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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]

The aim of this research was to analyze the level of mathematical understanding based on the mathematical connections made by a group of Mexican High School students when solving mathematical tasks related to the concepts of equation and linear function. The study employed the thinking aloud method to collect data, whereby students verbalized their thought processes while solving three mathematical tasks, followed by answering some final questions. The collected data were analyzed using a simplified version of thematic analysis based on a preliminary framework adopted in this research. The findings revealed that students demonstrated different levels of mathematical understanding depending on the types of mathematical connections they made. Moreover, these outcomes facilitated the refinement of the preliminary framework, providing a more precise set of indicators for each tier of mathematical understanding. These indicators can be valuable resources for educators and researchers, offering guidance in developing instructional strategies aimed at promoting higher levels of mathematical understanding within the classroom. [ABSTRACT FROM AUTHOR]

The paper examines entire solutions of differential equations of the Briot–Bouquet type. It is shown that (under some conditions satisfied by the polynomials and ) all entire transcendental solutions of such equations are quasipolynomials. [ABSTRACT FROM AUTHOR]

An HFMD outbreak spread over the city of Hải Phòng from summer 2011 to autumn 2012. This epidemic was chosen because it was the very first HFMD epidemic in North Vietnam, eliminating thus interferences with previous outbreaks. This epidemic displayed three separate waves. A complete dataset was collected for more than 9500 patients during this period, which enabled us to analyze this epidemic at different scales. Access to the healthcare system was crucial during this period, which was possible due to a reorganization of the system in February–March 2012. An analysis at the commune level enabled us to track the epidemic along certain communication routes. The three-waves structure reveals a wide disparity at the district level. We developed a mathematical model showing high accuracy at the adjustment of data for both the total number of cases and for the number of cases per week. As a consequence, the model was able to accurately determine the dates of the beginning and end of each wave and to show that they overlapped. Using mathematical functions associated with this model, it was possible to calculate the probability for a patient to belong to a specific wave. [ABSTRACT FROM AUTHOR]

This study looks closely into the analysis of the variation of constants formula given by Φ (t) = S (t) Φ (0) + ∫ 0 t S (t − σ) F (σ , Φ (σ)) d σ , for t ∈ [ 0 , T ] , T > 0 , within the context of modular function spaces L ρ . Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces L p (·) . Specifically, the study examines these spaces under certain conditions applied to the exponent function p (·) and the functions F as well as the semigroup S (t) , utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in L p (·) . [ABSTRACT FROM AUTHOR]

The objective of this case study was to identify the role of finger gestures in learning mathematics informally during play, especially in sociocultural settings. A mathematical activity involving addition was qualitatively analyzed at a Japanese preschool. We explored how the process of subjectification and objectification contributed to a mathematical activity at a Japanese preschool and how the role of preschoolers' finger gestures changed during the process of learning mathematics. We utilized Radford's theoretical construct of joint labor and analyzed Japanese preschool children's mathematical behaviors from a sociocultural perspective. The subjects were 15 Japanese preschool children and their teacher. We relied on both Radford's methodology and a microgenetic approach for the analysis. We found that subjectification and objectification proceeded in the scene of the conversations regarding addition; observing joint labor in a classroom activity offered valuable insights into these processes. In the activity, the children actively extended their practice of posing and answering quizzes, and learned how to resolve a conflict with the support of the teacher. Secondly, although the role of finger gestures was originally used to obtain correct answers to quizzes, it was reconstructed to solve the conflict between the children through the teacher's mediation. This showed that, even in an environment where children implicitly learn mathematics, they learn from one another, including the teacher, and that gestures in mathematical communications function well for developing mathematical thinking and skills. [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]

This paper presents a comprehensive analysis and solution methodology for simultaneous triple series equations involving generalized Bateman-k functions. The study extends the classical Bateman-k function, a notable special function in mathematical physics, to a more generalized form, enabling the exploration of its applications in solving complex simultaneous series equations. We derive explicit solutions by employing advanced mathematical techniques, including the method of integral transforms and series expansion. The results not only contribute to the theoretical understanding of Bateman-k functions but also offer practical computational tools for problems in mathematical physics, engineering, and applied mathematics where such functions naturally arise. The paper also discusses the convergence conditions and uniqueness of the solutions, providing a robust framework for future research in this area. In this paper an exact solution is obtained for the simultaneous triple series equations involving generalized Bateman k-Functions by multiplying factor method. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this manuscript, we address the estimation of the conditional regression function for a scalar response variable Y conditioned on a Hilbertian random variable X, under the assumption that the observations exhibit a single-index structure. The paper showcases the pointwise almost complete convergence, along with the corresponding rate, of the kernel estimator proposed for this particular model. To illustrate the applicability of our findings, we demonstrate how our outcomes manifest in the context of simulation studies involving functional data. This is achieved through the employment of the leave-one-out (LOO) technique within cross-validation for the purpose of selecting the bandwidth parameter governing the smoothness of the estimated function. We also analyze a spectrometric data set. [ABSTRACT FROM AUTHOR]

