Table of Content

30 December 2018, Volume 33 Issue 4

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General Expressions of Triple I Restriction Methods for Fuzzy Soft Reasoning

WANG Lu, QIN Ke-yun

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. 

The Approximation of the Exponential Weibull Renewal Function

CHENG Cong-hua

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. 

Construction of Self-dual Codes over F_p + vF_p

ZHANG Guang-hui, WANG Dong-qing

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. 

Periodic Solution for Stochastic Non-autonomous Schoener Competitive System

CHEN Hong-liang, LI Xiao-ping

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.

Existence of Positive Solutions for A Fourth-order Boundary Value Problems with p-Laplacian Operators

WANG Wan-peng

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. 

On the Restriction Functor of the Relative Stable Category

HUANG Wen-lin

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. 

The Leray-Stokes Type Integral Representation Formulas on the Analytic Varieties

CHEN Shu-jin

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 Cnconsists 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. 

Approximation by Interpolation Trigonometric Polynomial on the Unitary Group U(2)

YANG Zhu-yuan, YANG Zong-wen

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. 

On Bounds of Value-at-Risk and Convex Risk Measure of Portfolio of Weighted Dependent Risks

XING Guo-dong, LI Xiao-hu

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. 

Factorization Numbers of a Class of Finite p-groups

WANG Yu-lei, ZHANG Yuan-feng, GUO Peng

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].