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Acta Mathematica Scientia 2024年第5期44卷 2019-2040页

作者： Li HU Zhiyuan LI Xiaona YANG school of mathematics and Statistics Ningbo UniversityNingbo315211China school of Mathematical sciences Xiamen UniversityXiamen361005China

In this article,we consider the diffusion equation with multi-term time-fractional *** first derive,by a subordination principle for the solution,that the solution is positive when the initial value is *** an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a ***,several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

关键词： fractional diffusion equation inverse source problem nonlocal observation observation uniqueness Tikhonov regularization

Ramsey Numbers of Trees Versus Multiple Copies of Books

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 600-612页

作者： Xiao-bing GUO Si-nan HU Yue-jian PENG school of Mathematical sciences Luoyang Normal UniversityLuoyang 471934China school of mathematics Hunan UniversityChangsha 410082China

Given two graphs G and H,the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_(N) in red or blue yields a red G or a blue *** v(G) be the number of vertices of G and χ(G) be the chromatic number of *** s(G) denote the chromatic surplus of G,the number of vertices in a minimum color class among all proper χ(G)-colorings of *** showed that R(G,H)≥(v(G)-1)(χ(H)-1)+s(H) if G is connected and v(G)≥s(H).A connected graph G is H-good if R(G,H)=(v(G)-1)(χ(H)-1)+s(H).Let tH denote the disjoint union of t copies of graph H,and let G∨H denote the join of G and *** a complete graph on n vertices by K_(n),and a tree on n vertices by T_(n).Denote a book with n pages by B_(n),i.e.,the join K_(2) ∨■.Erd?s,Faudree,Rousseau and Schelp proved that T_(n) is B_(m)-good if n≥*** this paper,we obtain the exact Ramsey number of T_(n) versus 2B_(2).Our result implies that T_(n) is 2B_(2)-good if n≥5.

关键词： ramsey number ramsey goodness tree book

Nonlinear Potential Analysis in Morrey Spaces on Carnot Groups

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Journal of Mathematical Research with Applications 2024年第5期 669-680页

作者： Pinhong LONG Huili HAN school of mathematics and Statistics Ningxia University school of mathematics and computer Science Ningxia Normal University

In this paper, the nonlinear potential theory in the Morrey spaces on Euclidean spaces and the Lebesgue spaces on the Carnot group are studied. According to the methods of abstract harmonic analysis in Heisenberg group and abstract potential theory in carnot group, we mainly give some characterizations for Riesz, Bessel and Wolff potentials, and the corresponding capacities in the Morrey spaces on Carnot group. Meanwhile, we also interpret the relation among Riesz and Bessel type capacities and Housdorff content in the Morrey spaces on Carnot group. All these results above generalize the related ones in the Morrey spaces on Euclidean spaces and the Lebesgue spaces on the Carnot group.

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Tighter sum uncertainty relations via(α,β,γ)weighted Wigner–Yanase–Dyson skew information

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Communications in Theoretical Physics 2024年第3期76卷 91-99页

作者： Cong Xu Zhaoqi Wu Shao-Ming Fei school of Mathematical sciences Capital Normal UniversityBeijing 100048China Department of mathematics Nanchang UniversityNanchang 330031China Max-Planck-Institute for mathematics in the sciences 04103 LeipzigGermany

We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew *** results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew *** also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew *** examples are provided to illustrate the tightness of our uncertainty relations.

关键词： quantum channels (α,β,γ)WWYD skew information (α,β,γ)MWWYD skew information uncertainty relations

UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE MICROPOLAR NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： Micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

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Chinese Physics B 2024年第7期33卷 137-145页

作者：张晓娇吴祥 school of mathematics and Information Science Nanchang Normal UniversityNanchang 330032China school of Mathematical sciences Guizhou Normal UniversityGuiyang 550001China

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

关键词： contraction theory virtual system bipartite consensus Lurie multi-agent systems

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Frontiers of computer Science 2024年第3期18卷 227-229页

作者： Qianwen GOU Yunwei DONG YuJiao WU Qiao KE school of computer Science Northwestern Polytechnical UniversityXi’an 710129China school of mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710129China

1 Introduction Program retrieval aims to enable the flexible retrieval of program snippets based on a natural language query,significantly accelerating software development *** shows that over 60%of developers perform program retrieval daily[1].Recent years have witnessed an increasing interest in deep learning-based program retrieval,which aims to construct embedding representations for program snippets and ***,the distribution of natural languages and programs is inconsistent,resulting in a semantic *** critical challenge is to bridge the semantic gap between the programming language and natural language,and accurately measure their similarity.

关键词： semantic similarity retrieval

Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1059-1098页

作者： Donald A.DAWSON Jean VAILLANCOURT Hao WANG school of mathematics and Statistics Carleton UniversityOttawaCanada Department of Decision sciences HECMontrealCanada Department of mathematics University of OregonEugeneUSA

We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),... 详细信息

关键词： Measure-valued diffusions stochastic partial differential equations superprocesses branching processes local time Tanaka formula

Compound Product of Hypermatrices

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Journal of Systems Science & Complexity 2024年第1期37卷 169-183页

作者： CHENG Daizhan MENG Min ZHANG Xiao JI Zhengping Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Control Science and Engineering School of Electronics and Information EngineeringTongji UniversityShanghai 201210China National Center for mathematics and Interdisciplinary sciences Chinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100149China.

The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of *** product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general *** different types of hyperdeterminants are introduced and certain properties are *** Lie groups and Lie algebras corresponding to the hypermatrix products are ***,these results are applied to dynamical systems.

关键词： Compound semi-tensor product hyperdeterminants hypereigenvalues and hypereigenvectors hypergeneral linear groups hypermatrices.

The Enhanced Period Map and Equivariant Deformation Quantizations of Nilpotent Orbits

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Acta Mathematica Sinica,English Series 2024年第3期40卷 885-934页

作者： Shi Lin YU Department of mathematics School of Mathematical SciencesXiamen UniversityXiamen 361005P.R.China

In a previous paper,the author and his collaborator studied the problem of lifting Hamil-tonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie *** even quantizations were considered *** this paper,these results are generalized to the case of general quantizations with arbitrary *** key step is to introduce an enhanced version of the(truncated)period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth sym-plectic variety X,with values in the space of Picard Lie algebroid over *** an application,we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition.

关键词： Coadjoint orbit method deformation quantization Harish-Chandra modules semisimple Liegroups