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This article, titled "Historic Behavior in Nonautonomous Rock-Paper-Scissors Dynamics," explores the concept of historic behavior in dynamical systems. The author challenges the widely held belief that replicator equations in evolutionary game theory satisfy the "Folk Theorem of Evolutionary Game Theory." The paper proposes a class of replicator equations that exhibit historic behavior, where the time averages of the orbit do not converge. The article also presents some auxiliary results and provides a proof for the main theorem. The research was supported by ongoing institutional funding, and the author declares no conflicts of interest. [Extracted from the article]

Abstract: The study used the simulated e-paper to investigate how the bending radius of curvature (−10cm, plane, and 10cm) and 12 text/background color-combinations of e-paper affect subjects’ visual performance and subjective preference under various ambient illuminance conditions (200 and 500lx). Analysis results indicated that the bending curvature and ambient illuminance did not significantly affect subjects’ visual performance. However, subjects visual performance differed significantly for different text/background color combinations of the simulated e-paper. When the background color of the simulated e-paper was set to yellow-like condition and the luminance of the text was low (2.2 and 4.6cd/m2), subjects’ visual performance was best. Regarding the subjective preferences of subjects, the results of this research also demonstrated that the bending curvature, text/background color combinations and ambient illuminance all significantly affected the subjective preferences of subjects. Subjects exhibited the best preference under the following settings: bending curvature of the simulated e-paper set to plane; background color of the simulated e-paper set to yellow-like condition and low text luminance (2.2 or 4.6cd/m2); high ambient illuminance (500lx). [Copyright &y& Elsevier]

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

A simple scheme that achieves the capacity and the reliability function of the wideband Costa dirty-paper channel is proposed. The scheme can be interpreted as an opportunistic version of pulse position modulation (PPM). This interpretation suggests a natural generalization of the scheme which we show to achieve the capacity per unit cost of Gel'fand-Pinsker channels with a zero-cost input letter. [ABSTRACT FROM AUTHOR]

In this tutorial note we consider the class of non-convex semi-infinite optimization problems which are defined by (one or) finitely many objective functions as well as infinitely many constraints in a finitedimensional space. We present an overview of recent results on the so-called p-power transformation which changes the original problem equivalently locally around a solution point. This transformation is a convexification procedure for the Lagrangian where the functions in the original problem are substituted by their p-th powers. As a consequence, the convexity of the so-transformed Lagrangian allows the application of local duality theory and corresponding solution methods locally around this solution point of the original problem. [ABSTRACT FROM AUTHOR]

In the paper Patterson – Wiedemann construction revisited by Gangopadhyay et al. (2006), modifying an idempotent function f : G F ( 2 21 ) → G F ( 2 ) , which corresponds to a ( 337 , ( 127 ) ( 49 ) ) -interleaved sequence whose columns are either all 0’s or 1’s, a balanced function h having Δ h < 2 21 + 1 2 is obtained. In this short note, we find that Δ f is computed incorrectly in their paper (leading to Δ h ≮ 2 21 + 1 2 ) and correct their result by disproving the related conjecture for the 21-variable balanced functions. [ABSTRACT FROM AUTHOR]

In this paper, we collect some recent results on the approximation properties of generalized sampling operators and Kantorovich operators, focusing on pointwise and uniform convergence, rate of convergence, and Voronovskaya-type theorems in weighted spaces of functions. In the second part of the paper, we introduce a new generalization of sampling Durrmeyer operators including a special function ρ which satisfies certain assumptions. For the family of newly constructed operators, we obtain pointwise convergence, uniform convergence and rate of convergence for functions belonging to weighted spaces of functions. [ABSTRACT FROM AUTHOR]

Due to the rapid development of a global navigation satellite system and the rapid growth of ships, the traditional control algorithms are not suitable; hence, the longitudinal rocking phenomenon generated by external disturbances is more serious when a ship is sailing. This paper takes a mathematical model of the super large oil tanker "KVLCC2"'s longitudinal motion as the controlled plant, establishing a multi-input multi-output instability control system, using the root trajectory shaping method and a weighting matrix to ensure the stability of its transfer function's mathematical model. An improved closed-loop gain-shaping algorithm is utilized to design a simple robust controller. And a dual nonlinear positive feedback control algorithm is added to the control system to further improve the controller's pitching stabilization performance and reduce the controller's output energy. In order to verify that the controller has a consistently strong robustness, simulation experiments are carried out by adding a level 6, 7 and 8 wind wave model and a perturbation link to the control system, respectively. The results show that when the value of the hysteresis constant is taken as 0.25, the output values of the heave displacement and the pitch angle are greatly reduced, and the longitudinal rocking phenomenon is significantly improved. The dual nonlinear positive feedback control algorithm enhances the ship's pitching stabilization control capability and further reduces the controller's output energy, which provides technical support for the smooth and efficient sailing of super large ships under changing sea conditions. Combined with a global navigation satellite system, this algorithm provides a new method for pitching stabilization control of super large ships. [ABSTRACT FROM AUTHOR]

