with a small group of eight bricklayers, whose inclusion and exclusion group was the oldest bricklayers in the municipality and who have been working in the area for the longest time. The results obtained point to a rich set of mathematical knowledge (empirical and traditional) that has been acquired and transmitted over the years. Furthermore, the data leads to reflection on the pedagogical practice of teaching and learning mathematics and the importance of studying culture and its applicability in the classroom as a way of valuing and maintaining local traditions and mathematical knowledge. [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]

In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions. [ABSTRACT FROM AUTHOR]

This article describes a non-parametric clustering algorithm with an outlier removal step. Our method is based on tools from topological data analysis: we define a new filtration on metric spaces which is a variant of the Vietoris-Rips filtration that adds information about the points' nearest neighbor to the persistence diagram. We prove a stability theorem for this filtration, and evaluate our method on point cloud and graph datasets, showing that it can compete with state-of-the-art methods while being non-parametric. [ABSTRACT FROM AUTHOR]

This article, published in Mathematical Notes, discusses Meixner multiple orthogonal polynomials on interlacing lattices. The article explores the existence and normality of these polynomials, as well as their applications in number theory, approximation theory, random matrix theory, and operator theory. The authors provide proofs and formulas related to these polynomials and their properties. The article concludes with a discussion of the perfectness of the system of positive measures and the uniqueness of the polynomial of multiple orthogonality. [Extracted from the article]

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]

The nonlinear evolution equations (NLEEs) play a significant role in applied mathematics, including ordinary and partial differential equations, which are frequently used in many disciplines of applied sciences. The Drinfeld–Sokolov–Wilson (DSW) equation and the Burgers equation are the fundamental equations occurring in various areas of physics and applied mathematics, such as nonlinear acoustics and fluid mechanics. The new generalized (G ′ / G) -expansion method is an effective and more powerful mathematical tool for solving NLEEs arising in applied mathematics and mathematical physics. In this article, we investigate further exact solutions as well as soliton solutions to these couple of nonlinear evolution equations by executing the new generalized (G ′ / G) -expansion method. A large number of soliton solutions, including single soliton, bell-shaped soliton, kink-shaped soliton, singular kink soliton, singular soliton, periodic soliton, irregular periodic soliton solutions, and others, have been retrieved. Each of the derived solutions includes an explicit function of the variables in the equations under consideration. We provide some 3D plots to visualize and realize the characteristics of these solutions. It has been established that the suggested techniques are more potential and successful at obtaining soliton solutions for nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

This paper introduces the contents of the first of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue. [ABSTRACT FROM AUTHOR]

We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman–Ricci curvature.

This article, titled "Continuity Criteria for Locally Bounded Homomorphisms of Certain Lie Groups," discusses the continuity of locally bounded homomorphisms in Lie groups. The authors prove that a locally bounded homomorphism of a connected Lie group is continuous if and only if it is continuous on a closed supplementary subgroup. The article provides a theorem and a proof to support this claim. The research was partially supported by the Moscow Center for Fundamental and Applied Mathematics, and the author declares no conflict of interest. [Extracted from the article]