This study focuses on improving the predicting accuracy of the daily ASE's weighted price index of the insurance sector (ICI) using a nonlinear spectral model called maximum overlapping discrete wavelet transform (MODWT) with five mathematical functions, namely, Haar, Daubechies (d4), least square (la8), best localization (bl14), and Coiflet (c6). Using a nonlinear spectral model called maximum overlapping discrete wavelet transform (MODWT) with five mathematical functions--Haar, Daubechies (d4), least square (la8), best localization (bl14), and Coiflet (c6)--this study aims to increase the daily ASE's weighted price index of the insurance sector's (ICI) prediction accuracy. The model utilizes a genetic fuzzy system based on Thrift's methodology (GFS.Thrift). The Amman Stock Exchange (ASE) supplied a dataset with 4,478 observations for the purpose of the study. The dataset represented daily data from January 2, 2006, to March 24, 2024. The adaptive GFS.THRIFT model was trained with 90% of the dataset, while the remaining 10% was used to test its prediction performance. Multiple egressions and multicollinearity tests were used to select input variables such as standardized foreign direct investment (FDI), standardized value traded (VT) and consumer price index (CPI). Insights from this study indicate that all input variables are positively related to the output variable. Secondly, the proposed model (MODWT-Haar-GFS. Thrift) significantly outperforms other existing models including the GFS. Thrift model. [ABSTRACT FROM AUTHOR]

Different from the Mittag–Leffler stability or asymptotic stability, the exponential stability issue, which provides faster and explicit convergence rate, is studied in this paper for fractional‐order uncertain systems with asynchronous switching and impulses, where the impulsive functions rely on not only switching modes but also impulsive time. Instead of using the inequality Eα(t)≤1αexp(t1α)(0<α<1)$$ {E}_{\alpha }(t)\le \frac{1}{\alpha}\exp \left({t}^{\frac{1}{\alpha }}\right)\kern0.3em \left(0<\alpha <1\right) $$, by utilizing the theory of fractional‐order differential equations, the methods of Lyapunov function and mathematical induction, some novel and less‐conservative stability criteria are developed, respectively, for the case of switched stable subsystems or switched unstable subsystems. The obtained results build a tradeoff between impulsive function, impulsive interval, average dwell time and fractional order. In addition, our results with α=1$$ \alpha =1 $$ are also novel in contrast with the ones of integer‐order switched impulsive systems. Finally, five numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Praxis Filosófica is the property of Universidad del Valle and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Machine Tool & Hydraulics is the property of Guangzhou Mechanical Engineering Research Institute (GMERI) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article uses the Mittag-Leffler transformation to explore a specific category of harmonic meromorphic functions. The Mittag-Leffler transformation is a crucial tool for analysing meromorphic functions and provides essential properties and insights into their behavior. The main focus of this study is on harmonic meromorphic functions that can be represented by the MittagLeffler transformation. Furthermore, this research introduces an innovative derivative operator that incorporates this transformation into the domain of harmonic meromorphic functions. The Mittag-Leffler transformation is widely recognised as a powerful technique for analysing various mathematical functions, especially those with fractional order derivatives. It improves our understanding of harmonic meromorphic functions and their inherent characteristics. The research findings highlight the effectiveness of this new derivative operator in unraveling the complexities of these functions. They provide valuable insights into their behavior and fundamental traits. Additionally, the study offers coefficient inequalities, the distortion theorem, distortion bounds, extreme points, convex combinations, and convolution analyses specifically tailored to functions within this particular class. [ABSTRACT FROM AUTHOR]

