Most Down Articles

Published in last 1 year | In last 2 years| In last 3 years| All| Most Downloaded in Recent Month | Most Downloaded in Recent Year|

In last 2 years

Please wait a minute...


For Selected: Download Citations EndNote Ris BibTeX Toggle Thumbnails

Select

Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity PAN Jia-hui, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2023, 38 (4): 360-369.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.003 Abstract （80）      PDF（pc） （358KB）（167）       Knowledge map    Save  In this paper, we study the initial boundary value problem of pseudo-parabolic p-Laplacian type equation, which be use to model some important physical and biological phenomena. By using the potential well method, we obtain the global existence, asymptotic behavior and blow up results of weak solution with subcritical initial energy. Then we also extend these results to the critical initial energy. Related Articles | Metrics

Select

Hopf-Rinow Theorem on Convex Complex Finsler Manifolds LI Hong-jun Chinese Quarterly Journal of Mathematics    2024, 39 (1): 31-45.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.003 Abstract （125）      PDF（pc） （365KB）（142）       Knowledge map    Save Suppose (M,F) is a convex complex Finsler manifold. We prove that geodesics of (M,F) are locally minimizing. Hence, F introduces a distance function d such that (M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on (M,F). Related Articles | Metrics

Select

On the Stokes Phenomenon and Representation Theory of Quantum Groups XU Xiao-meng Chinese Quarterly Journal of Mathematics    2023, 38 (3): 311-330.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.005 Abstract （86）      PDF（pc） （458KB）（140）       Knowledge map    Save This is a survey paper that lists our research works in the study of Stokes phenomenon of meromorphic ordinary differential equations and its relation with representation theory of quantum groups Related Articles | Metrics

Select

Some Applications of Surface Curvatures in Theoretical Physics YANG Yi-song Chinese Quarterly Journal of Mathematics    2023, 38 (3): 221-253.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.001 Abstract （467）      PDF（pc） （496KB）（137）       Knowledge map    Save In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type energy called the Helfrich bending energy. In this formalism, the equilibrium shape of a cell vesicle may present itself in a rich variety of geometric and topological characteristics. We first show that there is an obstruction, arising from the spontaneous curvature, to the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. We then propose a scale-invariant anisotropic bending energy, which extends the Canham energy, and show that it possesses a unique toroidal energy minimizer, up to rescaling, in all parameter regime. Furthermore, we establish some genus-dependent topological lower and upper bounds, which are known to be lacking with the Helfrich energy, for the proposed energy. We also present the shape equation in our context, which extends the Helfrich shape equation. The second application arises from astrophysics in the search for a mechanism for matter accretion in the early universe in the context of cosmic strings. In this formalism, gravitation may simply be stored over a two-surface so that the Einstein tensor is given in terms of the Gauss curvature of the surface which relates itself directly to the Hamiltonian energy density of the matter sector. This setting provides a lucid exhibition of the interplay of the underlying geometry, matter energy, and topological characterization of the system. In both areas of applications, we encounter highly challenging nonlinear partial differential equation problems. We demonstrate that studies on these equations help us to gain understanding of the theoretical physics problems considered. Related Articles | Metrics

Select

A New Existence Theorem for Global Attractors and its Application to a Non-Classical Diffusion Equation QIN Yu-ming, CHEN Jia-le, JIANG Hui-te Chinese Quarterly Journal of Mathematics    2023, 38 (3): 276-289.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.003 Abstract （117）      PDF（pc） （364KB）（121）       Knowledge map    Save In this paper, we first survey existed theorems and propose all 46 related open problems of the existence of global attractors for autonomous dynamical systems, then establish a new existence theorem of global attractors which will be applied to a nonclassical diffusion equation for the norm-to-weak continuous, weakly compact semigroup on H01(Ω) and H2(Ω)∩H01(Ω) respectively. As an application of this new existence theorem of global attractors, we obtain the existence of the global attractors onH01(Ω) and H2(Ω)∩ H01(Ω) respectively for a nonclassical-diffusion equation. Related Articles | Metrics

Select

Some New Regularity Criteria for the 3D Boussinesq Equations in Homogeneous Besov Spaces ZOU Mian-lu, LI Qiang Chinese Quarterly Journal of Mathematics    2024, 39 (1): 73-81.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.007 Abstract （107）      PDF（pc） （355KB）（120）       Knowledge map    Save In this paper, we study the regularity criterion for the three-dimensional Boussinesq equations in Besov spaces. We show that the smooth solution (u,θ) is regular if the horizonal velocity uh holds Related Articles | Metrics

