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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 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]

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]

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 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 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]

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]

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]

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 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 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 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]

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]

Correction to: Transport in Porous Media (2024) 151:55–84https://doi.org/10.1007/s11242-023-02033-0. There are three numbers in Table 2 of the original paper that were incorrect. Specfically, the value of the density of hydrogen (H2) for the DB model and the values of density and viscosity of H2 for the TOUGH2 model listed in Table 2 of the original paper were incorrect. (Table presented.) Properties of the H2-water upconing system for comparison against the DB model. Property DB model Used for TOUGH2 Gas cap thickness, total reservoir thickness, and radial extent (outer radius) of the reservoir Infinite, infinite, infinite 50 m, 100 m (with open boundary at bottom), 100 m (open boundary condition) Porosity (ϕ) 0.10 0.10 Permeability (kH) 1.0 × 10−12 m2 1.0 × 10−12 m2 Permeability (kV) 1.0 × 10−12 m2 1.0 × 10−12 m2 Relative permeability (krel) Not applicable Linear with Slr = 0.99 Distance from well to H2-water interface (d) 10 m 10 m Extraction rate of rate of H2 (Qm) − 5.5 kg s−1 − 5.5 kg s−1 Density of water 996 kg m−3 996 kg m−3 Density of H2 7.32 kg m−3 7.87 kg m−3 Viscosity of water 6.54 × 10−4 Pa s 5.11 × 10−4 Pa s Viscosity of H2 9.31 × 10−6 Pa s 9.53 × 10−6 Pa s A corrected Table 2 is shown below. The erroneous values in Table 2 were not used in any of the modeling and simulation. Accurate values for density and viscosity in the modeling and simulation come from CoolProp for the DB model and from EOS7CH for the TOUGH2 simulations.

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]

Appell's functions F1-F4 turned out to be particularly useful in solving a variety of problems in both pure and applied mathematics. In literature, there have been published a significant number of interesting and useful results on these functions. In this paper, we prove that the branched continued fraction, which is an expansion of ratio of hypergeometric functions F2converges uniformly to a holomorphic function of two variables on every compact subset of some domain of C²; and that this function is an analytic continuation of such ratio in this domain. As a special case of our main result, we give the representation of hypergeometric functions F2 by a branched continued fraction. To illustrate this, we have given some numerical experiments at the end. [ABSTRACT FROM AUTHOR]

This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm's behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature. [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]

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]

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]

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]

This document is a preface for the second special issue of the Quarterly of Applied Mathematics, which is dedicated to Bob Pego on the occasion of his retirement from Carnegie Mellon University. The preface mentions that in addition to the papers listed in the first special issue, a paper by John Ball will be included in this issue, along with a corrigendum for a paper by Murray and Wilcox. The document also provides information about the author, Govind Menon, and acknowledges support from the National Science Foundation. [Extracted from the article]

In this paper we present a novel method for solving the shallow-shelf equations in the presence of grounding lines. The shallow-self equations are a two-dimensional system of nonlinear elliptic PDEs with variable coefficients that are discontinuous across the grounding line, which we treat as a sharp interface between grounded and floating ice. The grounding line is “reconstructed” from ice thickness and basal topography data to provide necessary geometric information for our cut-cell, finite volume discretization. Our discretization enforces jump conditions across the grounding line and achieves high-order accuracy using stencils constructed with a weighted least-squares method. We demonstrate second and fourth order convergence of the velocity field, driving stress, and reconstructed geometric information.

Spurred by the influential work of Viola (Journal of Computing 2012), the past decade has witnessed an active line of research into the complexity of (approximately) sampling distributions, in contrast to the traditional focus on the complexity of computing functions. We build upon and make explicit earlier implicit results of Viola to provide superconstant lower bounds on the locality of Boolean functions approximately sampling the uniform distribution over binary strings of particular Hamming weights, both exactly and modulo an integer, answering questions of Viola (Journal of Computing 2012) and Filmus, Leigh, Riazanov, and Sokolov (RANDOM 2023). Applications to data structure lower bounds and quantum-classical separations are discussed. This is an extended abstract. The full paper can be found at https://arxiv.org/abs/2402.14278.

Summary: This special issue on the Pervasive Nature of HPC (PN‐HPC) collects an extension of the most valuable works presented at the sixth Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP‐22), held in Gdansk (Poland) in September 2022, jointly with the 14th conference on Parallel Processing and Applied Mathematics (PPAM‐22). New original papers related to the workshop themes are also included. The final aim is to provide a glimpse of the current state of knowledge related to the development of efficient methodologies and algorithms for HPC systems with multiple forms of parallelism. [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]

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]

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]

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.

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]

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]

In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite–Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs. [ABSTRACT FROM AUTHOR]

This article delves into the intricate realm of literary translation through a thorough qualitative evaluation of Jayyusi and Le Gassick's rendition of Emile Habibi's novel, The Secret Life of Saeed The Pessoptomist. Given the novel's 'subaltern' nature, deeply entrenched in indigenous language and culture, the study aims to scrutinize the translation's validity through the lens of postcolonial translation theory, as represented by Lawrence Venuti's foreignizing perspective. Central to this scrutiny is the investigation of the translation's impact on the novel's linguistic, semantic, and cultural texture. Employing Antoine Berman's 'système de déformation des textes', known as negative analytic, the analysis unveils pervasive deforming tendencies, underscoring the extensive domestication and alteration to which the novel was subjected. This exploratory investigation contributes to the ongoing discourse in postcolonial studies, highlighting that translation serves as a fertile ground for both subversion and manipulation, especially when applied to narratives believed as belonging to subordinate cultures. [ABSTRACT FROM AUTHOR]

We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations. [ABSTRACT FROM AUTHOR]