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Radial solution of the Logarithmic Laplacian system

applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 114-124页

作者： ZHANG Li-hong NIE Xiao-feng WANG Guo-tao Bashir Ahmad School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041004China Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th... 详细信息

关键词： the Logarithmic Laplacian system radial symmetry the direct method of moving planes

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Numerical Modelling of The System of Doubly Nonlinear Diffusion Equations with Convective Transfer and Damping

Numerical Modelling of The System of Doubly Nonlinear Diffus...

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2024 Cognitive Models and Artificial Intelligence Conference, AICCONF 2024

作者： Sadullaeva, Shakhlo Azimbaevna Anarova, Shahzoda Amanbayevna Khaydarov, Abdugaffor Fayzullayeva, Zarnigor Nazirova, Dilorom Mirkhodzhaeva, Nazhiba departament Intellegent systems Joint Belarusian-Uzbek Intersectoral Institute of Applied Technical Qualifications Tashkent Uzbekistan Department of Convergence of Digital Technologies Computer Engineering Faculty Tashkent University of Information Technologies Tashkent Uzbekistan Department of Applied Mathematics and Computer Analysis National University of Uzbekistan Tashkent Uzbekistan Department of Informatics Computer Engineering Faculty Tashkent University of Information Technologies Tashkent Uzbekistan Department of Applied Mathematics and Computer Analysis NUUz Tashkent Uzbekistan

ISBN: (纸本)9798400716928

Currently, studies of double nonlinear equations and systems of double nonlinear equations representing many processes found in nature are considered relevant and necessary. These equations and systems, as a rule, are nonlinear, degenerate, and have properties that are absent in linear theory and therefore make them quite difficult for both analytical and numerical analysis of the solution. For this reason, great attention is paid to the research of nonlinear mathematical models, the construction of efficient numerical solution schemes and algorithms, and the creation of software using the capabilities of computer technologies. In this article, the mathematical model of the diffusion process in a two-component nonlinear medium under the influence of time-dependent convective transfer and damping is studied. The calculation scheme, algorithm, and software for nonlinear problems were developed. Based on a study of the qualitative properties of a nonlinear mathematical model of a reaction-diffusion system, computer modeling of reaction-diffusion processes was carried out. The developed computational schemes, algorithms, and software packages for solving systems of parabolic equations with double nonlinearity provide high productivity in studying the theory and processes of numerical solutions of such problems. © 2024 ACM.

关键词： Nonlinear equations

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The inverse nullity pair problem and the strong nullity interlacing property

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Linear Algebra and Its Applications 2024年 699卷 539-568页

作者： Abiad, Aida Curtis, Bryan A. Flagg, Mary Hall, H. Tracy Lin, Jephian C.-H. Shader, Bryan Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Ghent Belgium Department of Mathematics Iowa State University AmesIA50011 United States Department of Mathematics Statistics and Computer Science University of St. Thomas HoustonTX United States Hall Labs LLC ProvoUT United States Department of Applied Mathematics National Sun Yat-sen University Kaohsiung80424 Taiwan University of Wyoming Colorado United States

The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as (null(A),null(A(i)), where A(i) is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair. © 2024 Elsevier Inc.

关键词： Matrix algebra

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Sequential Solution Strategies for the Cahn-Hilliard-Biot Model

Sequential Solution Strategies for the Cahn-Hilliard-Biot ...

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European Conference on Numerical mathematics and Advanced Applications, ENUMATH 2023

作者： Storvik, Erlend Riethmüller, Cedric Both, Jakub W. Radu, Florin Adrian Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Centre for Modeling of Coupled Subsurface Dynamics Department of Mathematics University of Bergen Bergen Norway

ISBN: (纸本)9783031861680

This paper presents a study of solution strategies for the Cahn-Hilliard-Biot equations, a complex mathematical model for understanding flow in deformable porous media with changing solid phases. Solving the Cahn-Hilliard-Biot system poses significant challenges due to its coupled, nonlinear and non-convex nature. We explore various solution algorithms, comparing monolithic and splitting strategies, focusing on both their computational efficiency and robustness. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Computational efficiency

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Existence of solutions to the generalized periodic fractional boundary value problem

Existence of solutions to the generalized periodic fractiona...

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作者： Fečkan, Michal Marynets, Kateryna Wang, JinRong Department of Mathematical Analysis and Numerical Mathematics Comenius University in Bratislava Bratislava Slovakia Mathematical Institute of Slovak Academy of Sciences Bratislava Slovakia Delft Institute of Applied Mathematics Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Delft Netherlands Department of Mathematics Guizhou University Guiyang China

We study a boundary value problem for a Caputo-type fractional differential equation subjected to periodic boundary conditions. For an auxiliary problem with the simplified right-hand side, we explicitly construct its unique solution. In addition, based on the theory of the topological index, we prove existence of at least one solution to the original problem. © 2023 The Authors. Mathematical Methods in the applied Sciences published by John Wiley & Sons Ltd.