The correct organization of transfers in the public transport system allows to reduce the congestion of the route network while maintaining a sufficient level of service quality for users of transport services. When modelling the probability of transfer, it is advisable to separate the probability of a public transport user choosing a trip with a transfer and the probability of making a transfer at a certain stop of the public transport system. The first probability largely depends on the socio-economic characteristics of the passenger and the time parameters of the trip. The probability of transfer at a certain stop is affected by the information provision of the stop and the number of routes. The general configuration of the route network determines the "basic need for a transfer in the network" - the ratio of the number of pairs of transport zones between which there is no direct public transport route to the total number of pairs of transport zones. The simulation carried out in the PTV Visum software environment for Lviv city made it possible to assess the impact of the tariff system on the change in the number of transfers and to determine critical stops and routes of the network. The inclusion of data on the structure of the city's population in the model makes it possible to use mathematical functions of the probability of transfer on the socio-economic characteristics of the passenger (age, gender, income level) when calculating the forecast number of transfers on the network. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive investigation into the role of mathematics in everyday life and the pivotal function of mathematics teachers in fostering mathematical understanding and competence. Mathematics plays a crucial role in everyday life, enhancing decision-making, financial management, problem-solving, and critical thinking. The ubiquitous presence of mathematics in activities such as budgeting, cooking, shopping, and planning underscores its importance. Mathematics is essential for good governance, as it underpins data-driven decision-making, policy formulation, economic planning, and resource allocation. Recommendations for promoting mathematical proficiency include integrating real-world applications into the curriculum, offering professional development for teachers, and encouraging collaborative learning. Such measures can enhance mathematical literacy, contributing to personal development, societal progress, and effective governance. Mathematics, with its rich historical roots stretching back to ancient civilizations, has evolved into a broad discipline encompassing various branches such as arithmetic, algebra, geometry, and calculus. Each branch plays a crucial role in practical applications ranging from personal finance and cooking to navigation and health monitoring. Effective mathematics education, however, hinges on the proficiency and dedication of mathematics teachers who not only impart theoretical knowledge but also cultivate critical thinking and problem-solving skills in their students. To optimize performance in high-stakes assessments like the West African Examination Council (WAEC) Mathematics examination, it is essential to employ diverse instructional strategies, integrate technology, and provide continuous practice and assessment. It is recommended that governments should support teachers through robust remuneration, timely salary payments, and ongoing professional development to sustain motivation and high-quality instruction. Furthermore, the establishment of mathematics laboratories in schools is recommended to enhance practical learning experiences and deepen students' understanding of mathematical concepts. In the realm of governance, mathematics is indispensable for data analysis, policy formulation, and strategic planning. By addressing these areas comprehensively, we can create an educational environment that not only demystifies mathematics and reduces associated phobias but also prepares students to excel academically and apply mathematical principles effectively in their daily lives and future careers. [ABSTRACT FROM AUTHOR]

This research work envisages addressing fuzzy adjustment of parameters into a hybrid optimization algorithm for solving mathematical benchmark function problems. The problem of benchmark mathematical functions consists of finding the minimal values. In this study, we considered function optimization. We are presenting an enhanced Fuzzy Hybrid Algorithm, which is called Enhanced Fuzzy Hybrid Fireworks and Grey Wolf Metaheuristic Algorithm, and denoted as EF-FWA-GWO. The fuzzy adjustment of parameters is achieved using Fuzzy Inference Systems. For this work, we implemented two variants of the Fuzzy Systems. The first variant utilizes Triangular membership functions, and the second variant employs Gaussian membership functions. Both variants are of a Mamdani Fuzzy Inference Type. The proposed method was applied to 22 mathematical benchmark functions, divided into two parts: the first part consists of 13 functions that can be classified as unimodal and multimodal, and the second part consists of the 9 fixed-dimension multimodal benchmark functions. The proposed method presents better performance with 60 and 90 dimensions, averaging 51% and 58% improvement in the benchmark functions, respectively. And then, a statistical comparison between the conventional hybrid algorithm and the Fuzzy Enhanced Hybrid Algorithm is presented to complement the conclusions of this research. Finally, we also applied the Fuzzy Hybrid Algorithm in a control problem to test its performance in designing a Fuzzy controller for a mobile robot. [ABSTRACT FROM AUTHOR]

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavior of the oscillations, and to do this we use closed measures, a concept that complements the technique of asymptotic pseudotrajectories developed in this setting by Benaïm--Hofbauer--Sorin. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. Various cases are discussed, providing new insight into the oscillation and the stabilization phenomena. [ABSTRACT FROM AUTHOR]

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. [ABSTRACT FROM AUTHOR]

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the paper we apply the idea of weakly weighted sharing and relaxed weighted sharing to trace the uniqueness problems of entire functions whose differential difference polynomials share a small function. The results of the paper improve and extend some recent results due to V. HUSNA, S. RAJESHWARI AND S. H. NAVEEN KUMAR [Electronic Journal of Mathematical Analysis and Applications, 9 (2021), 248-260]. [ABSTRACT FROM AUTHOR]

