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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 （247）      PDF（pc） （462KB）（114）       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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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 （173）      PDF（pc） （366KB）（126）       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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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 （161）      PDF（pc） （365KB）（158）       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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Complete Co-Homogeneity One K¨ahler Metrics on the Affine Quadric of Complex Dimension Two (Related to a Cohomogeneity One Point of View on a Yau Conjecture)#br# GUAN Daniel, LIANG Meng-xiang Chinese Quarterly Journal of Mathematics    2024, 39 (2): 200-220.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.008 Abstract （161）      PDF（pc） （387KB）（55）       Knowledge map    Save  In this paper, we revisit the K¨ahler structures on the affine quadrics M1={z12 +z22 +z32 = 1} in the paper by Bo Yang and Fang-Yang Zheng. We found that theK¨ahler structures on the complex surface are more complicated than what they havethought. We shall also give some detail calculations and found that our results fit quitewell with earlier papers of the first author, one of them with X. X. Chen. 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 （159）      PDF（pc） （551KB）（135）       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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High Energy Normalized Solutions for the Schrödinger Equations with Exponential Critical Growth ZHANG Xiao-cang, XU Li-ping Chinese Quarterly Journal of Mathematics    2025, 40 (1): 1-19.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001 Abstract （153）      PDF（pc） （417KB）（47）       Knowledge map    Save In this paper, we study high energy normalized solutions for the following Schrödinger equation …… 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 （151）      PDF（pc） （465KB）（109）       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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Minimum Strong Radius of Strong Product Graphs LIU Shu-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (1): 68-72.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.006 Abstract （140）      PDF（pc） （267KB）（67）       Knowledge map    Save A strong product graph is denoted by G1 ⊠G2, where G1 and G2 are called its factor graphs. This paper gives the range of the minimum strong radius of the strong product graph. And using the relationship between the cartesian product graph G1 ×G2 and the strong product graph G1 ⊠G2, another different upper bound of the minimum strong radius of the strong product graph is given. 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 （138）      PDF（pc） （355KB）（124）       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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Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model ZHANG Ren-peng, WANG Bo, WANG Qiang, Chinese Quarterly Journal of Mathematics    2024, 39 (4): 355-365.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.002 Abstract （132）      PDF（pc） （1085KB）（72）       Knowledge map    Save In this article, we propose and research a first-order, linearized discontinuous Galerkin method for the approximation of the hydrodynamic and sediment transport model. The method is decoupled and fully discrete, and is shown to be unconditionally stable. Furthermore, error estimates are proved. Finally, the theoretical analysis is confirmed by numerical examples. 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 （129）      PDF（pc） （842KB）（83）       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 （128）      PDF（pc） （393KB）（71）       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

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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 （125）      PDF（pc） （330KB）（87）       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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On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2024, 39 (3): 262-269.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.004 Abstract （125）      PDF（pc） （321KB）（48）       Knowledge map    Save This paper studies the non-homogeneous generalized Riemann-Hilbert (RH) problems involving two unknown functions. Using the uniformization theorem, such problems are transformed into the case of homogeneous type. By the theory of classical boundary value problems, we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains, and analyze the conditions of solvability and properties of solutions in various domains. Related Articles | Metrics

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Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei Chinese Quarterly Journal of Mathematics    2025, 40 (3): 304-312.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006 Abstract （119）      PDF（pc） （354KB）（44）       Knowledge map    Save We investigate the blow-up effect of solutions for a non-homogeneous wave equation utt −∆u−∆ut =I0α+ (|u|p)+ω(x), where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent. Related Articles | Metrics

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Combinatorial Identities Concerning Harmonic Numbers CHEN Yu-lei, GUO Dong-wei Chinese Quarterly Journal of Mathematics    2024, 39 (3): 307-314.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.008 Abstract （118）      PDF（pc） （295KB）（57）       Knowledge map    Save In this paper, we firstly establish a combinatorial identity with a free parameter x, and then by means of derivative operation, several summation formulae concerning classical and generalized harmonic numbers, as well as binomial coefficients are derived. Related Articles | Metrics

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The Varieties of Semi-Conformal Vectors of Rank-One Even Lattice Vertex Operator Algebras CHU Yan-jun, GAO Yi-bo Chinese Quarterly Journal of Mathematics    2025, 40 (1): 36-48.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004 Abstract （116）      PDF（pc） （430KB）（31）       Knowledge map    Save In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras…… Related Articles | Metrics

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Upper Bounds on the Aα Spectral Radius of Irregular Weighted Digraphs XI Wei-ge, XU Tao Chinese Quarterly Journal of Mathematics    2024, 39 (2): 161-170.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.02.004 Abstract （115）      PDF（pc） （345KB）（37）       Knowledge map    Save  Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number. Let A(D) be the adjacency matrix of D and W(D) = diag(w1+,w2+,...,wn+). In this paper, we study the matrix Aα(D), which is defined as Aα(D) =αW(D)+ (1−α)A(D), 0≤α≤1. The spectral radius of Aα(D) is called the Aα spectral radius of D, denoted by λα(D). We obtain some upper bounds on the Aα spectral radius of strongly connected irregular weighted digraphs. Related Articles | Metrics

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The w-(b,c)-Core Inverse FANG Li, ZHAO Liang Chinese Quarterly Journal of Mathematics    2025, 40 (1): 26-35.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003 Abstract （114）      PDF（pc） （308KB）（72）       Knowledge map    Save We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core inverses are unified and generalized. Related Articles | Metrics

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Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy LIU Gong-wei, YANG Kun Chinese Quarterly Journal of Mathematics    2024, 39 (1): 97-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.010 Abstract （113）      PDF（pc） （348KB）（55）       Knowledge map    Save We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions. Related Articles | Metrics