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2017年 第32卷 第2期    刊出日期：2017-06-30

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Euler函数值在算术级数中的分布

冯彬

2017, 32(2):  111-117.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.001

摘要 ( 65 )   PDF (312KB) ( 154 )  

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Let φ（n） denote the Euler-totient function, we study the distribution of solutions of φ（n） ≤ x in arithmetic progressions, where n ≡ l（mod q） and an asymptotic formula was obtained by Perron formula. 

一类具有脉冲注射葡萄糖——胰岛素的糖尿病模型

王霞, 张营, 宋新宇

2017, 32(2):  118-133.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.002

摘要 ( 139 )   PDF (1111KB) ( 239 )  

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Impulsive injections of glucose and insulin analogues are very important strategies for the control of diabetes mellitus. We mainly imitate diabetes patients take insulin before eating, and eating approximately as a pulse blood glucose injection, as a result, a new mathematical model with impulsive injections of both glucose and insulin at different fixed times is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we show that the existence and uniqueness of a positive globally asymptotically stable periodic solution for type I diabetes. By impulsive comparison theorem, we obtain the glucose concentration level of the system is uniformly bounded above and below for type Ⅱ diabetes. Numerical analysis verifies our theoretical results. 

间断Sobolev空间上一类反应扩散问题的新的变分形式

葛志昊, 曹济伟

2017, 32(2):  134-141.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.003

摘要 ( 106 )   PDF (339KB) ( 81 )  

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In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.

算子化单叶解析函数的优化结果和系数边界

熊良鹏

2017, 32(2):  142-151.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.004

摘要 ( 120 )   PDF (429KB) ( 184 )  

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In this paper we introduce a new general subclass n,G∑ a,λ（A, B, α） of univalent functions related the known integral operator and differential operator. Some majorization results for n,G∑ a,λ（A, B, 1） as well as the other functions are given. Furthermore, we find the coefficients bounds on |a2| and |a3| for functions in*n,G∑ a,λ（A₁, B₁, A₂, B₂, α₁, α₂）, which is the bi-univalent functions defined by n,G ∑a,λ（A, B, α） and subordination. By giving specific values of the parameters of our main results, several（known or new） consequences of main results are also discussed. 

AANA随机变量移动平均过程的收敛性

檀佳欣, 黄倩, 胡琪, 杨文志

2017, 32(2):  152-160.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.005

摘要 ( 97 )   PDF (369KB) ( 202 )  

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Based on the asymptotically almost negatively associated（AANA） random variables, we investigate the complete moment convergence for a moving average process under the moment condition E[Y log（1 + Y）] < ∞. As an application, Marcinkiewicz-Zygmundtype strong law of large numbers for this moving average process is presented in this paper. 

φ混合序列加权和的完全收敛性

刘婷婷, 王学军, 王星惠

2017, 32(2):  161-171.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.006

摘要 ( 91 )   PDF (427KB) ( 122 )  

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In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution. 

GSDBM方程的多辛几何和多辛Preissman格式研究

王俊杰, 李胜平

2017, 32(2):  172-180.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.007

摘要 ( 94 )   PDF (638KB) ( 105 )  

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The multi-symplectic geometry for the GSDBM equation is presented in this paper. The multi-symplectic formulations for the GSDBM equation are presented and the local conservation laws are shown to correspond to certain well-known Hamiltonian functionals. The multi-symplectic discretization of each formulation is exemplified by the multisymplectic Preissmann scheme. The numerical experiments are given, and the results verify the efficiency of the Preissmann scheme. 

一类灰度形态学膨胀和腐蚀算子

郭艳艳, 国起

2017, 32(2):  181-186.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.008

摘要 ( 66 )   PDF (281KB) ( 156 )  

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We introduce first a sort of gray-scale morphological dilations and erosions, which might have some further applications in image analysis. Then we show that the dilation and the erosion defined here form adjunctive pairs. The duality between the dilation and the erosion and some other properties, such as the commuting property with translation and homothety, of these operators are discussed as well. 

次可加集值映射的可加选择映射的存在性定理的改进

朴勇杰

2017, 32(2):  187-193.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.009

摘要 ( 78 )   PDF (323KB) ( 103 )  

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In this paper, we will construct a new class of subadditive set-valued maps and use Cantor theorem to prove that the set-valued map has an unique additive selection map when the set-valued map satisfies some certain conditions, and then compare the obtained result with the well-known results. 

由相交体确定凸体的稳定性

马统一

2017, 32(2):  194-207.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.010

摘要 ( 48 )   PDF (507KB) ( 106 )  

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In this paper, by means of the dual Brunn-Minkowski theories and methods as well as the integral transform, we have established a stability version of nonsymmetric convex bodies from intersection bodies. In addition, a stability results of symmetric convex bodies from Lp-counterparts is established. 

关于时标上的适应Delta分数阶导数

游雪肖, 赵大方, 程舰

2017, 32(2):  208-215.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.011

摘要 ( 82 )   PDF (318KB) ( 199 )  

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In this paper, we introduce and investigate the concept of conformable delta fractional derivative on time scales. By using the theory of time scales, we obtain some basic properties of the conformable delta fractional derivative. Our results extend and improve both the results in [9] and the usual delta derivative. 

关于Gorenstein复型的维数分解

崔俊峰

2017, 32(2):  216-220.  doi:10.13371/j.cnki.chin.q.j.m.2017.02.012

摘要 ( 59 )   PDF (279KB) ( 137 )  

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Let W be a self-orthogonal class of R-modules. We prove that W-Gorenstein resolution dimension of a complex X is equivalent to the supremum of W-Gorenstein resolution dimension of modules X_i for all i ∈ Z.