Special functions represent a class of mathematical functions that have achieved a distinct and recognized status within the realms of mathematical analysis, functional analysis, geometry, physics, and diverse practical applications. These functions have emerged as notable tools in these disciplines, owing to their unique properties and inherent significance. Over time, they have become firmly established due to their ability to address specific mathematical challenges and contribute valuable insights to various branches of science and engineering. The primary objective of this paper is to establish a thorough definition of comprehensive finite integrals through the incorporation of both the Fresnel integral and incomplete Aleph-functions. By adopting a unified and general approach, these integrals are shown to yield a diverse range of new outcomes, particularly in specific scenarios. To elucidate and underscore the significance of our contributions, we present a detailed exposition of our findings, accompanied by specific corollaries. These corollaries, in turn, are emphasized as special cases derived directly from the fundamental results outlined in our study. [ABSTRACT FROM AUTHOR]

Copyright of Brazilian Journal of Education, Technology & Society (BRAJETS) / Cadernos de Educação Tecnologia e Sociedade (CETS) is the property of Brazilian Journal of Education, Technology & Society - BRAJETS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Let A,B be two rings and n ⩾ 2 be an integer. An additive map h: A → B is called an n-Jordan homomorphism if h(xn) = h(x)n for all x ∈ A; h is called an n-homomorphism or an anti-n-homomorphism if h(Πni=1 xi) = Πn i=1 h(xi) or h(Πni=1 xi) = Πn i=0 h(xn-i), respectively, for all x1, ..., xn ∈ A. We give the following variation of a theorem on n-Jordan homomorphisms due to I.N. Herstein: Let n ≥ 2 be an integer and h be an n-Jordan homomorphism from a ring A into a ring B of characteristic greater than n. Suppose further that A has a unit e, then h = h(e)τ, where h(e) is in the centralizer of h(A) and τ is a Jordan homomorphism. By using this variation, we deduce the following result of G. An: Let A and B be two rings, where A has a unit and B is of characteristic greater than an integer n ≥ 2. If every Jordan homomorphism from A into B is a homomorphism (anti-homomorphism), then every n-Jordan homomorphism from A into B is an n-homomorphism (anti-n-homomorphism). As a consequence of an appropriate lemma, we also obtain the following result of E. Gselmann: Let A,B be two commutative rings and B is of characteristic greater than an integer n ≥ 2. Then every n-Jordan homomorphism from A into B is an n-homomorphism. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the stability of weld seams in the neck of flexible containers made from polyethylene film for silage and storage of fresh ground corn mass as feed during thermal welding using a movable welding module. An analysis of the thermal conductivity of polyethylene film was conducted to determine temperature change pattern in the thin layer over time. The values obtained were used to establish optimal operating limits for the heating device during welding process. Subsequently, the resistance to rupture of the polyethylene film seams welded at different temperatures was evaluated by generating vacuum pressure in a specially designed installation. The results of polyethylene film PE-115 samples showed a pattern of limiting vacuum pressure values corresponding to different welding temperatures. The mathematical function obtained was used to identify the maximum value of the burst pressure of weld seams, which corresponded to 61.8 kPa at a temperature of 177oC. These results allowed for the determination of the optimal welding mode for sealing the container neck. [ABSTRACT FROM AUTHOR]

This paper addresses a debate on the immateriality of thought, focusing on James Ross's argument regarding the indeterminacy of physical processes with respect to pure functions. Ross posits that some human cognitive processes, particularly logical reasoning and mathematical functions, exhibit a formal determinacy that no physical process can have, challenging physicalist accounts of mind. A critical response by Peter Dillard, known as the "schmitosis objection," attempts to undermine Ross's argument by drawing a parallel between biological processes like mitosis and formal functions such as addition. This paper defends Ross's position by highlighting an overlooked distinction between transcendent and formal determinacy. By demonstrating that biological processes like mitosis are transcendentally determinate while pure functions are formally determinate, the paper refutes Dillard's objection and supports Ross's claim of the partial non-physicality of thought. The argument contributes to ongoing debates in the philosophy of mind and metaphysics by clarifying the distinct ways physical and non-physical processes relate to determinacy. [ABSTRACT FROM AUTHOR]

