当期目录

2026年 第41卷 第1期    刊出日期：2026-03-30

上一期   

常黎曼数量曲率Hermitian结构中的临界Hermitian度量研究

关庄丹, 闫笑峰

2026, 41(1):  1-14.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.001

摘要 ( 18 )   PDF (341KB) ( 6 )  

相关文章 | 计量指标

It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is also
Einstein or isometric to a standard sphere. In the Riemannian case, it’s tangent space satisfies a decomposition. In this paper, we prove that if we only consider the Hermitian metrics, it also have a decomposition. Then we obtain the equation of the critical points among the Hermitian metrics.


非交换留数和扭化BCV空间的次黎曼极限

李洪峰, 刘克峰, 王勇

2026, 41(1):  15-37.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.002

摘要 ( 21 )   PDF (369KB) ( 4 )  

相关文章 | 计量指标

In this paper, we derive the sub-Riemannian version of the Kastler-KalauWalze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces. We also compute the Connes conformal invariants for the twisted product, as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.


航空器供油问题的优先准则及梯度排序算法

林浩, 何程

2026, 41(1):  38-49.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.003

摘要 ( 12 )   PDF (346KB) ( 0 )  

相关文章 | 计量指标

The airplane refueling problem can be stated as follows. We are given n airplanes which can refuel one another during the flight. Each airplane has a reservoir volume w_j (liters) and a consumption rate p_j (liters per kilometer). As soon as one airplane runs out of fuel, it is dropping out of the flight. The problem asks for finding a refueling scheme such that the last plane in the air reach a maximal distance. An equivalent version is the n-vehicle exploration problem. The computational complexity of

this non-linear combinatorial optimization problem is open so far. This paper employs the neighborhood exchange method of single-machine scheduling to study the precedence relations of jobs, so as to improve the necessary and sufficiency conditions of optimal solutions, and establish an efficient heuristic algorithm which is a generalization of several existing special algorithms.

极小化线性分式函数的全局优化算法

赵鹏, 申培萍, 钟哲伟

2026, 41(1):  50-59.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.004

摘要 ( 13 )   PDF (295KB) ( 2 )  

相关文章 | 计量指标

In this paper, we study a class of Linear Fractional Programming on a nonempty bounded set, called the Problem (LFP), and design a branch and bound algorithm to find the global optimal solution of the problem (LFP). First, we convert the problem (LFP) to the equivalent problem (EP2). Secondly, by applying the linear relaxation technique to the problem (EP2), the linear relaxation programming problem (LRP2_Y ) was obtained. Then, the overall framework of the algorithm is given, and the convergence and complexity of the algorithm are analyzed. Finally, experimental results are listed to illustrate the effectiveness of the algorithm.


Stefan同调谱序列的新构造

刘立宇

2026, 41(1):  60-67.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.005

摘要 ( 9 )   PDF (319KB) ( 1 )  

相关文章 | 计量指标

In this paper, we offer a new construction of Stefan’s homological spectral sequence for Hopf Galois extensions, by using the double complex argument. Under the faithfully flat condition, a method for computation of Hochschild homology is given.


一类具有个人意识影响的 S₁S₂EIQR 猴痘模型

吴文哲, 张太雷

2026, 41(1):  68-81.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.006

摘要 ( 9 )   PDF (1258KB) ( 1 )  

相关文章 | 计量指标

According to the characteristics of mpox transmission, we establish a class of S₁S₂EIQR mpox infectious disease models with individual consciousness influence, and obtain the basic reproduction number of the model by using the next generation matrix method. The existence of the endemic equilibrium is demonstrated, and the global asymptotic stability of the disease-free equilibrium is obtained when R₀ ≤1. When R₀ >1, the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable. The data of mpox cases from Beijing are collected to simulating the epidemic trends of mpox in the next few months. The results show that increasing the isolation ratio of infected patients, increasing the cure rate of infected patients, and increasing the rate of unconscious to conscious transfer could reduce the cumulative number of mpox infections.


具位势项的非齐次四阶Schrödinger方程的适定性研究

夏素霞, 李烁

2026, 41(1):  82-91.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.007

摘要 ( 18 )   PDF (367KB) ( 2 )  

相关文章 | 计量指标

The paper considers the initial value problem of inhomogeneous fourth-order Schrödinger equation with potential in energy space H²(R^d). The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle, Strichartz estimates, Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.


系数矩阵相似于diag(λ,J₂(λ)) 的类Yang-Baxter方程的所有非交换解

王云杰

2026, 41(1):  92-110.  doi:10.13371/j.cnki.chin.q.j.m.2026.01.008

摘要 ( 12 )   PDF (359KB) ( 3 )  

相关文章 | 计量指标

Let A be a 3×3 singular or diagonalizable matrix, all solutions to the Yang-Baxter-like matrix equation have been determined. However, finding all solutions for full rank, non-diagonalizable matrices remains challenging. By utilizing classification techniques, we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J₂(λ)) with λ= 0. More specifically, we divide the non-diagonal elements of the solution into 10 different cases. By discussing each situation, we establish all solutions of the YangBaxter-like matrix equation. The results of this work enrich the existing ones.