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ON THE DISCRETE DISTRIBUTION GENERATED BY LEVY PROBABILITY

Journal of Mathematical Sciences (United States) 2024年第2期280卷 198-211页

作者： Farbod, Davood Basirat, Maryam Department of Mathematics Faculty of Engineering Science Quchan University of Technology Quchan Iran Department of Mathematics and Statistics Mashhad Branch Islamic Azad University Mashhad Iran

In this paper, we consider one-parameter regularly varying discrete distribution generated by Levy probability (RDLP). Some useful plots of the models are illustrated. Mathematically, to propose the RDLP model as a discrete distribution in bioinformatics, some common statistical facts such as unimodality, skewness to the right, upward/downward convexity, regular variation at infinity, and asymptotically constant slowly varying component are established for the model. Based on the Monte Carlo method and limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, simulation studies are done to estimate bias, mean square error, and maximum likelihood estimation for the unknown parameter of the model. Some asymptotic properties and asymptotic expansions are given for useful functions. Moreover, we shall attempt to examine the RDLP model with a real count data set to show its application, and also compare it with two rival models. © 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： 60E05 62E10 62F10 62F12 Levy probability Maximum likelihood estimation Monte Carlo method Statistical facts

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ONE-PARAMETER FINITE DIFFERENCE METHODS AND THEIR ACCELERATED SCHEMES FOR SPACE-FRACTIONAL SINE-GORDON EQUATIONS WITH DISTRIBUTED DELAY

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Journal of Computational mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1D)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1D problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

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Formulation and Solution Approach for Uncertain Multi-Objective Material Requirement Planning Problem with Multi-Mode Demand, Overtime Production, and Outsourcing Possibilities

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Journal of Systems Science and Systems engineering 2025年第1期34卷 1-28页

作者： Sadegh Niroomand Dragan Pamucar Ali Mahmoodirad Department of Industrial Engineering Firouzabad Higher Education CenterShiraz University of TechnologyShirazIran Department of Operations Research and Statistics Faculty of Organizational SciencesUniversity of BelgradeBelgradeSerbia Department of Industrial Engineering and Management Yuan Ze UniversityTaoyuan CityTaiwanChina Department of Mechanics and Mathematics Western Caspian UniversityBakuAzerbaijan Department of Mathematics Babol BranchIslamic Azad UniversityBabolIran

Material requirement planning is a type of production planning problems that is used to plan about a final product, its sub-assemblies, and its raw parts simultaneously by considering time phased demands of the final product. In this study a multi-product material requirement planning problem with limited manufacturing resources is considered. As an important novelty, a multi-mode demand strategy is considered in this problem where the total customers’ satisfaction degrees of the selected demand modes is maximized. Furthermore, three types of capacities such as regular, over time, and outsourcing capacities are considered for such system as another novelty. The problem is formulated as a bi-objective model to maximize total profit and total satisfaction degree of the customers simultaneously. To respect the uncertain nature of the problem, it is formulated in a belief-degree based uncertain form. This is for the first time in the literature of material requirement planning that this type of uncertainty is considered. The uncertain problem is converted to a crisp form using some techniques such as expected value model and chance constrained model. Then, a new hybrid form of the fuzzy programming approach is developed to solve the bi-objective crisp formulations. A case study from the petroleum industries of Iran is used to perform the required computational experiments. The required experiments are done, and possible comparisons are made on the obtained results. Furthermore, some managerial insights are given in order to be used in the production system of the case study. According to the obtained results, the proposed hybrid fuzzy programming approach is superior to existing approaches in at least 38 percent of the experiments.