Select

Harvesting in a Toxic Predator-Prey Model with Carrying Capacity and Maturation Double Delays ZHONG Ying, WEI Yu-ming Chinese Quarterly Journal of Mathematics    2023, 38 (4): 331-348.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.001 Abstract （147）      PDF（pc） （589KB）（119）       Knowledge map    Save  In this paper, a model of predator-prey with dual delay in maturation and carrying capacity is discussed, in which the past activity of the prey should have an impact on the carrying capacity, the mature prey initiates defense mechanisms to release toxins when subjected to predation, and a commercial harvest of the prey is performed. The stability of the equilibrium of the system in the absence of delay is examined and the optimal harvesting strategy of the model is proven. By investigating the roots of the characteristic equation and applying normalized theory, the properties of the coexistence equilibrium of the system and the conditions for the occurrence of the Hopf bifurcation in the neighborhood of the positive equilibrium are described for various combinations of delays. In the end, numerical simulations are used to verify theoretical analysis results. Related Articles | Metrics

Select

The Explicit Formula for the Moore-Penrose Inverse of a 2×2 Block Matrix ZENG Min, YUAN Yong-xin Chinese Quarterly Journal of Mathematics    2023, 38 (4): 401-409.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.007 Abstract （73）      PDF（pc） （347KB）（116）       Knowledge map    Save The representation for the Moore-Penrose inverse of the matrix A B C D  is derived by using the solvability theory of linear equations, where A∈Cm×n, B∈Cm×p, C∈Cq×n and D∈Cq×p, with which some special cases are discussed. Related Articles | Metrics

Select

Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions TANG Zhong-hua, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2024, 39 (1): 18-30.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.002 Abstract （128）      PDF（pc） （366KB）（111）       Knowledge map    Save In this paper, an efficient numerical method is proposed to solve the Caputo-Riesz fractional diffusion equation with fractional Robin boundary conditions. We approximate the Riesz space fractional derivatives using the fractional central difference scheme with second-order accurate. A priori estimation of the solution of the numerical scheme is given, and the stability and convergence of the numerical scheme are analyzed. Finally, a numerical example is used to verify the accuracy and efficiency of the numerical method. Related Articles | Metrics

Select

Maximal Resonance of {(3,4),4}-Fullerene Graphs YANG Rui, MA Yan-fei Chinese Quarterly Journal of Mathematics    2024, 39 (1): 1-17.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.001 Abstract （115）      PDF（pc） （551KB）（110）       Knowledge map    Save A {(3,4),4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4. It follows from Euler’s formula that the number of triangular faces is eight. A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating. Let k be a positive integer, S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern. Moreover, if graph S is k-resonant for any integer k, then S is called maximally resonant. Related Articles | Metrics

Select

Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation LI Ping, LI Feng-jie Chinese Quarterly Journal of Mathematics    2024, 39 (4): 331-354.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.001 Abstract （199）      PDF（pc） （462KB）（101）       Knowledge map    Save This paper deals with an initial-boundary value problem of a fourth-order parabolic equation involving Logarithmic type p-Laplacian, which could be proposed as a model for the epitaxial growth of thin films. By using the variational method and the logarithmic type Sobolev inequality, we give some threshold results for blow-up solutions and global solutions, which could be classified by the initial energy. The asymptotic estimates about blow-up time and decay estimate of weak solutions are obtained. Related Articles | Metrics

Select

Local Existence and Blow-Up of Solutions for Pseudo-Parabolic Equation with Singular Potential and General Nonlinearity JIANG Dong-yue, TANG Zhong-hua, FANG Shao-mei Chinese Quarterly Journal of Mathematics    2024, 39 (2): 111-127.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.001 Abstract （111）      PDF（pc） （465KB）（89）       Knowledge map    Save In this paper, a semilinear pseudo-parabolic equation with a general nonlinearity and singular potential is considered. We prove the local existence of solution by Galerkin method and contraction mapping theorem. Moreover, we prove the blow-up of solution and estimate the upper bound of the blow-up time for J(u0)≤0. Finally, we prove the finite time blow-up and estimate the upper bound of blow-up time for J(u0)>0. Related Articles | Metrics