Cognitive benefits have been reported in early bilinguals as well as in children attending a Content and Language Integrated Learning (CLIL) school programme. Recent findings, however, show divergent results. These inconsistent findings seem to be attributable, among other factors, to the divergent tasks applied. This study aimed to determine whether a two-year CLIL programme has positive effects by applying the same tasks for which advantages were shown previously and to examine whether potential gains might impact children's academic performance. Thirty 7-year-old French-speaking pupils who had been enrolled in a CLIL programme since the age of 5 and 30 French-speaking monolinguals following a traditional school programme were compared on different attentional and executive tasks after being matched on potential confounding variables. No attentional and executive differences were observed, but a significant effect was observed in favour of monolinguals on a task assessing mathematical skills. The implications of these results are discussed. Résumé: Des bénéfices cognitifs ont été rapportés chez des bilingues précoces ainsi que chez des enfants suivant un programme scolaire d'enseignement d'une matière par l'intégration d'une langue étrangère (EMILE). Cependant, des résultats récents montrent des divergences. Ces résultats incohérents semblent être attribuables, entre autres facteurs, aux différentes tâches appliquées. Cette étude visait à déterminer si un programme EMILE de deux ans a des effets positifs en appliquant les mêmes tâches pour lesquelles des avantages ont été démontrés précédemment et à examiner si les gains potentiels peuvent avoir un impact sur les performances scolaires des enfants. Trente élèves francophones de 7 ans inscrits dans un programme EMILE depuis l'âge de 5 ans et 30 monolingues francophones suivant un programme traditionnel ont été comparés sur différentes tâches attentionnelles et exécutives après avoir été appariés sur plusieurs variables confondantes potentielles. Aucune différence attentionnelle et exécutive n'a été observée, mais un effet significatif a été observé en faveur des monolingues dans une tâche évaluant les compétences mathématiques. Les implications de ces résultats sont discutées. [ABSTRACT FROM AUTHOR]

As the demand for more complex circuits increases, so does the duration of creating and testing them. The most time-consuming task in circuit development is notoriously the verification process, primarily due to the large number of simulations (hundreds or even thousands) required to ensure that the circuits adhere to the specifications regardless of the operating conditions. In order to decrease the number of required simulations, various verification algorithms have been proposed over the years, but this comes with an additional issue: the thorough validation of the algorithms. As simulations on real circuits are significantly time-consuming, synthetic circuits can offer precious insights into the capabilities of the verification algorithm. In this paper, we propose a benchmark of synthetic circuits that can be used to exhaustively validate pre-silicon (Pre-Si) verification algorithms. The newly created benchmark consists of 900 synthetic circuits (mathematical functions) with input dimensions (variables) ranging from 2 to 10. We design the benchmark to include functions of varying complexities, reflecting real-world circuit expectations. Eventually, we use this benchmark to evaluate a previously proposed state-of-the-art Pre-Si circuit verification algorithm. We show that this algorithm generally obtains relative verification errors below 2% with fewer than 150 simulations if the circuits have less than six to seven operating conditions. In addition, we demonstrate that some of the most complex circuits in the benchmark pose serious problems to the verification algorithm: the worst case is not found even when 200 simulations are used. [ABSTRACT FROM AUTHOR]

Considering the high importance of the optimization problem, this study evaluated mathematical programming models by considering various methods of estimating model coefficients. Correct and accurate data must be entered into the model to get accurate and robust result from the model. Most input data to the presented model are technical and objective function coefficients. Therefore, it is necessary to determine the information related to these coefficients with the utmost precision and, as much as possible, to develop a suitable scientific method to estimate the value of these coefficients [5]. Finding the best method for estimating the coefficients of mathematical programming models can significantly optimize the final values of the variables extracted from the mathematical programming model. For this reason, it is essential to study the methods used so far in this field and examine their advantages and disadvantages. This review study investigated various methods of estimating technical coefficients of mathematical planning models in the conditions of possible decision-making and uncertainty after reviewing 117 articles published between 1955 and 2022. These methods include fuzzy methods, statistical methods, and data analysis methods. Statistical methods such as regression methods, time series methods, exponential smoothing, and linear non-linear and non-parametric, machine learning and data mining methods were investigated in this article. The methods of data-driven analysis explained in this article can be referred to as decision trees, random forests and the Lasso methods. After evaluating and comparing these methods, suggestions for choosing the best method were provided. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with some of the theoretical aspects of equitable multi-objective optimization. By using the equitability preference structure, we discuss some properties of the equitably nondominated set, such as nonemptiness, external stability and connectedness. Also, we introduce the concept of proper equitable nondominance, and show that these solutions can be obtained by minimizing a weighted sum of the sort of objective functions where all weights are positive and decreasing. Moreover, we present a hybrid scalarization problem to generate equitably nondominated solutions. This method also provides a necessary condition for the existence of properly equitable nondominated solutions. [ABSTRACT FROM AUTHOR]