关键词： Boundary value problems

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Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds

arXiv

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arXiv 2024年

作者： Shalova, Anna Schlichting, André Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Institute of Applied Analysis Ulm University Germany

We study stationary solutions of McKean-Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the corresponding free energy functional. On a sphere, we employ the properties of spherical convolution to study the bifurcation branches around the uniform state. We also give a sufficient condition for an existence of a discontinuous transition point in terms of the interaction kernel and compare it to the Euclidean setting. We illustrate our results on a range of system, including the particle system arising from the transformer models and the Onsager model of liquid crystals. Copyright © 2024, The Authors. All rights reserved.

关键词： Spheres

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New concept of centrality measurement in fuzzy social networks

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Journal of Intelligent and Fuzzy Systems 2024年第4期46卷 10665-10681页

作者： Mahapatra, Rupkumar Samanta, Sovan Pal, Madhumangal Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India Department of Mathematics Tamralipta Mahavidyalaya West Bengal Tamluk India Research Center of Performance and Productivity Analysis Istinye University Istanbul Turkey

The most critical task of a social network is to identify a central node. Numerous methods for determining centrality are documented in the literature. It contributes to online commerce by disseminating news, advertisements and other content via central nodes. Existing methods capture the node's direct reachability. This study introduces a novel method for quantifying centrality in a fuzzy environment. This measurement takes into account the reachability of nodes and their direct connections. Several critical properties have been demonstrated. A small Facebook network is used to illustrate the issue. Additionally, appropriate tables and graphs present a comparative study with existing methods for centrality measurement. © 2024-IOS Press. All rights reserved.

关键词： Fuzzy sets

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Modeling and analysis of Induction Machine Considering the Effects of Saturation

Modeling and Analysis of Induction Machine Considering the E...

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Circuit, Systems and Communication (ICCSC), International Conference on

作者： Es-Semyhy Mustapha Ba-Razzouk Abdellfattah El Haroussi Mustapha Department of Applied Physics Mathematics Computer and Engineering Sciences Laboratory (MISI) Systems Analysis and Information Processing Team (ASTI) Settat Morocco

ISBN: (数字)9798350365306

ISBN: (纸本)9798350365313

This paper focuses on the modeling of an induction machine, with a specific emphasis on saturation of the main path. The model, formulated in a two-axis system, considers the saturation effect to accurately represent the behavior of the machine. Two scenarios are studied namely nominal and high-level saturation cases. All parameters of the machine are treated as variables, and a comprehensive discussion is provided regarding the effects of certain parameters, shedding light on their influence on the induction machine’s dynamic performance. Simulation work is carried out using the MATLAB/Simulink environment, providing valuable insights into the system’s dynamic behavior under different saturation conditions.

关键词： Analytical models Torque Stators Observers Motors Mathematical models Induction machines

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Designing the Algorithms for Constructing a Triangle with Maximum Area 18

Designing the Algorithms for Constructing a Triangle with Ma...

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18th IEEE International Conference on computer Science and Information Technologies, CSIT 2023

作者： Mulesa, Oksana Rublyov, Bogdan Povkhan, Igor Sihetii, Ihor Kocherha, Nika Bilak, Yurii Uzhhorod National University Department of Software Systems Uzhhorod Ukraine Taras Shevchenko National University of Kyiv Department of Applied Mathematics Kyiv Ukraine Uzhhorod National University Department of Probability Theory and Mathematical Analysis Uzhhorod Ukraine Taras Shevchenko National University of Kyiv Department of Computer Science Kyiv Ukraine

ISBN: (纸本)9798350360462

The problem of constructing a triangle with a maximum area in a plane is considered. Approximate algorithms were developed to solve the problem using point elimination based on proposed heuristics. All algorithms are brought to software implementations. Computational experiments were conducted for samples ranging from 100 to 500 points. The accuracy of the obtained solutions varied from 94% to 99.99%. The execution time of the algorithms, compared to the exact method, is 1.2 to 206 times faster. © 2023 IEEE.

关键词： Python

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Analytic weak-stable manifolds in unfoldings of saddle-nodes

arXiv

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arXiv 2024年

作者： Kristiansen, Kristian Uldall Szmolyan, Peter Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs Lyngby2800 Denmark Institute of Analysis and Scientific Computing Technical University of Vienna Austria

Any attracting, hyperbolic and proper node of a two-dimensional analytic vector-field has a unique strong-stable manifold. This manifold is analytic. The corresponding weak-stable manifolds are, on the other hand, not unique, but in the nonresonant case there is a unique weak-stable manifold that is analytic. As the system approaches a saddle-node (under parameter variation), a sequence of resonances (of increasing order) occur. In this paper, we give a detailed description of the analytic weak-stable manifolds during this process. In particular, we relate a "flapping-mechanism", corresponding to a dramatic change of the position of the analytic weak-stable manifold as the parameter passes through the infinitely many resonances, to the lack of analyticity of the center manifold at the saddle-node. Our work is motivated and inspired by the work of Merle, Raphaël, Rodnianski, and Szeftel, where this flapping mechanism is the crucial ingredient in the construction of C∞-smooth self-similar solutions of the compressible Euler *** Codes 34C23, 34C45, 37G05, 37G10 Copyright © 2024, The Authors. All rights reserved.

关键词： Euler equations

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