关键词： Material requirement planning multi-mode demand belief-degree based uncertainty multi-objective optimization fuzzy programming approach

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Mixed convective flow of a Newtonian fluid through a porous medium with a lack of thermal equilibrium

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International Journal of Ambient Energy 2023年第1期44卷 984-994页

作者： Siddabasappa, C. Babitha Department of Mathematics and Statistics M. S. Ramaiah University of Applied Sciences Karnataka Bengaluru India Department of Mathematics School of Engineering Presidency University Karnataka Bengaluru India

The primary focus of this work is on the effects of thermal radiation and heat generation on mixed convective MHD steady flow of a Newtonian fluid via a porous channel under local thermal non-equilibrium (LTNE) condition. The resulting governing equations are converted into a set of ordinary differential equations (ODEs) using the proper similarity transformation. The shooting method is implemented in MATLAB code, which is then used to solve the set of dimensionless coupled ODEs. In the fluid phase, the external effects of heat generation and thermal radiation are taken into account. The effect of individual parameters on flow and heat transfer phenomena are discussed in detail with the help of plots and tables. From the study, it is noted that LTNE is predominant near the wedge compared to that far away from the wedge and also as heat transfer rate increases for greater values of thermal conductivity ratio parameter. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

关键词： Heat radiation

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Propulsion of a three-sphere microrobot in a porous medium

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Physical Review E 2024年第6期109卷 065106-065106页

作者： Chih-Tang Liao Andrew Lemus Ali Gürbüz Alan C. H. Tsang On Shun Pak Abdallah Daddi-Moussa-Ider Department of Mechanical Engineering Department of Applied Mathematics School of Mathematics and Statistics

Microorganisms and synthetic microswimmers often encounter complex environments consisting of networks of obstacles embedded into viscous fluids. Such settings include biological media, such as mucus with filamentous networks, as well as environmental scenarios, including wet soil and aquifers. A fundamental question in studying their locomotion is how the impermeability of these porous media impacts their propulsion performance compared with the case of that in a purely viscous fluid. Previous studies showed that the additional resistance due to the embedded obstacles leads to an enhanced propulsion of different types of swimmers, including undulatory swimmers, helical swimmers, and squirmers. In this paper, we employ a canonical three-sphere swimmer model to probe the impact of propulsion in porous media. The Brinkman equation is utilized to model a sparse network of stationary obstacles embedded into an incompressible Newtonian liquid. We present both a far-field theory and numerical simulations to characterize the propulsion performance of the swimmer in such porous media. In contrast to enhanced propulsion observed in other swimmer models, our results reveal that both the propulsion speed and efficiency of the three-sphere swimmer are largely reduced by the impermeability of the porous medium. We attribute the substantial reduction in propulsion performance to the screened hydrodynamic interactions among the spheres due to the more rapid spatial decays of flows in Brinkman media. These results highlight how enhanced or hindered propulsion in porous media is largely dependent on individual propulsion mechanisms. The specific example and physical insights provided here may guide the design of synthetic microswimmers for effective locomotion in porous media in their potential biological and environmental applications.

关键词： Microswimmers

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Identifiability and Observability of Nonsmooth Systems via Taylor-Like Approximations

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IEEE Transactions on Automatic Control 2025年第6期70卷 4178-4185页

作者： Stechlinski, Peter Eisa, Sameh A. Abdelfattah, Hesham University of Maine Department of Mathematics and Statistics Maine United States University of Cincinnati Department of Aerospace Engineering and Engineering Mechanics OH United States University of Cincinnati Department of Mathematical Sciences OH United States

New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic derivatives are used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are practically implementable, accurate, and analogous to (and indeed recover) their smooth counterparts. To accomplish this, a novel first-order Taylor-like approximation theory is developed to directly treat nonsmooth (i.e., continuous but nondifferentiable) functions. An L-SERC algorithm is proposed that determines partial structural identifiability or observability, which are useful characterizations in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling. © 1963-2012 IEEE.

