数学季刊

赵包, 杨赟瑞, 马竹艳

2020, 35(4): 331-343. doi:10.13371/j.cnki.chin.q.j.m.2020.04.001

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This paper is concerned with traveling waves for an epidemic model with spatio-temporal delays. It is shown that the traveling wave solutions are still persistently existing in the model when the non-locality is caused by small average time delays via the geometric singular perturbation theory and the center manifold theorems.

广义的Orlicz空间上的Korn不等式与散度方程

吴芮民, 王松柏

2020, 35(4): 344-353. doi:10.13371/j.cnki.chin.q.j.m.2020.04.002

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Let ϕ be a generalized Orlicz function satisfying (A0), (A1), (A2), (aInc) and (aDec). We prove that the mapping

f →f ^#:=sup_B 1/\int_|B||f(x)-f_B|dx is continuous on L^ϕ(·)(Rⁿ) by extrapolation. Based on this result we generalize Korn’s inequality to the setting of generalized Orlicz spaces, i.e., ||\triangledown f||_{L^{ϕ(·)}(Ω)}\lesssim||DF|||_L^{ϕ}(Ω) . Using the Calder´on–Zygmund theory on generalized Orlicz spaces, we obtain that the divergence equation divu=f has a solution u∈(W0^1,ϕ(·)(Ω))ⁿsuch that ||\triangledown u||_L^{_ϕ(·)}(Ω) \lesssim ||f||_L^{ϕ}(Ω).

求解箱式约束全局优化问题的新的填充函数

屈德强, 吴丹, 尚有林

2020, 35(4): 354-362. doi:10.13371/j.cnki.chin.q.j.m.2020.04.003

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本文考虑利用辅助函数法求解箱式约束全局优化问题。首先，提出了一个新的与目标函数具有相同局部极小点的无参数填充函数。该填充函数的局部极小点是目标函数更优的局部极小点，基于这一特征设计的填充函数方法，目标函数只需要被极小化一次。改变了传统填充函数法目标函数和填充函数交替极小化的算法框架，能有效减少算法的迭代次数，加快寻找全局极小点的速度。随后进一步讨论了填充函数的理论性质，并建立了相应的算法。最后，通过数值实验验证了算法的可行性和有效性。

全平面上Laplace-Stieltjes变换所表示整函数的增长性

宁菊红, 宋文佩, 黄文平

2020, 35(4): 363-369. doi:10.13371/j.cnki.chin.q.j.m.2020.04.004

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In the paper, the α-order of the Laplace-Stieltjes Transform is introduced firstly, then we get the relationship between

α-order represented by the maximum modulus and α-order represented by A^∗_n, λn. Lastly, we obtain the relationship between type τ represented by the maximum modulus and type τ represented by A^∗_n, λ_n.

模糊数值函数的强广义凸性及其在模糊优化中的应用

白玉娟, 刘坤, 张琛

2020, 35(4): 370-387. doi:10.13371/j.cnki.chin.q.j.m.2020.04.005

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Based on the ordering of fuzzy numbers proposed by Goetschel and Voxman, the representations and some properties of strongly preinvex fuzzy-valued function are defined and obtained, several new concepts of strongly monotonicities fuzzy functions are introduced, the relationship among the strongly preinvex, strongly invex and monotonicities under some suitable and appropriate conditions is established and a necessary condition for strongly pseudoinvex functions is given. As an application, the conditions of local optimal solution and global optimal solution in the mathematical programming problem are discussed.

关于余挠三元组的n-星子范畴和n-P-倾斜子范畴

何东林, 李煜彦

2020, 35(4): 388-396. doi:10.13371/j.cnki.chin.q.j.m.2020.04.006

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In this paper, we introduce the definition of n-star subcategories, which is a generalization of n-star modules and n-C-star modules. We give some characterizations of n-star subcategories, and prove that M is an n-P-tilting subcategory with respect to cotorsion triple (P, R-Mod, I), if and only if M is an n-star subcategory with I ⊆Presⁿ(M), where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.

多维整数序列的乘积不等式的注记

马丽, 王如, 韩新方

2020, 35(4): 397-400. doi:10.13371/j.cnki.chin.q.j.m.2020.04.007

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For multi-dimensional integer-valued sequence, a new proof of the upperbound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution, random partial differential equation and other problems.

关于图的主特征向量的一些结论

吴春杰

2020, 35(4): 401-409. doi:10.13371/j.cnki.chin.q.j.m.2020.04.008

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For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G) (resp. Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G) (resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.

非线性分数微分方程边值问题单调正解的存在性

岳俊瑞, 白庆月

2020, 35(4): 410-417. doi:10.13371/j.cnki.chin.q.j.m.2020.04.009

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In this paper, we consider a class of nonlinear fractional differential equation boundary value problem. The existence of monotone positive solution is derived by the iterative technique.

Besov空间中三维Micropolar流体方程组弱解的正则性准则

李晓

2020, 35(4): 418-423. doi:10.13371/j.cnki.chin.q.j.m.2020.04.010

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This paper studies the regularity criterion of weak solutions to the micropolar
fluid equations in three dimensions. Let (∇u∈L ^{2/ 2- γ} (0,T; ˙B^{- γ}_∞,∞),∇ω ∈L²(0,T; ˙B^-1 _∞,∞), it
is showed that the weak solution (u,ω) is globally regular for the case 0< γ <2.

有向图强乘积的代数群性质

阴浩然, 李峰

2020, 35(4): 424-430. doi:10.13371/j.cnki.chin.q.j.m.2020.04.011

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The strong product digraph G1 G2 is constructed by the known digraph G1 and G2 of small order. The digraph G1 G2 constructed by the strong product method contain G1 and G2 as its sub-graphs. Therefore, the topological structure and properties of these small digraphs G1 and G2 must affect the topological structure and properties of the large digraph. By using group theory, we prove some algebraic properties of strong product of digraphs, such as commutative law, associative law and so on.

经典Hilbert不等式的p进制版本

金建军, 李春华

2020, 35(4): 431-440. doi:10.13371/j.cnki.chin.q.j.m.2020.04.012

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In this note, we introduce and study a p-adic Hilbert-type integral operator and obtain its sharp norm estimate. As applications, we establish a p-adic Hilbert-type inequality with the best constant and its equivalent form.

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