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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

CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS

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Acta Mathematica Scientia 2024年第1期44卷 369-385页

作者：曹南斌李尊凤杨贺菊乔玉英 School of Mathematics and Science Hebei GEO UniversityShijiazhuang050031China College of Science Hebei University of Science and TechnologyShijiazhuang050018China School of Mathematical Sciences Hebei Normal UniversityShijiazhuang050024China

Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value *** this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for ***,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford ***,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.

关键词： Clifford analysis Cauchy type integral Plemelj formula Holder continuous boundary value problems

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

Completeness of Induced Cotorsion Pairs in Representation Categories of Rooted Quivers

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2436-2452页

作者： Zhen Xing DI Li Ping LI Li LIANG Fei XU School of Mathematical Sciences Huaqiao University LCSM (Ministry of Education) School of Mathematics and Statistics Hunan Normal University Department of Mathematics Lanzhou Jiaotong University Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics Department of Mathematics Shantou University

This paper focuses on a question raised by Holm and J?rgensen, who asked if the induced cotorsion pairs(Φ（X）, Φ（X）⊥) and(⊥Ψ（Y）, Ψ（Y）) in Rep（Q, A）—the category of all A-valued representations of a quiver Q—are complete whenever（X, Y） is a complete cotorsion pair in an abelian category A satisfying some mild conditions. We give an affirmative answer if the quiver Q is rooted. As an application, we show under certain mild conditions that if a subcategory L, which is not necessarily closed under direct summands, of A is special precovering（resp., preenveloping）, then Φ（L）(resp.,Ψ（L）) is special precovering（resp., preenveloping） in Rep（Q, A）.

关键词： 16G20 18G25 complete cotorsion pair Rooted quiver special precovering (preenveloping) subcategory

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

ON A UNIVERSAL INEQUALITY FOR APPROXIMATE PHASE ISOMETRIES

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Acta Mathematica Scientia 2024年第3期44卷 823-838页

作者：戴端旭阙海新孙龙发郑本拓 School of Science Jimei UniversityXiamen361021China Hebei Key Laboratory of Physics and Energy Technology School of Mathematics and PhysicsNorth China Electric Power UniversityBaoding071003China Department of Mathematical Sciences University of MemphisMemphisTN38152USA

Let X and Y be two normed *** U be a non-principal ultrafilter on *** g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=*** this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u))|≤5/2εα,for all u ∈ *** particular,let X be a smooth Banach *** we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).

关键词： ε-phase isometry phase isometry Banach space

On the improved dynamics approach in loop quantum black holes

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Communications in Theoretical Physics 2024年第3期76卷 138-143页

作者： Hongchao Zhang Wen-Cong Gan Yungui Gong Anzhong Wang Institute for Theoretical Physics&Cosmology Zhejiang University of TechnologyHangzhou310023China United Center for Gravitational Wave Physics(UCGWP) Zhejiang University of TechnologyHangzhou310023China College of Physics and Communication Electronics Jiangxi Normal UniversityNanchang 330022China GCAP-CASPER Physics DepartmentBaylor UniversityWacoTX 76798-7316United States of America School of Physics Huazhong University of Science and TechnologyWuhanHubei 430074China Department of Physics School of Physical Science and TechnologyNingbo UniversityNingboZhejiang 315211China

In this paper,we consider the B?hmer–Vandersloot(BV)model of loop quantum black holes obtained from the improved dynamics *** adopt the Saini–Singh gauge,in which it was found analytically that the BV spacetime is geodesically *** show that black/white hole horizons do not exist in this geodesically complete ***,there exists only an infinite number of transition surfaces,which always separate trapped regions from anti-trapped *** on the improved dynamics approach adopted in other models of loop quantum black holes are also given.

关键词： loop quantum gravity black hole dynamics approach

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

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