数学季刊

李平, 李锋杰

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.

水沙输运模型的间断有限元方法

张任鹏, 王波, 王强

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.

涉及 q-微分积分算子的某些解析函数类的 Fekete-Szegö 不等式与对称Toeplitz 行列式

裴柯柯, 龙品红, 刘金林, 甘加达兰穆鲁古桑德拉姆斯

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.

单层圆柱形网格图的独立多项式和Merrifield-Simmons指数

季琳星, 张科, 胡文军

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 ......

全局求解Minimax线性分式规划的分支定界算法

王慧满, 申培萍, 梁雨欣

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.

(E,q)(C,α,β) 平均在Orlicz空间内的逼近阶

陈琳, 吴嘎日迪

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.

N-比特系统更紧的单配性不等式

张露露, 杨彦敏, 陈伟

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.

一些非齐次常微分方程的 Hyers-Ulam 稳定性与 Hyers-Ulam 不稳定性

邓婧涛

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.

图包含 (a,b) 奇偶因子的谱半径条件

王俊杰, 余洋, 胡建彪, 温芃

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......

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