Nonlinearity exerts a profound influence on the displacement performance of actuators within electro-hydraulic servo systems, particularly in the context of hysteresis. This article analyses a specific hysteresis responsible for control instability, a consequence of the concave-hysteresis loop, giving rise to a notable peak phenomenon in displacement. The behavior of the concave-hysteresis loop is studied in the step load experiment of a triaxial apparatus. Subsequently, an accurately formulated mathematical model utilizing a mathematical function is derived. Notably, the article introduces an efficacious model-based compensation algorithm that integrates nonlinear iteration and fuzzy control. This strategic approach effectively addresses the issue associated with calculating the inverse model when the sensor is located in a nonlinear, hook-shaped domain. Simulation and experimentation verified the concave-hysteresis loop model and the compensation algorithm. The experiment demonstrated the elimination of peak phenomena and a decrease in sensor error from 3.7 mm to below 0.5 mm. [ABSTRACT FROM AUTHOR]

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]

In this work, a comparative study of four functional forms used to represent potential energy curves (PECs) is presented. The starting point is the Hulburt‐Hirschfelder, followed by the Extended Rydberg potential function, ending with two of the most recent potentials presented in the literature for diatomic systems: the Araújo‐Ballester potential and the Improved Extended Lennard‐Jones potential. The chosen potentials have in common the fact that all their parameters are algebraically calculated, without any fitting procedure, and all of them have direct dependence on Dunham's parameters. The mathematical behavior of these functions for the short‐ and long‐range regions is discussed. As study case, the diatomic system CO$$ \mathrm{CO} $$ in its ground electronic state was selected. To quantify the accuracy of the potential energy functions, the least‐squares Z‐test method, proposed by Murrell and Sorbie, is used. Furthermore, the main spectroscopic constants and vibrational energy levels are calculated and compared for all potentials. A comparative study on functions to represent the potential energy interactions of the CO diatomic system is presented. The Hulburt‐Hirschfelder, Extended Rydberg, Araújo‐Ballester and Improved Extended Lennard‐Jones potentials were chosen because they have in common the fact that all their parameters are calculated without any fitting procedure. To quantify the accuracy of potential energy functions, the least squares Z test method is used, and the main spectroscopic constants and vibrational energy levels are calculated. [ABSTRACT FROM AUTHOR]

Introduction: The activity changes of cytochrome P450 (CYP450) enzymes, along with the complicated medication scenarios in diabetes mellitus (DM) patients, result in the unanticipated pharmacokinetics (PK), pharmacodynamics (PD), and drug–drug interactions (DDIs). Physiologically based pharmacokinetic (PBPK) modeling has been a useful tool for assessing the influence of disease status on CYP enzymes and the resulting DDIs. This work aims to develop a novel diabetic PBPK population model to facilitate the prediction of PK and DDI in DM patients. Methods: First, mathematical functions were constructed to describe the demographic and non-CYP physiological characteristics specific to DM, which were then incorporated into the PBPK model to quantify the net changes in CYP enzyme activities by comparing the PK of CYP probe drugs in DM versus non-DM subjects. Results: The results show that the enzyme activity is reduced by 32.3% for CYP3A4/5, 39.1% for CYP2C19, and 27% for CYP2B6, while CYP2C9 activity is enhanced by 38% under DM condition. Finally, the diabetic PBPK model was developed through integrating the DM-specific CYP activities and other parameters and was further used to perform PK simulations under 12 drug combination scenarios, among which 3 combinations were predicted to result in significant PK changes in DM, which may cause DDI risks in DM patients. Conclusions: The PBPK modeling applied herein provides a quantitative tool to assess the impact of disease factors on relevant enzyme pathways and potential disease-drug–drug-interactions (DDDIs), which may be useful for dosing regimen optimization and minimizing the DDI risks associated with the treatment of DM. [ABSTRACT FROM AUTHOR]

