数学季刊

李洪峰, 刘克峰, 王勇

2025, 40(2): 111-134. doi:10.13371/j.cnki.chin.q.j.m.2025.02.001

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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.

呈指数型增长的函数类中的Volterra奇异积分方程的解的存在性

张雯雯, 李平润

2025, 40(2): 135-147. doi:10.13371/j.cnki.chin.q.j.m.2025.02.002

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The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations (VSIEs) with convolution and Cauchy kernels in a more general function class. To obtain the analytic solutions, we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis. In view of the analytical Riemann-Hilbert method, the generalized Liouville theorem and Sokhotski-Plemelj formula, we get the uniqueness and existence of solutions for such problems, and study the asymptotic property of solutions at nodes. Therefore, this paper improves the theory of singular integral equations and boundary value problems.

简单几何区域上庞加莱不等式中的最佳常数

陈红如, 马高超, 张蓓

2025, 40(2): 148-157. doi:10.13371/j.cnki.chin.q.j.m.2025.02.003

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In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain.

余图的完美双罗马控制

李鹏, 薛心怡, 龙旸靖, 李雪波

2025, 40(2): 158-168. doi:10.13371/j.cnki.chin.q.j.m.2025.02.004

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Consider a graph G = (V,E). A perfect double Roman dominating function (PDRDF for short) is a function h:V → {0,1,2,3} that satisfies the condition

具有多时滞的非对称大规模环形神经网络的动态行为

张文喻, 李明慧, 程尊水

2025, 40(2): 169-179. doi:10.13371/j.cnki.chin.q.j.m.2025.02.005

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The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results.

不连续振子在非共振情形下的有界性

边静珂, 刘杰

2025, 40(2): 180-202. doi:10.13371/j.cnki.chin.q.j.m.2025.02.006

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In this paper, we first consider a specific discontinuous differential equation for a smooth and discontinuous (SD) oscillator

关于 Strongly Semipotent 环的一个注记

蒙燕媚, 郭勇华

2025, 40(2): 203-210. doi:10.13371/j.cnki.chin.q.j.m.2025.02.007

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This note is to investigate the properties of strongly semipotent rings. It is proved that every strongly semipotent ring is a idempotent unit regular ring, i.e., there exist a non-zero idempotent e and a unit u such that er =eu for all r /∈J(R), where J(R) is the Jacobson radical of ring R.

关于Hermite-Hadamard (p,q)-积分不等式的推广

刘雪, 成立花

2025, 40(2): 211-220. doi:10.13371/j.cnki.chin.q.j.m.2025.02.008

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This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via (p,q)-quantum integrals. First, based on the definitions of (p,q)-derivatives and integrals over finite intervals, we establish a unified (p,q)-Hermite-Hadamard inequality framework, combining midpoint-type and trapezoidal-type inequalities into a single form. Furthermore, by introducing a parameter λ, we propose a generalized (p,q)-integral inequality, whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature. Furthermore, using hybrid integral techniques, we construct refined inequalities that incorporate (p,q)-integral
terms, and by adjusting λ, we demonstrate their improvements and extensions to known inequalities. Specific examples are provided to validate the applicability of the results. The findings indicate that the proposed (p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error, convex optimization problems, and analysis of system performance in control theory, thus enriching the research results of quantum calculus in the field of inequalities.

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