检索结果-内蒙古大学图书馆

Symplectic integration with Jacobi polynomials

学校读者我要写书评

暂无评论

arXiv 2018年

In this paper, we study symplectic integration of canonical Hamiltonian systems with Jacobi polynomials. The relevant theoretical results of continuous-stage Runge-Kutta methods are revisited firstly and then symplectic methods with Jacobi polynomials will be established. A few numerical experiments are well performed to verify the efficiency of our new methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Runge Kutta methods

An extended framework of continuous-stage Runge-Kutta methods

学校读者我要写书评

暂无评论

arXiv 2018年

We propose an extended framework for continuous-stage Runge-Kutta methods which enables us to treat more complicated cases especially for the case weighting on infinite intervals. By doing this, various types of weighted orthogonal polynomials (e.g., Jacobi polynomials, Laguerre polynomials, Hermite polynomials etc.) can be used in the construction of Runge-Kutta-type methods. Particularly, families of Runge-Kutta-type methods with geometric properties can be constructed in this new framework. As examples, some new symmetric and symplectic integrators by using Legendre polynomials, Laguerre polynomials and Hermite polynomials are constructed. Copyright © 2018, The Authors. All rights reserved.

关键词： Runge Kutta methods

Energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods

学校读者我要写书评

暂无评论

arXiv 2018年

As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preserve it. In this paper, we are concerned with the energy-preserving integration of non-canonical Hamiltonian systems by continuous-stage methods. Algebraic conditions in terms of the Butcher coefficients for ensuring the energy preservation, symmetry and quadratic-Casimir preservation respectively are presented. With the presented condition and in use of orthogonal expansion techniques, the construction of energy-preserving integrators is examined. A new class of energy-preserving integrators which is symmetric and of order 2m is constructed. Some numerical results are reported to verify our theoretical analysis and show the effectiveness of our new methods. Copyright © 2018, The Authors. All rights reserved.

关键词： Numerical methods

Explicit representation for a class of Type 2 constacyclic codes over the ring F2m[u]/(u2λ) with even length

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Cao, Yuan Cao, Yonglin Dinh, Hai Q. Sriboonchitta, Songsak Wang, Guidong School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Economics Chiang Mai University Chiang Mai 52000 Thailand

Let F2m be a finite field of cardinality 2m, λ and k be integers satisfying λ, k ≥ 2 and denote R = F2m[u]/hu2λ. Let δ, α ∞ F2m. For any odd positive integer n, we give an explicit representation and enumeration for all distinct (δ+αu2)-constacyclic codes over R of length 2kn, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every (δ + αu2)-constacyclic code over R of length 2kn is an ideal generated by at most 2 polynomials in the residue class ring R[x]/(x2kn-(δ + αu2). Copyright © 2019, The Authors. All rights reserved.

关键词： Codes (symbols)

An efficient method to construct self-dual cyclic codes of length ps over Fpm + uFpm

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Cao, Yuan Cao, Yonglin Dinh, Hai Q. Jitman, Somphong School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Department of Mathematics Faculty of Science Silpakorn University Nakhon Pathom73000 Thailand

Let p be an odd prime number, Fpm be a finite field of cardinality pm and s a positive integer. Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over Fp with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length ps over the finite chain ring Fpm+uFpm (u2 = 0). Moreover, We provide an efficient method to construct every self-dual cyclic code of length ps over Fpm + uFpm precisely. Copyright © 2019, The Authors. All rights reserved.

关键词： Matrix algebra

Construction and enumeration for self-dual cyclic codes of even length over F2m + uF2m

学校读者我要写书评

暂无评论

arXiv 2019年

作者： Caoa, Yuan Cao, Yonglin Dinh, Hai Q. Fu, Fang-Wei Ma, Fanghui School of Mathematics and Statistics Shandong University of Technology Zibo Shandong255091 China Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and Statistics Hubei University Wuhan430062 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha Hunan410114 China Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Viet Nam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam Chern Institute of Mathematics and LPMC Nankai University Tianjin300071 China

Let F2m be a finite field of cardinality 2m, R = F2m + uF2m (u2 = 0) and s, n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length 2sn and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over F2m of length 2s+1n can be obtained from self-dual cyclic code over R of length 2sn and by a Gray map preserving orthogonality and distances from R onto F22m. Copyright © 2019, The Authors. All rights reserved.

关键词：

Correction to: Numerical study of the unsteady thermal transport of nanofluid with mixed convection and modified Fourier’s law: an application perspective in irrigation systems and biotechnology

学校读者我要写书评

暂无评论

Applied Nanoscience 2021年第3期12卷 293-293页

作者： Faiza Chu, Y. M. Abbas, S. Z. Chammam, W. Khan, W. A. Riahi, A. Rebei, H. Zaway, M. Department of Mathematics and Statistics Hazara University Mansehra Pakistan Department of Mathematics Huzhou University Huzhou People’s Republic of China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha People’s Republic of China School of Mathematics and Statistics Beijing Institute of Technology Beijing People’s Republic of China Department of Mathematics College of Science Al-Zulfi Majmaah University Al-Majmaah Saudi Arabia Department of Mathematics College of Science Qassim University Qassim Saudi Arabia Department of Mathematics College of Science and Humanities AdDwadimi Shaqra University Shaqra Saudi Arabia

Apollonian metric, uniformity and gromov hyperbolicity

学校读者我要写书评

暂无评论

arXiv 2018年

作者： Li, Yaxiang Vuorinen, Matti Zhou, Qingshan Department of Mathematics Hunan First Normal University Changsha Hunan410205 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology ChangshaHunan410114 China Department of Mathematics and Statistics University of Turku FIN Turku20014 Finland School of Mathematics and Big Data Foshan University Foshan Guangdong528000 China

The main purpose of this paper is to investigate the properties of a mapping which is required to be roughly bilipschitz with respect to the Apollonian metric (roughly Apollonian bilipschitz) of its domain. We prove that under these mappings the uniformity, φ-uniformity and δ-hyperbolicity (in the sense of Gromov with respect to quasihyperbolic metric) of proper domains of Rnare invariant. As applications, we give four equivalent conditions for a quasiconformal mapping which is defined on a uniform domain to be roughly Apollonian bilipschitz, and we conclude that φ-uniformity is invariant under quasimöbius mappings. Copyright © 2018, The Authors. All rights reserved.

关键词： Mapping

Corrigendum to “A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme”

学校读者我要写书评

暂无评论

mathematical Problems in engineering 2021年第1期2021卷

作者： Rabia Hameed Ghulam Mustafa Amina Liaqat Dumitru Baleanu Faheem Khan Maysaa M. Al-Qurashi Yu-Ming Chu Department of Mathematics The Government Sadiq College Women University Bahawalpur Bahawalpur Pakistan Department of Mathematics The Islamia University of Bahawalpur Bahawalpur Pakistaniub.edu.pk Department of Mathematics Cankaya University Ankara 06530 Turkeycankaya.edu.tr Institute of Space Sciences Magurele-Bucharest 077125 Romaniaspacescience.ro Department of Medical Research China Medical University Hospital China Medical University Taichung 40402 *** Department of Mathematics University of Sargodha Sargodha Pakistanuos.edu.pk Department of Mathematics Faculty of Sciences King Saud University Riyadh 11451 Saudi Arabiaksu.edu.sa Department of Mathematics Huzhou University Huzhou 313000 *** Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha 410114 ***