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An extended framework of continuous-stage Runge-Kutta methods

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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

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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

Symplectic integration with Jacobi polynomials

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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

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

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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

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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

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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.

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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

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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

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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

Amplitude analysis of the radiative decay Bs0 → K+K−γ

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arXiv 2024年

作者： Aaij, R. Abdelmotteleb, A.S.W. Abellán Beteta, C. Abudinen Gallego, F.J. Ackernley, T. Adeva, B. Adinolfi, M. Afsharnia, H. Agapopoulou, C. Aidala, C.A. Aiola, S. Ajaltouni, Z. Akar, S. Albrecht, J. Alessio, F. Alexander, M. Alfonso Albero, A. Aliouche, Z. Alkhazov, G. Alvarez Cartelle, P. Amato, S. Amey, J.L. Amhis, Y. An, L. Anderlini, L. Andreianov, A. Andreotti, M. Archilli, F. Artamonov, A. Artuso, M. Arzymatov, K. Aslanides, E. Atzeni, M. Audurier, B. Bachmann, S. Bachmayer, M. Back, J.J. Baladron Rodriguez, P. Balagura, V. Baldini, W. Baptista Leite, J. Barbetti, M. Barlow, R.J. Barsuk, S. Barter, W. Bartolini, M. Baryshnikov, F. Basels, J.M. Bashir, S. Bassi, G. Batsukh, B. Battig, A. Bay, A. Beck, A. Becker, M. Bedeschi, F. Bediaga, I. Beiter, A. Belavin, V. Belin, S. Bellee, V. Belous, K. Belov, I. Belyaev, I. Bencivenni, G. Ben-Haim, E. Berezhnoy, A. Bernet, R. Berninghoff, D. Bernstein, H.C. Bertella, C. Bertolin, A. Betancourt, C. Betti, F. Bezshyiko, Ia. Bhasin, S. Bhom, J. Bian, L. Bieker, M.S. Bifani, S. Billoir, P. Birch, M. Bishop, F.C.R. Bitadze, A. Bizzeti, A. Bjørn, M. Blago, M.P. Blake, T. Blanc, F. Blusk, S. Bobulska, D. Boelhauve, J.A. Boente Garcia, O. Boettcher, T. Boldyrev, A. Bondar, A. Bondar, N. Borghi, S. Borisyak, M. Borsato, M. Borsuk, J.T. Bouchiba, S.A. Bowcock, T.J.V. Boyer, A. Bozzi, C. Bradley, M.J. Braun, S. Brea Rodriguez, A. Brodzicka, J. Brossa Gonzalo, A. Brundu, D. Buonaura, A. Buonincontri, L. Burke, A.T. Burr, C. Bursche, A. Butkevich, A. Butter, J.S. Buytaert, J. Byczynski, W. Cadeddu, S. Cai, H. Calabrese, R. Calefice, L. Calero Diaz, L. Cali, S. Calladine, R. Calvi, M. Calvo Gomez, M. Camargo Magalhaes, P. Campana, P. Campoverde Quezada, A.F. Capelli, S. Capriotti, L. Carbone, A. Carboni, G. Cardinale, R. Cardini, A. Carli, I. Carniti, P. Carus, L. Carvalho Akiba, K. Casais Vidal, A. Casse, G. Cattaneo, M. Cavallero, G. Celani, S. Cerasoli, J. Cervenkov, D. Chadwick, A.J. Chapman, M.G. Charles, M. Rio de Janeiro Brazil Rio de Janeiro Brazil Center for High Energy Physics Tsinghua University Beijing China Beijing China School of Physics State Key Laboratory of Nuclear Physics and Technology Peking University Beijing China University of Chinese Academy of Sciences Beijing China Institute of Particle Physics Central China Normal University Hubei Wuhan China Univ. Savoie Mont Blanc CNRS IN2P3-LAPP Annecy France Université Clermont Auvergne CNRS/IN2P3 LPC Clermont-Ferrand France Aix Marseille Univ CNRS/IN2P3 CPPM Marseille France Université Paris-Saclay CNRS/IN2P3 IJCLab Orsay France Laboratoire Leprince-Ringuet CNRS/IN2P3 Ecole Polytechnique Institut Polytechnique de Paris Palaiseau France LPNHE Sorbonne Université Paris Diderot Sorbonne Paris Cité CNRS/IN2P3 Paris France I. Physikalisches Institut RWTH Aachen University Aachen Germany Fakultät Physik Technische Universität Dortmund Dortmund Germany Heidelberg Germany Physikalisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany School of Physics University College Dublin Dublin Ireland INFN Sezione di Bari Bari Italy INFN Sezione di Bologna Bologna Italy INFN Sezione di Ferrara Ferrara Italy INFN Sezione di Firenze Firenze Italy INFN Laboratori Nazionali di Frascati Frascati Italy INFN Sezione di Genova Genova Italy INFN Sezione di Milano Milano Italy INFN Sezione di Milano-Bicocca Milano Italy INFN Sezione di Cagliari Monserrato Italy Universita degli Studi di Padova Universita e INFN Padova Italy INFN Sezione di Pisa Pisa Italy INFN Sezione di Roma La Sapienza Roma Italy INFN Sezione di Roma Tor Vergata Roma Italy Nikhef National Institute for Subatomic Physics Amsterdam Netherlands Nikhef National Institute for Subatomic Physics VU University Amsterdam Amsterdam Netherlands AGH University of Science and Technology Faculty of Physics and Applied Computer Science Kraków Poland Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy

A search for radiative decay of Bs0 mesons to orbitally excited K+K− states is performed using proton proton collisions recorded by the LHCb experiment, corresponding to an integrated luminosity of 9 fb−1. The dikaon spectrum in the mass range mKK 2 is dominated by the (1020) resonance that accounts for almost 70% of the decay rate. Considering the possible contributions of f2(1270), f2′ (1525) and f2(2010) meson states, the overall tensor contribution to the amplitude is measured to be © 2024, CC BY.

关键词： Bosons