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Quasi-shadowing for Z^(d)-actions

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1563-1580页

作者： Juan PAN Xian Kun REN Yun Hua ZHOU school of mathematics and statistics Chongqing Technology and Business UniversityChongqing 400067P.R.China College of mathematics and statistics Chongqing UniversityChongqing 401331P.R.China

A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov *** prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the genera... 详细信息

关键词： Quasi-shadowing Z^(d)-action non-uniformly partially hyperbolic ergodic measure

The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li school of mathematics Jilin UniversityChangchun 130012China Institute of mathematics Jilin UniversityChangchun 130012China school of mathematics and statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also *** our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

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A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

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Journal of Computational mathematics 2024年第3期42卷 784-813页

作者： Bo Zhang Yuelin Gao Xia Liu Xiaoli Huang school of Civil and Hydraulic Engineering School of Mathematics and StatisticsNingxia UniversityYinchuan 750021China school of mathematics and Information Science North Minzu UniversityYinchuan 750021China Ningxia Province Key Laboratory of Intelligent Information and Data Processing Yinchuan 750021China school of mathematics and statistics Ningxia UniversityYinchuan 750021China

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network ***,most of the solutions to such problems are often designed for their unique *** paper puts forward a new global optimization algorithm for solving the problem *** first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer ***,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative *** that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is ***,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

关键词： Global optimization Branch and bound Quadratic fractional programming Mixed integer programming

A Note on the Signless Laplacian Spectral Ordering of Graphs with Given Size

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Journal of Mathematical Research with Applications 2024年第3期44卷 304-312页

作者： Nannan LIU Shuguang GUO school of mathematics and statistics Qinghai Normal University school of mathematics and statistics Yancheng Teachers University

Abstract For a simple undirected graph G with fixed size m≥2k （k∈Z+） and maximum degree?（G）≤m-k,we give an upper bound on the signless Laplacian spectral radius q（G）of *** two connected graphs G1and G2with size m≥8,employing this upper bound,we prove that q（G1）>q（G2） if?（G1）>?（G2）+1 and■.For triangle-free graphs,we prove two stronger *** an application,we completely characterize the graph with maximal signless Laplacian spectral radius among all graphs with size m and circumference c for m≥max{2c,c+9},which partially answers the question proposed by Chen et ***[Linear Algebra Appl.,2022,645:123–136].

关键词： signless Laplacian spectral radius upper bound ordering size circumference

Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1521-1532页

作者： Peng Cheng LI Dong He PEI Xin ZHAO school of mathematics and statistics Northeast Normal UniversityChangchun 130024P.R.China Department of mathematics Harbin Institute of TechnologyWeihai 264209P.R.China school of mathematics and statistics Qingdao UniversityQingdao 266071P.R.China

In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski *** is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike ***,we show a new geometric invariant to characterise singularities of the focal ***,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.

关键词： Evolutes focal surfaces spacelike framed curves singularities

A SCALAR AUXILIARY VARIABLE (SAV) FINITE ELEMENT NUMERICAL SCHEME FOR THE CAHN-HILLIARD-HELE-SHAW SYSTEM WITH DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第2期42卷 544-569页

作者： Changhui Yao Fengdan Zhang Cheng Wang school of mathematics and statistics Zhengzhou UniversityZhengzhou 450001China Department of mathematics University of MassachusettsNorth DartmouthMA 02747USA

In this paper,we consider the Cahn-Hilliard-Hele-Shaw(CHHS)system with the dynamic boundary conditions,in which both the bulk and surface energy parts play important *** scalar auxiliary variable approach is introduced for the physical system;the mass conservation and energy dissipation is proved for the CHHS ***,a fully discrete SAV finite element scheme is proposed,with the mass conservation and energy dissipation laws established at a theoretical *** addition,the convergence analysis and error estimate is provided for the proposed SAV numerical scheme.

关键词： Cahn-Hilliard-Hele-Shaw system Dynamic boundary conditions Bulk energy and surface energy Scalar auxiliary variable formulation Energy stability Convergence analysis

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

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Acta Mathematica Scientia 2024年第1期44卷 78-102页

作者：段晓曼关庄丹 school of mathematics and statistics Henan UniversityKaifeng475004China Department of mathematics The University of California at RiversideRiversideCA92521USA

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)***,we apply a strategy to a famou... 详细信息

关键词： Kahler Metrics complete Riemannian metrics open complex manifolds holomorphic bisectional curvature C*bundle almost homogeneous manifolds

The Non-inclusion Diagnosability of Hypercubes Under the PMC Model

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Journal of the Operations Research Society of China 2024年第2期12卷 478-484页

作者： Mei-Jie Ma Min Xu Tong-Tong Ding Xiang-Jun Li Qiang Zhu school of mathematics and statistics Qilu University of Technology(Shandong Academy of Sciences)Jinan 250353ShandongChina school of Mathematical Sciences Beijing Normal UniversityLaboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China school of Information and mathematics Yangtze UniversityJingzhou 434023HubeiChina school of mathematics and statistics XiDian UniversityXi'an 710071ShaanXiChina

Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection ***-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor *** on a sound assumption proposed by Zhu et ***,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability t_(N)(Q_(n))of the hypercube under the PMC model is *** is,assume that if two vertex sets F_(1) and F_(2) are both consistent with a syndrome and F_(1)C F_(2),then F_(2) is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Q_(n) under the PMC model.

关键词： Interconnection network Diagnosability Hypercube PMC model

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

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Applied mathematics and Mechanics(English Edition) 2024年第1期45卷 179-196页

作者： Yali ZHANG Yueting ZHOU Shenghu DING school of mathematics and statistics Ningxia UniversityYinchuan 750021China school of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical *** sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this *** simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert *** analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature *** contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi ***,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact *** on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact *** distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction ***,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

关键词： wavy surface periodic contact thermoelectric(TE)material Hilbert integral kernel