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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 （115）      PDF（pc） （490KB）（166）       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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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 （287）      PDF（pc） （462KB）（115）       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 （150）      PDF（pc） （387KB）（94）       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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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 （117）      PDF（pc） （328KB）（87）       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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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 （150）      PDF（pc） （308KB）（84）       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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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 （136）      PDF（pc） （271KB）（84）       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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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 （126）      PDF（pc） （11638KB）（81）       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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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 （164）      PDF（pc） （1085KB）（77）       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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Moments of Dirichlet L-Functions HUANG Bing-rong, HUANG Jun-hao Chinese Quarterly Journal of Mathematics    2025, 40 (4): 360-371.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.003 Abstract （217）      PDF（pc） （346KB）（71）       Knowledge map    Save In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin. Related Articles | Metrics

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Italian Domination of Strong Product of Two Paths WEI Li-yang, LI Feng Chinese Quarterly Journal of Mathematics    2024, 39 (3): 221-234.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.001 Abstract （150）      PDF（pc） （392KB）（66）       Knowledge map    Save The domination problem of graphs is an important issue in the field of graph theory. This paper mainly considers the Italian domination number of the strong product between two paths. By constructing recursive Italian dominating functions, the upper bound of its Italian domination number is obtained, and then a partition method is proposed to prove its lower bound. Finally, this paper yields a sharp bound for the Italian domination number of the strong product of paths. 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 （152）      PDF（pc） （295KB）（58）       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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A Spectral Radius Condition for a Graph to Have (a,b)-Parity Factors WANG Jun-jie, YU Yang, HU Jian-biao, WEN Peng Chinese Quarterly Journal of Mathematics    2024, 39 (4): 431-440.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.009 Abstract （115）      PDF（pc） （367KB）（54）       Knowledge map    Save Let a,b be two positive integers such that a≤b and a≡b (mod 2). We say that a graph G has an (a,b)-parity factor if G has a spanning subgraph F such that...... Related Articles | Metrics

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Pseudo S-Asymptotically (ω,c)-Periodic Solutions to Fractional Differential Equations of Sobolev Type MAO Hang-ning, CHANG Yong-kui Chinese Quarterly Journal of Mathematics    2024, 39 (3): 295-306.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.007 Abstract （145）      PDF（pc） （402KB）（52）       Knowledge map    Save In this paper, we firstly recall some basic results on pseudo S-asymptotically (ω,c)-periodic functions and Sobolev type fractional differential equation. We secondly investigate some existence of pseudo S-asymptotically (ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type. We finally present a simple example. 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 （204）      PDF（pc） （417KB）（50）       Knowledge map    Save In this paper, we study high energy normalized solutions for the following Schrödinger equation …… 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 （182）      PDF（pc） （354KB）（50）       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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ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces LI Hong-feng, LIU Ke-feng, WANG Yong Chinese Quarterly Journal of Mathematics    2025, 40 (2): 111-134.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.001 Abstract （163）      PDF（pc） （367KB）（49）       Knowledge map    Save In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces. Related Articles | Metrics

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The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations DENG Jing-tao Chinese Quarterly Journal of Mathematics    2024, 39 (4): 420-430.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.04.008 Abstract （159）      PDF（pc） （341KB）（49）       Knowledge map    Save In this paper, we get a necessary and sufficient condition such that a class of differential inequalities hold. Using this necessary and sufficient condition, we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability. And then, we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions. 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 （184）      PDF（pc） （321KB）（49）       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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Applications of Matrix Equations in Linear Time-Invariant Systems ZHOU Yan-ping, CHEN Yan-ping, ZHANG Juan Chinese Quarterly Journal of Mathematics    2025, 40 (3): 221-237.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.001 Abstract （133）      PDF（pc） （337KB）（48）       Knowledge map    Save With the development of science and technology, the design and optimization of control systems are widely applied. This paper focuses on the application of matrix equations in linear time-invariant systems. Taking the inverted pendulum model as an example, the algebraic Riccati equation is used to solve the optimal control problem, and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix. Then, the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems, with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration. Two methods for solving the Lyapunov equations are introduced, providing references for related research. Related Articles | Metrics

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Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential LI Nan, ZHAO Hui-yan, XU Li-ping Chinese Quarterly Journal of Mathematics    2024, 39 (3): 250-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2024.03.003 Abstract （147）      PDF（pc） （425KB）（46）       Knowledge map    Save  In this paper, we mainly focus on the following Choquard equation...... Related Articles | Metrics