Select

Construction of a Class of Gerstenhaber Algebras HOU Bo, KOU Wen Chinese Quarterly Journal of Mathematics    2023, 38 (4): 370-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.004 Abstract （86）      PDF（pc） （320KB）（88）       Knowledge map    Save For any K-algebra A, based on Hochschild complex and Hochschild cohomology of A, we construct a new Gerstenhaber algebra, and give Gerstenhaber algebra epimorphism from the new Gerstenhaber algebra to the Gerstenhaber algebra of the Hochschild cohomology of A. Related Articles | Metrics

Select

Some Applications of Group Actions in Complex Geometry GUAN Daniel Chinese Quarterly Journal of Mathematics    2023, 38 (3): 254-275.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.002 Abstract （144）      PDF（pc） （399KB）（86）       Knowledge map    Save In this article, we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020, mostly related to my own interests. Related Articles | Metrics

Select

Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs JI Lin-xing, ZHANG Ke, HU Wen-jun Chinese Quarterly Journal of Mathematics    2024, 39 (4): 379-387.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.004 Abstract （40）      PDF（pc） （490KB）（84）       Knowledge map    Save Research on the independence polynomial of graphs has been very active. However, the computational complexity of determining independence polynomials for general graphs remains NP-hard. Let α(G) be the independence number of G and i(G; k) be the number of independent sets of order k in G, then the independence polynomial is defined as ...... Related Articles | Metrics

Select

Global Well-Posedness of the Initial-Boundary Value Problem on Incompressible MHD-Boussinesq Equations with Nonlinear Boundary Conditions WANG Shu, SUN Rui Chinese Quarterly Journal of Mathematics    2023, 38 (3): 290-310.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.03.004 Abstract （92）      PDF（pc） （400KB）（80）       Knowledge map    Save The global well-posedness of another class of initial-boundary value problem on two/three-dimensional incompressible MHD-Boussinesq equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD-Boussinesq equation with the given pressure-velocity’s relation boundary condition for the fluid field, one generalized perfectly conducting boundary condition for the magnetic field and one density/temperature-velocity’s relation boundary condition for the density/temapture at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also proven. Related Articles | Metrics

Select

Boundedness of Integral and Discrete Operators Between Two Types of Weighted Spaces and Estimation of Operator Norm HONG Yong, ZHAO Qian Chinese Quarterly Journal of Mathematics    2024, 39 (1): 59-67.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.005 Abstract （84）      PDF（pc） （330KB）（80）       Knowledge map    Save Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space. Related Articles | Metrics

Select

Subordination and Superordination Results for a Certain of Integral Operator Involving Generalized Mittag-Leffler Functions WANG Xiao-yuan, LIU Ya-juan Chinese Quarterly Journal of Mathematics    2023, 38 (4): 379-391.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.005 Abstract （79）      PDF（pc） （335KB）（78）       Knowledge map    Save  In the paper, by making use of the principle of subordination between analytic functions with the multiplier transforms defined by generalized Mittag-Leffler function, the authors investigate subclasses of univalent analytic functions, such as starlike functions, convex functions, close-to-convex functions and quasiconvex functions. Several inclusion relationships, inequality properties, subordination and superordination results associated with the multiplier transforms are proved and the sandwich-type results are also obtained. Related Articles | Metrics

Select

Codimension-Two Bifurcations Analysis of a Discrete Predator-Prey Model Incorporating a Prey Refuge PANG Ru-yi, CHEN Qiao-ling Chinese Quarterly Journal of Mathematics    2024, 39 (2): 128-143.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.002 Abstract （80）      PDF（pc） （842KB）（76）       Knowledge map    Save  In this paper, a discrete predator-prey model with prey refuge is investigated. It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances. The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors, such as limit cycle, periodic solutions, chaos and codimension-1 bifurcations. Related Articles | Metrics

Select

The Existence and Uniqueness of Self–Dual Monopole Solutions in Gauge Field Theory CHEN Xiao Chinese Quarterly Journal of Mathematics    2024, 39 (1): 86-96.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.009 Abstract （70）      PDF（pc） （316KB）（74）       Knowledge map    Save Magnetic monopoles stand for the static solution arising from a (1+ 3)– dimensional theory describing the interaction between a real scalar triplet and non–Abelian gauge field. In this paper, we obtain a two–point boundary value problem of a first–order ordinary differential equations from the self–dual monopole model. Then we establish the existence and uniqueness theorem for the problem by using a dynamical shooting method, we also obtain sharp asymptotic estimates for the solutions at infinity. Related Articles | Metrics