Studies on nonlinear analysis of system dynamics have increased in recent years. Since most systems that exist in nature have complex dynamics and therefore exhibit nonlinear behavior; there are various methods and theories developed in this context. Self-similar functions are mathematical functions exhibiting self-similar and scale-invariant behaviors performing fractal structures. Singularities are the basis for producing the self-similar behavior of these functions. Singularity analysis is mainly carried out by using wavelet transform (WT). The cusp singularities are non-oscillating singularities which are characterized by their singularity strength. However, the representation and behavior of this type of singularity differs depending on the sign of the exponent, known as the singularity strength. The cusp singularity functions with negative exponent show irregular behavior progressively different than positively valued functions since the value of the function is undefined at that particular singular point. It is commonly accepted that the singularity strength is studied as Hölder exponent of the cusp function, but by definition, the value of this exponent cannot take negative values. We present a new method to estimate the singularity strength of cusp singularities with negative exponent. The developed method is based on analyzing and redistributing the amplitudes of a cusp function with negative exponent by taking the WT. The redistribution of amplitudes over time is achieved by applying curve fitting process to frequency values of the analyzing function. [ABSTRACT FROM AUTHOR]

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In this study, we obtain a sex prediction algorithm based on CNN in two ways - building a red Convolutional Neural Network (CNN) model from scratch and via transfer learning. We built a model from scratch and compared it with fine-tuned EfficientNetB1. We use these models for gender determination using periocular images and compare the two models depending on the accuracy of the models. The CNN model proposed from scratch yields an accuracy of 94.46% while the fine-tuned EfficientNetB1 yields an accuracy of 97.94%. This paper is one of the first works in determining gender from periocular images in the visible spectrum using a CNN model built from the outset. [ABSTRACT FROM AUTHOR]

Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This set of equations includes the one-dimensional (1D) Oskolkov equation, the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation, the generalized hyperelastic rod wave (HERW) equation, and the Oskolkov Benjamin Bona Mahony Burgers (OBBMB) equation. We employ the new extended direct algebraic (NEDA) method to tackle these equations. The NEDA method serves as a powerful tool for our analysis, enabling us to obtain solutions grounded in various mathematical functions, such as hyperbolic, trigonometric, rational, exponential, and polynomial functions. As we delve into the physical implications of these solutions, we uncover complex structures with well-known characteristics. These include entities like dark, bright, singular, combined dark-bright solitons, dark-singular-combined solitons, solitary wave solutions, and others. [ABSTRACT FROM AUTHOR]

This study investigated novice mathematics teachers participating in an online teacher education course focused on covariational reasoning and understanding the behavior of functions. The analysis centered on documenting the emergence of participants' sociomathematical norms for engaging in online asynchronous discussions. In this paper, we characterized participants' initial mathematical discourse and documented two emergent sociomathematical norms, namely explaining why and emergent shape discourse. When participants explained why, they used specific quantities or symbolic representations of functions to justify why function graphs have particular visual features. When participants engaged in emergent shape discourse, they coordinated change between covarying quantities to justify why function graphs behave in certain ways. This study provides evidence that online settings can provide context for mathematics teachers engaging in legitimate collaborative mathematical activity and that activity can be enhanced by participation in discourse featuring specific sociomathematical norms. We discuss conjectures regarding the potential of reflective discussion activities paired with the Notice and Wonder Framework to support the emergence of generative sociomathematical norms. We also discuss potential relationships between characteristics of participants' mathematical discourse and their membership with the core and periphery of a social network. [ABSTRACT FROM AUTHOR]

Our mathematical thinking sheds light on how we see our world and what knowledge we have about it. In spite of this, mathematical performance is still mostly measured in calculation skills, and this also predestines the success of learning. So at school, what is important is how correctly we solved the task and not the way we got there. An internationally unique Hungarian-developed test (DPV—Pedagogical Examination of Dyscalculia/Diszkalkulia Pedagógiai Vizsgálata) draws our attention to the opposite of this. The special feature of the test is its criterion orientation, which emphasizes the correctness of mathematical thinking while examining the abilities necessary for learning mathematics. The aim of our study was to investigate, as a function of background variables (gender and socioeconomic status (SES)), (1) whether the abilities and thought processes required for learning mathematics function at an adequate level, (2) what effect these may have on mathematical performance, and (3) to what extent all of this is influenced by mathematical anxiety. Our background variables were gender and socioeconomic status. A total of 999 Hungarian students aged 10–15 participated in our study, including 483 boys and 516 girls. In general, we can say that the development of the skills necessary for learning mathematics is closely related to the students' performance. Nevertheless, it happens that we encounter low performance despite good skills. In several cases, we can experience the presence of anxiety, especially math anxiety, which in most cases, regardless of the level of abilities, negatively affects the success of math learning processes. The findings confirm that socioeconomic status, gender, and performance are risk factors for mathematical anxiety. The following hypotheses have been formulated along the lines of the research objectives set out in the abstract: There are no differences in ability and mathematical performance between boys and girls. Girls are more anxious when they have to solve a mathematical problem. Socioeconomic status predicts ability level and the presence of math anxiety. Mathematical anxiety (MA) modifies the validity of mathematical ability (DPV). [ABSTRACT FROM AUTHOR]

