Chinese Quarterly Journal of Mathematics

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

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.

xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions

ZHANG Wen-wen, LI Ping-run

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.

On the Best Constant in Poincar´e Inequality over Simple Geometric Domains

CHEN Hong-ru, MA Gao-chao, ZHANG Bei

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.

Perfect Double Roman Domination on Cographs

LI Peng, XUE Xin-yi, LONG Yang-jing, LI Xue-bo

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

The Dynamic Behavior of Asymmetric Large-Scale Ring Neural Network with Multiple Delays

ZHANG Wen-yu, LI Ming-hui, CHENG Zun-shui

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.

Boundedness in Discontinuous Oscillations at Nonresonance

BIAN Jing-ke, LIU Jie

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

A Note on Strongly Semipotent Rings

MENG Yan-mei, GUO Yong-hua

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.

On New Generalizations of Hermite-Hadamard Inequalities via (p,q)-Integral

LIU Xue, CHENG Li-hua

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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