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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 （127）      PDF（pc） （490KB）（184）       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

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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 （170）      PDF（pc） （358KB）（179）       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

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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 （149）      PDF（pc） （316KB）（179）       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

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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 （213）      PDF（pc） （365KB）（162）       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

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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 （218）      PDF（pc） （551KB）（147）       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

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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 （239）      PDF（pc） （366KB）（147）       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

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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 （152）      PDF（pc） （347KB）（138）       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

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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 （264）      PDF（pc） （589KB）（137）       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

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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 （198）      PDF（pc） （355KB）（133）       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

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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 （189）      PDF（pc） （465KB）（126）       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

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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 （302）      PDF（pc） （462KB）（122）       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

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Fekete-Szegö Inequalities and the Symmetric Toeplitz Determinants for Certain Analytic Function Class Involving q-Differintegral Operator PEI Ke-ke, LONG Pin-hong, LIU Jin-lin, GANGADHARAN Murugusundaramoorthy Chinese Quarterly Journal of Mathematics    2024, 39 (4): 366-378.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.003 Abstract （165）      PDF（pc） （387KB）（112）       Knowledge map    Save In this paper, we introduce and investigate certain subclass of analytic and univalent functions involving q-differintegral operator. For this function class, we give the bound estimates of the coefficients a2 and a3 and some Fekete-Szegö functional inequalities. Besides, we also estimate the corresponding symmetric Toeplitz determinants. Furthermore, we point out some consequences and connections to these results above. Related Articles | Metrics

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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 （245）      PDF（pc） （320KB）（112）       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

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The Existence of Ground State Solutions for a Class of Sublinear Kirchhoff Equations XU Na Chinese Quarterly Journal of Mathematics    2023, 38 (4): 410-414.   DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.008 Abstract （152）      PDF（pc） （349KB）（102）       Knowledge map    Save In this paper,  we study  a class of sublinear Kirchhoff equations: - (a+  b \int_{\mathbb{R}^N} |\nabla u|^2dx)\Delta u+ V(x)u =f(x,u) \  \   &\text{in}\ \mathbb{R}^N, where a,b>0, V :RN→R can be sign-changing, and f :RN×R→R. Under some conditions on V and f, we verify that the problem possesses   at least one energy  solution by using variational method. Related Articles | Metrics

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Novel Results on the Multi-Parameters Mittag-Leffler Function PAN Yu-mei, LI Yu-fen, CAI Dong-xin, YAN Xing-jie Chinese Quarterly Journal of Mathematics    2025, 40 (1): 82-92.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.008 Abstract （131）      PDF（pc） （328KB）（100）       Knowledge map    Save In this article, the multi-parameters Mittag-Leffler function is studied in detail. As a consequence, a series of novel results such as the integral representation, series representation and Mellin transform to the above function, are obtained. Especially, we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions. Meanwhile, some interesting integral operators and derivative operators of this function, are also discussed Related Articles | Metrics

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Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations LI Xiang, YU Bo, TANG Qiong Chinese Quarterly Journal of Mathematics    2024, 39 (3): 235-249.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.002 Abstract （129）      PDF（pc） （11638KB）（96）       Knowledge map    Save We introduce a factorized Smith method (FSM) for solving large-scale highranked J-Stein equations within the banded-plus-low-rank structure framework. To effectively reduce both computational complexity and storage requirements, we develop techniques including deflation and shift, partial truncation and compression, as well as redesign the residual computation and termination condition. Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time. Related Articles | Metrics

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On the Weyl’s Lemma for Triharmonic Functions ZHENG Run-jie, ZENG Jia-min, FANG Yi Chinese Quarterly Journal of Mathematics    2024, 39 (3): 288-294.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.006 Abstract （150）      PDF（pc） （271KB）（93）       Knowledge map    Save In this paper, by choosing some appropriate test functions, we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas. Related Articles | Metrics

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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 （168）      PDF（pc） （330KB）（92）       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

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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 （191）      PDF（pc） （842KB）（89）       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

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Sure Independence Screening via Semiparameteric Copula Learning XIN Xin, XIE Bo-yi, LIU Ke-ke Chinese Quarterly Journal of Mathematics    2024, 39 (2): 144-160.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.003 Abstract （217）      PDF（pc） （393KB）（89）       Knowledge map    Save  This paper is concerned with ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula (CC-SIS, for short). The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation, conditional mean and distance correlation (SIS, SIRS and DC-SIS, for short) and can significantly improve the performance of feature screening. We establish the sure screening property for the CC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models. At last, we also illustrate the CC-SIS through a real data example. Related Articles | Metrics