In this paper, we investigated the contribution of both cognitive and affective factors to mathematical skills. In particular, we looked at the protective role of self-concept for mathematical learning and performance. In a field study, we tested the relation of math self-concept and short-term visuo-spatial working memory to the mathematical abilities of second- grade primary school children in Italy (N = 105). Measures included the "Test for the evaluation of calculating and problem-solving abilities" (AC-MT 6–11), the backward Corsi blocks test (Battery for Visuo-Spatial Memory), and the mathematics self-concept sub-scale of the Self-Description Questionnaire-I (SDQ-I, Italian version). As expected, correlation and moderated regression analyses showed that mathematics self-concept and working memory both positively predict mathematical operations and numeracy, but not accuracy. Simple slope analysis confirmed our moderation hypothesis, with working memory predicting mathematical abilities at low levels of math self-concept, but not at medium and high levels. The theoretical and practical implications are discussed. [ABSTRACT FROM AUTHOR]

The document "Advances in Uncertain Information Fusion" published in the journal Entropy discusses the importance of information fusion in drawing accurate inferences from multiple sources. It explores various theories, such as Dempster–Shafer evidence theory, fuzzy set theory, possibility theory, and classical Bayesian theory, for handling uncertain information. The document features six articles that delve into measuring uncertainty in negation evidence, correlation between belief functions, membership function assignment, autonomous search for targets, multi-modal fusion for emotion recognition, and combining segmentation models for improved performance. The conclusion highlights the significance of representing and qualifying uncertainty in next-generation information fusion systems, emphasizing the integration of classical approximate reasoning theories with advanced deep learning models for future developments. [Extracted from the article]

The firefly algorithm (FA) is a popular swarm intelligence optimization algorithm. The FA is used to solve various optimization problems, but it still has some deficiencies, such as high complexity, slow convergence rate, and low accuracy of the solution. This paper proposes a highly efficient quantum firefly algorithm with stochastic search strategies (QSSFA). In QSSFA, individuals are generated in the way of quantum angle coding by introducing the laws of quantum physics and quantum gates, and combined with the random neighborhood attraction model, an adaptive step size strategy is also introduced in the optimization. The complexity of the algorithm is greatly reduced, and the global search ability of the algorithm is optimized. The convergence speed of the algorithm, the ability to jump out of the local optimum, and the algorithm accuracy are improved. The proposed QSSFA's performance is tested on ten mathematical test functions. The obtained results show that the QSSFA algorithm is very competitive compared to the firefly algorithm and three other FA variants. [ABSTRACT FROM AUTHOR]

The object of the research is to identify the influence of the pitch of the hammers with cutting edges on the determination of the average length of feed, crushed from by-product stem raw materials in hammer crushers. However, a problem was identified such as the lack of an analytical expression for determining the average length of chopped stem feed by a hammer grinder depending on the distance between the edges of adjacent hammers. With a simultaneous change in the angles of the location of the stem with the maximum size in the layer and, using the methods of probability theory for determining the mathematical descriptions of the function of two arguments, in this study an analytical expression was obtained for determining the average length of particles crushed by hammer crushers depending on the distance between the faces of adjacent hammers. Hammers with cutting edges are used to crush feed from by-product stem raw materials. The end working part of the hammer is milled at an angle of 90°, i.e. two cutting edges are processed at the end of the hammer. As a result of the practical calculations, the average length of feed crushed from by-product stem raw materials was determined depending on the parameters of the hammer crusher. From the resulting graph of the influence of the distance between the faces of adjacent hammers on the average length of crushed particles, it is evident that when the distance between the faces of adjacent hammers changes, the average length of crushed particles varies within the range of 36.19...53.39 mm. To verify the reliability of the obtained expression, experiments were carried out on a crusher with a distance between the faces of adjacent hammers of 20 mm. In this case, the average length of the crushed particles was equal to 38.75 mm, and the theoretical value was 40.16 mm. The difference between them was 3.64 %, which proves the reliability of the obtained analytical expression. The conducted theoretical studies with the receipt of an analytical expression, ensuring the determination of the average length of feed, chopped from by-product stem raw materials, is the solution to an important problem in the development of theoretical foundations of chopping machines, significantly affecting the efficiency of mechanization and operation of feed choppers in practice. [ABSTRACT FROM AUTHOR]