关键词： Climate models

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Efficient Numerical Scheme for Solving Large System of Nonlinear Equations

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Computers, Materials & Continua 2023年第3期74卷 5331-5347页

作者： Mudassir Shams Nasreen Kausar Shams Forruque Ahmed Irfan Anjum Badruddin Syed Javed Department of Mathematics and Statistics Riphah International UniversityI-14Islamabad44000Pakistan Department of Mathematics Yildiz Technical UniversityFaculty of Arts and ScienceEsenler34210IstanbulTurkey Science and Math Program Asian University for WomenChattogramBangladesh Mechanical Engineering Department College of EngineeringKing Khalid UniversityAbha61421Saudi Arabia

A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this *** analysis demonstrates that the local order of convergence of the numerical method is *** computer algebra system CAS-Maple,Mathematica,or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical *** numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms.A dynamic evaluation of the presented methods is also presented utilizing basins of attraction to analyze their convergence *** from visualizing iterative processes,this methodology provides useful information on iterations,such as the number of diverging-converging points and the average number of iterations as a function of initial *** numerous highly nonlinear boundary value problems and large nonlinear systems of equations of higher dimensions demonstrate the performance,efficiency,precision,and applicability of a newly presented technique.

关键词： Nonlinear equations convergence order boundary value problem computational time basins of attraction converging points

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Inertia and Spectral Symmetry for the Eccentricity Matrices of Clique Trees

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Acta Mathematicae Applicatae Sinica 2024年

作者： Xiao-hong LI Jian-feng WANG Maurizio BRUNETTI School of Mathematics and Statistics Shandong University of Technology Basic Education Department Weifang Engineering Vocational College Department of Mathematics and Applications University Federico II'

The eccentricity matrix E(G) of a connected graph G is obtained from the distance matrix of G by leaving unchanged the largest nonzero entries in each row and each column,and replacing the remaining ones with *** this paper,we consider the set CT of clique trees whose blocks contain at most two cut-vertices of the clique *** with studying the structural properties of a clique tree in CT,we prove its eccentricity matrix to be irreducible,and then determine its inertia showing that every graph in CT with more than four vertices and odd diameter has two positive and two negative *** E-eigenvalues and negative E-eigenvalues turn out to be equal in number even for graphs in CT with even diameter;that shared cardinality also counts the‘diametrally distinguished’***,we prove that the spectrum of the eccentricity matrix of a clique tree G in CT is symmetric with respect to the origin if and only if G has an odd diameter and exactly two adjacent central *** results generalize those achieved on trees by *** and *** in 2022.

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Dynamical analysis,control,boundedness,and prediction for a fractional-order financial risk system

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Chinese Physics B 2024年第11期33卷 223-235页

作者： Kehao Yang Song Zheng Tianhu Yu Aceng Sambas Muhamad Deni Johansyah Hassan Saberi-Nik Mohamad Afendee Mohamed School of Data Science Zhejiang University of Finance & EconomicsHangzhou 310018China Department of Mathematics Luoyang Normal UniversityLuoyang 471934China Faculty of Informatics and Computing Universiti Sultan Zainal AbidinBesut Campus22200TerengganuMalaysia Department of Mechanical Engineering Universitas Muhammadiyah TasikmalayaTasikmalayaJawa Barat46196Indonesia Department of Mathematics Universitas PadjajdaranJatinangorKabupaten Sumedang 45363Indonesia Department of Mathematics and Statistics University of NeyshaburNeyshabur ***Iran

This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function *** this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order *** stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of *** the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are ***,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

关键词： FOFR system dynamical analysis control boundedness forecasting

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Comments on "relaxed Conditions for the Input-to-State Stability of Switched Nonlinear Time-Varying Systems"

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IEEE Transactions on Automatic Control 2025年第6期70卷 4233-4236页

作者： Şahan, Gökhan Trenn, Stephan Izmir Institute of Technology Department of Mathematics and Computational Science and Engineering Program Urla Izmir Turkey University of Groningen Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence Groningen9722BA Netherlands

This study addresses the deficiencies in the assumptions of the results in Chen and Yang, 2017 [1] due to the lack of uniformity. We first show the missing hypothesis by presenting a counterexample. Then we prove why they are wrong in that form and show the errors in the proof of the main result of [1]. Next, we compare the assumptions and related results of [1] with similar works in the literature. Lastly, we give suggestions to complement the shortcomings of the hypotheses and thus correct them. © 1963-2012 IEEE.

关键词： Nonlinear simulations

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