The article examines papers and lectures on statistical applications of methods of weak convergence presented in a Statistical Services Centre (SSC) session. One lecturer discussed two kinds of data which are d-dimensional random variables and random variables indexed by Zd. It adds that the so-called Theorem 2 of another lecturer and its method of proof can be used in statistical applications related to aggregate data resulting from irreducible positive recurrent Markov chains.

In this paper, we consider and study in detail the generalized Fox–Wright function Ψ ˜ q p introduced in our recent work as an extension of the Fox–Wright function Ψ q p . This special function can be seen as an important case of the so-called I-functions of Rathie and H ¯ -functions of Inayat-Hussain, that in turn extend the Fox H-functions and appear to include some Feynman integrals in statistical physics, in polylogarithms, in Riemann Zeta-type functions and in other important mathematical functions. Depending on the parameters, Ψ ˜ q p is an entire function or is analytic in an open disc with a final radius. We derive its basic properties, such as its order and type, and its images under the Laplace transform and under classical fractional-order integrals. Particular cases of Ψ ˜ q p are specified, including the Mittag-Leffler and Le Roy-type functions and their multi-index analogues and many other special functions of Fractional Calculus. The corresponding results are illustrated. Finally, we emphasize the role of these new generalized hypergeometric functions as eigenfunctions of operators of new Fractional Calculus with specific I-functions as singular kernels. This paper can be considered as a natural supplement to our previous surveys "Going Next after 'A Guide to Special Functions in Fractional Calculus': A Discussion Survey", and "A Guide to Special Functions of Fractional Calculus", published recently in this journal. [ABSTRACT FROM AUTHOR]

We consider the class S(λ, β, τ) of convergent for all x ≥ 0 Taylor-Dirichlet type series of the form F(x) = X+∞ n=0 bnexλn+τ(x)βn, bn ≥ 0 (n ≥ 0), where τ: [0,+∞) → (0,+∞) is a continuously differentiable non-decreasing function, λ = (λn) and β = (βn) are such that λn ≥ 0, βn ≥ 0 (n ≥ 0). In the paper we give a partial answer to a question formulated by Salo T.M., Skaskiv O.B., Trusevych O.M. on International conference "Complex Analysis and Related Topics" (Lviv, September 23-28, 2013) ([2]). We prove the following statement: For each increasing function h(x): [0,+∞) → (0,+∞), h′(x) ↗ +∞ (x → +∞), every sequence λ = (λn) such that X+∞ n=0 1 λn+1 - λn < +∞ and for any non-decreasing sequence β = (βn) such that βn+1 - βn ≤ λn+1 - λn (n ≥ 0) there exist a function τ (x) such that τ ′(x) ≥ 1 (x ≥ x0), a function F ∈ S(α, β, τ), a set E and a constant d > 0 such that h-meas E := R E dh(x) = +∞ and (∀x ∈ E): F(x) > (1 + d)μ(x, F), where μ(x, F) = max{|an|exλn+τ(x)βn: n ≥ 0} is the maximal term of the series. At the same time, we also pose some open questions and formulate one conjecture. [ABSTRACT FROM AUTHOR]

This paper explores cost-effective alternatives for resource-constrained environments in the context of language models by investigating methods such as quantization and CPUbased model implementations. The study addresses the computational efficiency of language models during inference and the development of infrastructure for text document processing. The paper discusses related technologies, the CLARIN-PL infrastructure architecture, and implementations of small and large language models. The emphasis is on model formats, data precision, and runtime environments (GPU and CPU). It identifies optimal solutions through extensive experimentation. In addition, the paper advocates for a more comprehensive performance evaluation approach. Instead of reporting only average token throughput, it suggests considering the curve’s shape, which can vary from constant to monotonically increasing or decreasing functions. Evaluating token throughput at various curve points, especially for different output token counts, provides a more informative perspective. [ABSTRACT FROM AUTHOR]

