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Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation

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Communications in Theoretical Physics 2024年第2期76卷 45-50页

作者： Maebel Mesfun Da-jun Zhang Song-lin Zhao Department of Mathematics Shanghai UniversityShanghai 200444China Newtouch Center for Mathematics of Shanghai University Shanghai 200444China Department of Applied Mathematics Zhejiang University of TechnologyHangzhou 310023China

In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries *** nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice *** such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.

关键词： discrete Korteweg-de Vries equation nonsymmetric multi-dimensional consistency Backlund transformation solution

Continuous Orbit Equivalence of Semigroup Actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1581-1598页

作者： Xiang Qi QIANG Cheng Jun HOU School of Mathematical Science Yangzhou UniversityYangzhou 225002P.R.China

We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms,and characterize them in terms of the corresponding transformation groupoids and their operator *** particular,we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C^(∗)-isomorphism between the associated transformation groupoid C^(∗)-*** also give some examples of orbit equivalence,consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.

关键词： Semigroup action continuous one-sided orbit equivalence continuous orbit equivalence groupoid C^(∗)-algebras

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Differential Operator Approach to■quantum Groups and Their Oscillator Representations

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1360-1374页

作者： Zhao Bing FAN Ji Cheng GENG Shao Long HAN College of Mathematical Science Harbin Engineering UniversityHarbin 150001P.R.China

For a quasi-split Satake diagram,we define a modified q-Weyl algebra,and show that there is an algebra homomorphism between it and the corresponding■quantum *** other words,we provide a differential operator approach to■quantum ***,the oscillator representations of■quantum groups are *** crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

关键词： ■quantum group differential operator oscillator representation crystal basis

A novel method for determining the resistivity of compressed superconducting materials

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Matter and Radiation at Extremes 2024年第4期9卷 1-3页

作者： Liling Sun Qi Wu Shu Cai Yang Ding Ho-kwang Mao Center for High Pressure Science and Technology Advanced Research Beijing 100094China Institute of Physics Chinese Academy of SciencesBeijing 100190China

The measurement of resistivity in a compressed material within a diamond anvil cell presents significant *** high-pressure exper-imental setup makes it difficult to directly measure the size changes induced by pressure in the three crystallographic directions of the *** this study,we introduce a novel and effective method that addresses these technical *** method is anticipated to offer a valuable foundation for high-pressure investigations on quantum materials,particularly those with anisotropic layered structures.

关键词： resistivity method foundation

The Weighted Basis for PHT-Splines

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工程与科学中的计算机建模(英文) 2024年第1期138卷 739-760页

作者： Zhiguo Yong Hongmei Kang Falai Chen School of Mathematical Sciences Soochow UniversitySuzhou215006China School of Mathematical Sciences University of Science and Technology of ChinaHefei230026China

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement *** original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical *** non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of *** the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate *** this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et *** be appropriately modified to form a partition of *** non-decay basis function is multiplied by a positive weight to form the weighted *** weights are solved such that the sum of weighted bases is equal to 1 on the *** provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of *** are given in the form of explicit formulas and can be efficiently *** also prove that the weights on the admissible hierarchical T-meshes are positive.

关键词： PHT-splines partition of unity weighted bases PHT-splines subdivision

UNCONDITIONAL ERROR ANALYSIS OF VEMS FOR A GENERALIZED NONLINEAR SCHRODINGER EQUATION

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Journal of Computational Mathematics 2024年第2期42卷 500-543页

作者： Meng Li Jikun Zhao Shaochun Chen School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China

In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error *** constructing a time-discrete system,the error between the solutions of the continuous model and the numerical scheme is separated into the temporal error and the spatial error,which makes the spatial error τ-*** inverse inequalities in the existing conforming and new constructed nonconforming virtual element spaces are utilized to derive the L^(∞)-norm uniform boundedness of numerical solutions without any restrictions on time-space step ratio,and then unconditionally optimal error estimates of the numerical schemes are obtained *** needs to be emphasized is that if we use the pre-existing nonconforming virtual elements,there is no way to derive the L^(∞)-norm uniform boundedness of the functions in the nonconforming virtual element spaces so as to be hard to get the corresponding inverse ***,several numerical examples are reported to confirm our theoretical results.

关键词： Conforming and nonconforming Virtual element methods Leap-frog scheme Generalized nonlinear Schrodinger system Unconditionally optimal error estimates

Homological Transfer between Additive Categories and Higher Differential Additive Categories

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1325-1344页

作者： Xi TANG Zhao Yong HUANG School of Science Guilin University of Aerospace TechnologyGuilin 541004P.R.China Department of Mathematics Nanjing UniversityNanjing 210093P.R.China

Given an additive category C and an integer n≥*** higher differential additive category consists of objects X in C equipped with an endomorphism ϵ_(X)satisfying ϵ_(X)^(n).Let R be a,finite-dimensional basic algebra over an algebraically closed field and T the augmenting functor from the category of finitely generated left R-modules to that of finitely generated left R/(t^(n))-*** is proved that a finitely generated left R-module M isτ-rigid(respectively,(support)τ-tilting,almost completeτ-tilting)if and only if so is T(M)as a left R[t]/(t^(n))-***,R isτm-selfinjective if and only if so is R[t]/(t^(n)).

关键词： Higher differential objects Wakamatsu tilting subcategories G_(ω)-projective modules sup-portτ-tilting modules τ_(m)-selfinjective algebras precluster tilting subcategories

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WEAK APPROXIMATIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH FRACTIONAL NOISE

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Journal of Computational Mathematics 2024年第3期42卷 735-754页

作者： Meng Cai Siqing Gan Xiaojie Wang School of Mathematics and Statistics HNP-LAMACentral South UniversityChangshaChina

This paper aims to analyze the weak approximation error of a fully discrete scheme for a class of semi-linear parabolic stochastic partial differential equations(SPDEs)driven by additive fractional Brownian motions with the Hurst parameter H∈(1/2,1).The spatial approximation is performed by a spectral Galerkin method and the temporal discretization by an exponential Euler *** far as we know,the weak error analysis for approximations of fractional noise driven SPDEs is absent in the literature.A key difficulty in the analysis is caused by the lack of the associated Kolmogorov *** the present work,a novel and efficient approach is presented to carry out the weak error analysis for the approximations,which does not rely on the associated Kolmogorov equations but relies on the Malliavin *** the best of our knowledge,the rates of weak convergence,shown to be higher than the strong convergence rates,are revealed in the fractional noise driven SPDE setting for the first *** examples corroborate the claimed weak orders of convergence.

关键词： Parabolic SPDEs Fractional Brownian motion Weak convergence rates Spec-tral Galerkin method Exponential Euler method Malliavin calculus

Module Structures on U(ε^(-))for the Euclidean Algebra

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Algebra Colloquium 2024年第1期31卷 49-56页

作者： Yixin Bao Yan'an Cai School of Sciences Harbin Institute of Technology ShenzhenGuangdong 518055China Department of Mathematics Soochow University SuzhouJiangsu 215006China

We classify modules which are free of rank 1 when restricted to the negative part for the Euclidean Lie *** and necessary conditions for the simplicity of these modules are *** these modules we construct modules which... 详细信息

关键词： Euclidean algebra free module simple module nonweight module