数学季刊

王璐, 秦克云

2018, 33(4): 331-340. doi:10.13371/j.cnki.chin.q.j.m.2018.04.001

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The aim of this paper is to discuss the Triple Ⅰ restriction reasoning methods for fuzzy soft sets. Triple Ⅰ restriction principles for fuzzy soft modus ponens(FSMP) and fuzzy soft modus tollens(FSMT) are proposed, and then, the general expressions of the Triple Ⅰ restriction reasoning method for FSMP and FSMT with respect to residual pairs are presented respectively. Finally, the optimal restriction solutions for Lukasiewicz and Godel implication operators are examined.

指数威布尔更新函数的近似计算

程从华

2018, 33(4): 341-357. doi:10.13371/j.cnki.chin.q.j.m.2018.04.002

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The analytical renewal function(RF) is not tractable of the exponential Weibull(EW) distribution. In the proposed model, the n-fold convolution of the EW cumulative distribution function(CDF) is approximated by a n-fold convolutions of Gamma and normal CDFs. We obtain the EW RF by a series approximation model. The method is very simple in the computation. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via some numerical experiments.

环F_p+vF_p上自对偶码的构造

张光辉, 王冬晴

2018, 33(4): 358-368. doi:10.13371/j.cnki.chin.q.j.m.2018.04.003

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In this paper, we give an explicit construction for self-dual codes over F_p+vF_p(v²= v) and determine all the self-dual codes over F_p+ vF_p by using self-dual codes over finite field F_p, where p is a prime.

随机非自治Schoener竞争系统的周期解

陈红亮, 李小平

2018, 33(4): 369-376. doi:10.13371/j.cnki.chin.q.j.m.2018.04.004

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In this paper, we consider a stochastic non-autonomous Schoener competitive system. Firstly, we prove the existence of positive periodic solution when the coefficients of Schoener competitive system satisfied certain conditions. Then the global attractiveness of positive periodic solution is also proved by constructing appropriate Lyapunov function. In addition, we show that the stronger noises will lead to the extinction of competitive systems.

四阶p-Laplacian边值问题正解的存在性

王万鹏

2018, 33(4): 377-385. doi:10.13371/j.cnki.chin.q.j.m.2018.04.005

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This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ*such that the above problem has at least two positive solutions for 0 < λ < λ* , at least one positive solution for λ = λ* and no solution forλ > λ* by using the upper and lower solutions method and fixed point theory.

关于相对稳定范畴的限制函子

黄文林

2018, 33(4): 386-394. doi:10.13371/j.cnki.chin.q.j.m.2018.04.006

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We prove that, confined that G > H > P and P is a proper p-subgroup of H, if H ∩_gH ≤ P for any g ∈ G-H, then the operator of the restriction to RH of RG-modules induces a triangulated equivalence from StmodP(RG) to StmodP(RH); if the normal subgroup H controls the fusion of p-subgroups of G, the restriction functor is a faithful triangulated functor; if P is strongly closed in H respect to G, the same functor is also a faithful triangulated functor.

解析簇上Leray-Stokes型积分表示公式

陈叔瑾

2018, 33(4): 395-416. doi:10.13371/j.cnki.chin.q.j.m.2018.04.007

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The closure of the bounded domains D in Cⁿ consists of a chain of the slit spaces,and may be divided into two types. Based on the two types of bounded domains in Cⁿ, firstly using different method and technique we derive the corresponding integral representation formulas of differentiable functions for complex n-m（0 ≤ m < n） dimensional analytic varieties in the two types of the bounded domains. Secondly we obtain the unified integral representation formulas of differentiable functions for complex n-m（0 ≤ m < n） dimensional analytic varieties in the general bounded domains. When functions are holomorphic, the integral formulas in this paper include formulas of Stout[1], Hatziafratis[2] and the author[3],and are the extension of all the integral representations for holomorphic functions in the existing papers to analytic varieties. In particular, when m = 0, firstly we gave the integral representation formulas of differentiable functions for the two types of bounded domains in Cⁿ. Therefore they can make the concretion of Leray-Stokes formula. Secondly we obtain the unified integral representation formulas of differentiable functions for general bounded domains in Cⁿ. So they can make the Leray-Stokes formula generalizations.

酉群U(2)上的插值三角多项式逼近

杨柱元, 杨宗文

2018, 33(4): 417-420. doi:10.13371/j.cnki.chin.q.j.m.2018.04.008

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In this paper we study the approximation of interpolation trigonometric polynomial of a continuous class function on a unitary group U(2), we obtain the Jackson-type error estimation of Bernstein-type operator.

关于加权相依风险的风险价值和凸风险测度的界

邢国东, 李效虎

2018, 33(4): 421-433. doi:10.13371/j.cnki.chin.q.j.m.2018.04.009

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This note analytically derives lower and upper bounds for Value-at-Risk and convex risk measures of a portfolio of weighted risks in the context of positive dependence.The bounds serve as extensions of the corresponding ones due to Bignozzi et al.(2015).Also, DUspread of value-at-risk and expected shortfall of Bignozzi et al.(2015) are also improved in some particular cases.

一类有限p-群的因子分解数

王玉雷, 张元锋, 郭鹏

2018, 33(4): 434-440. doi:10.13371/j.cnki.chin.q.j.m.2018.04.010

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Let p be a prime number and f₂（G） be the number of factorizations G = AB of the group G, where A, B are subgroups of G. Let G be a class of finite p-groups as follows,G =< a, b |_apⁿ= _bp^m= 1, a^b= _ap^n-1+1>, where n > m ≥ 1. In this article, the factorization number f₂（G） of G is computed, improving the results of Saeedi and Farrokhi in [5].

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