This paper investigates diverse classes of multidimensional Weyl and Doss ρ -almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ -almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl-p-almost periodic functions is introduced, where the exponent p > 0 is general. This paper delves into the abstract Volterra integro-differential inclusions, showcasing the practical implications of the derived results. This work builds upon the extensions made in the realm of Levitan N-almost periodic functions, contributing to the broader understanding of mathematical functions in diverse measure spaces. [ABSTRACT FROM AUTHOR]

This paper describes the development and optimization plans for the China Railway Express (CR Express). As a new type of international land transport organization, CR Express has emerged with the continuous expansion of China toward European investment and trade, and in particular, has expanded with the continuous progress of the One Belt and One Road (OBOR) initiative. In addition to improving the service quality of CR Express, the operating costs must be reduced for developing "smart railways" that serve "smart cities". We propose a dualobjective-based function mathematical optimization model; the satisfaction of the cargo owner is considered, and the timeliness, transportation capacity, and goods category constraints of CR Express transportation are designed. Moreover, we present the normalized equivalent method of the two-objective function of the model. Finally, a case study is conducted against the background of certain trains in the western corridor of CR Express to validate the effectiveness of the model and research methods proposed in this study. [ABSTRACT FROM AUTHOR]

Economic dispatch is an important issue in the management of power systems and is the current focus of specialists. In this paper, a new metaheuristic optimization algorithm is proposed, named Social Small Group Optimization (SSGO), inspired by the psychosocial processes that occur between members of small groups to solve real-life problems. The starting point of the SSGO algorithm is a philosophical conception similar to that of the social group optimization (SGO) algorithm. The novelty lies in the introduction of the small group concept and the modeling of individuals' evolution based on the social influence between two or more members of the small group. This conceptual framework has been mathematically mapped through a set of heuristics that are used to update the solutions, and the best solutions are retained by employing a greedy selection strategy. SSGO has been applied to solve the economic dispatch problem by considering some practical aspects, such as valve-point loading effects, sources with multiple fuel options, prohibited operating zones, and transmission line losses. The efficiency of the SSGO algorithm was tested on several mathematical functions (unimodal, multimodal, expanded, and composition functions) and on power systems of varying sizes (ranging from 10-units to 1280-units). The SSGO algorithm was compared with SGO and other algorithms belonging to various categories (such as: evolution-based, swarm-based, human behavior-based, hybrid algorithms, etc.), and the results indicated that SSGO outperforms other algorithms applied to solve the economic dispatch problem in terms of quality and stability of the solutions, as well as computation time. [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]

Functionally graded materials (FGMs) are revolutionizing various industries with their customizable properties, a key advantage over traditional composites. The rise of voxel-based 3D printing has furthered the development of FGMs with complex microstructures. Despite these advances, current design methods for FGMs often use abstract mathematical functions with limited relevance to actual performance. Furthermore, conventional micromechanics models for the analysis of FGMs tend to oversimplify, leading to inaccuracies in effective property predictions. To address these fundamental deficiencies, this paper introduces new gradation functions for functionally graded beams (FGBs) based on bending strain energy density, coupled with a voxel-based design and analysis approach. For the first time, these new gradation functions directly relate to structural performance and have proven to be more effective than conventional ones in improving beam performance, particularly under complex bending moments influenced by various loading and boundary conditions. This study reveals the significant role of primary and secondary gradation indices in material composition and distribution, both along the beam axis and across sections. It identifies optimal combinations of these indices for enhanced FGB performance. This research not only fills gaps in FGB design and analysis but also opens possibilities for applying these concepts to other strain energy density types, like shearing and torsion, and to different structural components such as plates and shells. [ABSTRACT FROM AUTHOR]

Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely the Maxwell–Boltzmann distribution, the pathway distribution, and the Mittag-Leffler distribution. Moreover, a natural generalization of the Maxwell–Boltzmann velocity distribution is discussed. Furthermore, an explicit evaluation of the reaction rate integral in the high-energy cut-off case is carried out. Generalized special functions of mathematical physics like Meijer's G-function and Fox's H-functions and their utilization in mathematical physics are the prime focus of this paper. [ABSTRACT FROM AUTHOR]