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Journal of Computational mathematics 2024年第3期42卷 705-734页

作者： Tao Sun Chengjian Zhang Haiwei Sun School of mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China department of {1. University of MacaoMacaoChina

This paper deals with numerical methods for solving one-dimensional(1.)and twodimensional(2D)initial-boundary value problems(IBVPs)of space-fractional sine-Gordon equations(SGEs)with distributed *** 1. problems,we construct a kind of oneparameter finite difference(OPFD)*** is shown that,under a suitable condition,the proposed method is convergent with second order accuracy both in time and *** implementation,the preconditioned conjugate gradient(PCG)method with the Strang circulant preconditioner is carried out to improve the computational efficiency of the OPFD *** 2D problems,we develop another kind of OPFD *** such a method,two classes of accelerated schemes are suggested,one is alternative direction implicit(ADI)scheme and the other is ADI-PCG *** particular,we prove that ADI scheme can arrive at second-order accuracy in time and *** some numerical experiments,the computational effectiveness and accuracy of the methods are further ***,for the suggested methods,a numerical comparison in computational efficiency is presented.

关键词： Fractional sine-Gordon equation with distributed delay One-parameter finite difference methods Convergence analysis ADI scheme PCG method

Turán number of Berge linear forests in uniform hypergraphs

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Frontiers of mathematics in China 2024年第1期19卷 25-35页

作者： Liying KANG Jiawei HUANG Yisai XUE Zhiwei WU department of {1. Shanghai UniversityShanghai 200444China

Let F be a graph and H be a *** say that H contains a Berge-F If there exists a bijectionψ:E(F)→E(H)such that for Ve E E(F),e C(e),and the Turan number of Berge-F is defined to be the maximum number of edges in an r-uniform hypergraph of order n that is Berge-F-free,denoted by ex,(n,Berge-F).A linear forest is a graph whose connected components are all paths or isolated *** Ln,k be the family of all linear forests of n vertices with k *** this paper,Turan number of Berge-Ln,in an r-uniform hypergraph is *** r≥k+1.and 3≤r≤l[]=1.we determine 2 the exact value of ex,(n,Berge-Ln,)*** K-1.r≤k,we 2 determine the upper bound of ex,(n,Berge-Ln,).

关键词： Uniform hypergraph Berge hypergraph linear forest Turán number

Dynamics of some new solutions to the coupled DSW equations traveling horizontally on the seabed

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Journal of Ocean Engineering and Science 2024年第2期9卷 154-163页

作者： Raj Kumar Ravi Shankar Verma department of {1. Faculty of Engineering&TechnologyVeer Bahadur Singh Purvanchal UniversityJaunpur 222003India

The system of(1.1.-coupled Drinfel’d-Sokolov-Wilson equations describes the surface gravity waves travelling horizontally on the *** objective of the present research is to construct a new variety of analytical solutions for the *** invariants are derived with the aid of Killing form by using the optimal algebra classification via Lie symmetry *** invariant solutions involve time,space variables,and arbitrary *** adequate constraints on arbitrary constants,solutions are represented graphically to make them more applicable in designing sea *** behavior of solutions shows asymptotic,bell-shaped,bright and dark soliton,bright soliton,parabolic,bright and kink,kink,and periodic *** constructed results are novel as the reported results[26,28,29,30,33,38,42,49]can be deduced from the results derived in this *** remaining solutions derived in this study,are absolutely different from the earlier *** this study,the physical character of analytical solutions of the system could aid coastal engineers in creating models of beaches and ports.

关键词： Coupled Drinfel’d-Sokolov-Wilson model Invariants Killing form Optimal sub algebra Lie symmetry reductions

Multicolored Bipartite Ramsey Numbers of Large Cycles

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 347-357页

作者： Shao-qiang LIU Yue-jian PENG College of mathematics and Statistics Hanshan Normal UniversityChaozhou 521041China School of mathematics Hunan UniversityChangsha 410082China

For an integer r≥2 and bipartite graphs Hi,where 1.i≤r,the bipartite Ramsey number br(H1.H2,…,Hr)is the minimum integer N such that any r-edge coloring of the complete bipartite graph KN;N contains a monochromatic subgraph isomorphic to Hi in color i for some 1.i≤*** show that if r≥3;α1.α2>0,αj+2≥[(j+2)!-1.Σi=1.(j+1.α1.for j=1.2…r-2,then br(C2[α1.],C2[α2n],…,C2[αrn]=(Σ=j=1.(r)a j+o(1.)n.

关键词： ramsey number bipartite ramsey number regularity lemma

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Planar Graphs whose Second Largest Eigenvalue Smaller than ■

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Journal of Mathematical Research with Applications 2024年第1期44卷 1-6页

作者： Zihao GENG Jiming GUO department of {1. East China University of Science and Technology

A graph G is said to be planar if G can be drawn on the plane in such a way that its edges intersect only at their *** this paper,all the planar graphs without isolated vertices whose second largest eigenvalue smaller... 详细信息

关键词： planar graph the second largest eigenvalue complete product

On asymptotic stability of the 3D Boussinesq equations without heat conduction

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Science China mathematics 2024年第2期67卷 253-280页

作者： Lihua Dong Yongzhong Sun School of Physical and Mathematical Sciences Nanjing Tech UniversityNanjing 211816China department of {1. Nanjing UniversityNanjing 210093China

We investigate the asymptotic stability of the solutions to Boussinesq equations without heat conduction with the initial data near a specific stationary solution in the three-dimensional domain Ω=R^(2)×(0,1..It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.

