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News
News1
2020-07-24
Current Issue
30 June 2025, Volume 40 Issue 2
Previous Issue
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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n 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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