数学季刊

白雨杰, 毋述斐

2021, 36(3): 221-234. doi:10.13371/j.cnki.chin.q.j.m.2021.03.001

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Let G =( V,E ) be a graph. For a vertex labeling f : V →Z₂ , it induces an edge labeling f ⁺ : E→Z ₂ , where for each edge v ₁ v ₂ ∈E we have f ⁺ ( v ₁ v ₂ )= f ( v ₁ )+ f ( v ₂ ). For each i∈Z ₂, we use v_f( i ) (respectively, e _f ( i )) to denote the number of vertices (respectively, edges) with label i . A vertex labeling f of G is said to be friendly if vertices with different labels differ in size by at most one. The full friendly index set of a graph G , denoted by FFI ( G ), consists of all possible values of e _f (1) −e _f (0), where f ranges over all friendly labelings of G . In this paper, motivated by a problem raised by [6], we study the full friendly index sets of a family of cubic graphs.

一类具有导数型非线性记忆项的半线性波动方程的爆破结果

欧阳柏平, 肖胜中

2021, 36(3): 235-243. doi:10.13371/j.cnki.chin.q.j.m.2021.03.002

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In this paper, we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type. By using methods of an iteration argument and differential inequalities, we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions. Meanwhile, we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

局部共形拟 Kähler Finsler 流形

李鸿军

2021, 36(3): 244-251. doi:10.13371/j.cnki.chin.q.j.m.2021.03.003

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In this paper, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kähler Finsler. As an application, we find any complete strongly convex and locally conformal pseudo-Kähler Finsler manifold, which is simply connected or whose fundamental group contains elements of finite order only, can be given a Kähler metric.

具有非齐次核的半离散 Hilbert 型多重积分不等式的最佳搭配参数及其应用

洪勇, 和炳

2021, 36(3): 252-262. doi:10.13371/j.cnki.chin.q.j.m.2021.03.004

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By using the weight function method, the matching parameters of the half discrete Hilbert type multiple integral inequality with a non-homogeneous kernel K ( n,||x|| _ρ,m ) = G ( n^{λ 1} ||x|| ^{λ 2}_ρ,m) are discussed, some equivalent conditions of the optimal matching parameter are established, and the expression of the optimal constant factor is obtained. Finally, their applications in operator theory are considered.

一个新的无参数填充函数及其在最小二乘法中的应用

李硕, 尚有林, 屈德强

2021, 36(3): 263-274. doi:10.13371/j.cnki.chin.q.j.m.2021.03.005

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The filled function algorithm is an important method to solve global optimization problems. In this paper, a parameter-free filled function is proposed for solving general global optimization problem, discuss the theoretical properties of this function and give the corresponding algorithm. The numerical experiments on some typical test problems using the algorithm and the numerical results show that the algorithm is effective. Applying the filled function method to the parameter solving problem in the logical population growth model, and then can be effectively applied to Chinese population prediction. The experimental results show that the algorithm has good practicability in practical application.

带有异常点检测的稀疏降秩回归

梁冰洁

2021, 36(3): 275-287. doi:10.13371/j.cnki.chin.q.j.m.2021.03.006

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Based on the multivariate mean-shift regression model, we propose a new
sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier
detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate
outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix
encourage the low-rank row sparse structure of coefficient matrix and help to achieve
dimension reduction and variable selection. An algorithm is developed for solving our
problem. In our simulation and real-data application, our new method shows competitive
performance compared to other methods.

Y-Gorenstein 余挠模

何东林, 李煜彦

2021, 36(3): 288-295. doi:10.13371/j.cnki.chin.q.j.m.2021.03.007

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Let R be an associative ring with identity, and Y be a class of right R -modules,
which contains all injective right R -modules. In this paper, we introduce the definition of
Y -Gorenstein cotorsion modules, which is a generalization of cotorsion and Gorenstein
cotorsion modules. We discuss the relationship between Gorenstein cotorsion, weakly
Gorenstein cotorsion and Y -Gorenstein cotorsion modules. We investigate properties and
characterizations of Y-Gorenstein cotorsion modules.

随机力作用下大尺度海洋三维原始方程的连续依赖性

李远飞

2021, 36(3): 296-307. doi:10.13371/j.cnki.chin.q.j.m.2021.03.008

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In this paper, we consider the initial-boundary value problem for the large scale
three-dimensional (3D) viscous primitive equations under random force. Assuming that
the random force and the heat source satisfy the some assumptions, we firstly establish
rigorous a priori bounds with coefficients which depend only on boundary data, initial
data and the geometry of the problem, and then with the aid of these a priori bounds,
the continuous dependence of the solution on changes in the heat source is obtained.

一类溶解度与温度相关的 Brinkman-Forchheimer 方程组解的连续依赖性

石金诚, 肖胜中

2021, 36(3): 308-319. doi:10.13371/j.cnki.chin.q.j.m.2021.03.009

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The structural stability for the Brinkman-Forchheimer equations with temperature-dependent solubility in a bounded region in R3 was studied. The reaction boundary conditions for the temperature T and the salt concentration were imposed.
With the aid of some useful a priori bounds, we were able to demonstrate the continuous dependence result for the Forchheimer coefficient λ.

自入射二次领关系代数的 Hochschild 的上同调上的 Batalin-Vilkovisky 结构

高谨, 侯波

2021, 36(3): 320-330. doi:10.13371/j.cnki.chin.q.j.m.2021.03.010

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We give a complete description of the Batalin-Vilkovisky algebra structure on
Hochschild cohomology of the self-injective quadratic monomial algebras.

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