关键词： Boussinesq equations stationary solutions asymptotic stability decay rates

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A COUPLED METHOD COMBINING CROUZEIX-RAVIART NONCONFORMING AND NODE CONFORMING FINITE ELEMENT SPACES FOR BOIT CONSOLIDATION MODEL

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Journal of Computational mathematics 2024年第4期42卷 911-931页

作者： Yuping Zeng Mingchao Cai Liuqiang Zhong School of mathematics Jiaying UniversityMeizhou 514015China department of {1. Morgan State University1700 E Cold Spring LnBaltimoreMD 21251USA School of Mathematical Science South China Normal UniversityGuangzhou 520631China

A mixed finite element method is presented for the Biot consolidation problem in *** precisely,the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements,while the fuid pressure is approximated by using the node conforming finite *** well-posedness of the fully discrete scheme is established,and a corresponding priori error estimate with optimal order in the energy norm is also *** experiments are provided to validate the theoretical results.

关键词： Poroelasticity Nonconforming finite element Inf-sup condition A priori error estimate

A Local Macroscopic Conservative(LoMaC)Low Rank Tensor Method with the Discontinuous Galerkin Method for the Vlasov Dynamics

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Communications on Applied mathematics and Computation 2024年第1期6卷 550-575页

作者： Wei Guo Jannatul Ferdous Ema Jing-Mei Qiu department of {1. and Statistics Texas Tech UniversityLubbockTX70409USA department of Mathematical Sciences University of DelawareNewarkDE19716USA

In this paper,we propose a novel Local Macroscopic Conservative(LoMaC)low rank tensor method with discontinuous Galerkin(DG)discretization for the physical and phase spaces for simulating the Vlasov-Poisson(VP)*** LoMaC property refers to the exact local conservation of macroscopic mass,momentum,and energy at the discrete *** recently developed LoMaC low rank tensor algorithm(arXiv:2207.0051.)simultaneously evolves the macroscopic conservation laws of mass,momentum,and energy using the kinetic flux vector splitting;then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic *** paper is a generalization of our previous work,but with DG discretization to take advantage of its compactness and flexibility in handling boundary conditions and its superior accuracy in the long *** algorithm is developed in a similar fashion as that for a finite difference scheme,by observing that the DG method can be viewed equivalently in a nodal *** the nodal DG method,assuming a tensorized computational grid,one will be able to(i)derive differentiation matrices for different nodal points based on a DG upwind discretization of transport terms,and(ii)define a weighted inner product space based on the nodal DG grid *** algorithm can be extended to the high dimensional problems by hierarchical Tucker(HT)decomposition of solution tensors and a corresponding conservative projection *** a similar spirit,the algorithm can be extended to DG methods on nodal points of an unstructured mesh,or to other types of discretization,e.g.,the spectral method in velocity *** numerical results are performed to showcase the efficacy of the method.

关键词： Hierarchical Tucker(HT)decomposition Conservative SVD Energy conservation Discontinuous Galerkin(DG)method

Noncommutative analysis of Hermite expansions

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Science China mathematics 2024年

作者： Bang Xu department of {1. University of Houston department of Mathematical Sciences Seoul National University

This paper is devoted to the study of semi-commutative harmonic analysis associated with Hermite semigroups. In the first part, we establish the noncommutative maximal inequalities for Bochner-Riesz means associated with Hermite operators and then obtain the corresponding pointwise convergence theorems. In particular, we develop a noncommutative version of Stein’s theorem of Bochner-Riesz means for Hermite operators. In the second part, we investigate two noncommutative multiplier theorems. Our approach in this part relies on a noncommutative analog of the classical Littlewood-Paley-Stein theory associated with Hermite semigroups.

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Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

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Communications on Applied mathematics and Computation 2024年第1期6卷 190-217页

作者： Fangyao Zhu Juntao Huang Yang Yang department of Mathematical Sciences Michigan Technological UniversityHoughtonMI49931USA department of {1. and Statistics Texas Tech UniversityLubbockTX79409USA

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive *** are several difficulties in constructing suitable numerical *** of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and ***,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step *** obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG *** traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1.of the mass *** solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is *** the above two conditions,the positive mass fractions have summation 1.and then,they are all between 0 and *** time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the *** methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be ***,it is not straightforward to combine the bound-preserving DG methods and the Patankar time *** positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target *** match the degree of freedom,we use polynomials on rectangular meshes for problems in two space *** evolve in time,we first read the polynomials at the Gaussian ***,suitable slope l

关键词： Compressible Euler equations Chemical reacting flows Bound-preserving Discontinuous Galerkin(DG)method Modified Patankar method