Chinese Quarterly Journal of Mathematics

Current Issue

30 December 2024, Volume 39 Issue 4

Previous Issue

Blow-Up and Decay Estimate in a Logarithmic p-Laplace Parabolic Equation

LI Ping, LI Feng-jie

2024, 39(4): 331-354.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.001

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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.

Discontinuous Galerkin Method for Hydrodynamic and Sediment Transport Model

ZHANG Ren-peng, WANG Bo, WANG Qiang,

2024, 39(4): 355-365.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.002

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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.

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

2024, 39(4): 366-378.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.003

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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.

Independence Polynomials and the Merrifield-Simmons Index of Mono-Layer Cylindrical Grid Graphs

JI Lin-xing, ZHANG Ke, HU Wen-jun

2024, 39(4): 379-387.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.004

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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 ......

Branch and Bound Algorithm for Globally Solving Minimax Linear Fractional Programming

WANG Hui-man, SHEN Pei-ping, LIANG Yu-xin

2024, 39(4): 388-398.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.005

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In this paper, we study the minimax linear fractional programming problem on a non-empty bounded set, called problem (MLFP), and we design a branch and bound algorithm to find a globally optimal solution of (MLFP). Firstly, we convert the problem (MLFP) to a problem (EP2) that is equivalent to it. Secondly, by applying the convex relaxation technique to problem (EP2), a convex quadratic relaxation problem (CQRP) is obtained. Then, the overall framework of the algorithm is given and its convergence is proved, the worst-case iteration number is also estimated. Finally, experimental data are
listed to illustrate the effectiveness of the algorithm.

The Degree of Approximation by (E,q)(C,α,β) Means in Orlicz Spaces

CHEN Lin, WU Ga-ridi

2024, 39(4): 399-406.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.006

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In this paper, we study the trigonometric approximation problems of functions which belong to the Lipα class, the Lip(ξ(t)) class, and the W(L^∗_M;ξ(t)) class in Orlicz spaces by using the tools Hölder inequality in Orlicz spaces, the second mean value theorem for integrals, and (E,q)(C,α,β) means etc. At the same time, we give the corresponding degree of approximation.

Some Tighter Monogamy Inequalities in N-Qubit Systems

ZHANG Lu-lu, YANG Yan-min, CHEN Wei

2024, 39(4): 407-419.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.007

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We construct a piecewise function to investigate some monogamy inequalities in terms of the αth power of concurrence and negativity (α≥2), entanglement of formation (α≥\sqrt{2}), and Tsallis-q entanglement (α≥1). These inequalities are tighter than the existing results with detailed examples. Particularly, it is worth highlighting some classes of quantum states which can saturate these monogamy inequalities for α= 2, 4 and 6 in terms of concurrence and negativity and for α= 1, 2 and 3 in terms of Tsallis-q entanglement.

The Hyers-Ulam Stability and Hyers-Ulam Instability for Some Nonhomogeneous Ordinary Differential Equations

DENG Jing-tao

2024, 39(4): 420-430.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.008

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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.

A Spectral Radius Condition for a Graph to Have (a,b)-Parity Factors

WANG Jun-jie, YU Yang, HU Jian-biao, WEN Peng

2024, 39(4): 431-440.

doi:10.13371/j.cnki.chin.q.j.m.2024.04.009

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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......