数学季刊

陈婷, 姚静荪

2012, 27(3): 317-322.

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The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.

Cⁿ中单位球上全纯映射凸半径一个注记

徐继军, 王晓凤, 刘浩

2012, 27(3): 323-327.

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In this paper, we prove that: if M is a family which has convexity radius, then the convexity radius for M and the second order item coefficients of every mapping in M are closely related to each other. As an application, we show that the convexity radius of starlike mappings r(S*) < 2-√3.

联图C_mVG_n的邻点可区别Ｅ-全染色

王继顺

2012, 27(3): 328-336.

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Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_at(G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs Cm∨Gn are obtained, where G_n is one of a star S_n, a fan F_n , a wheel W_nand a complete graph K_n. As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed.

一阶时标动态方程周期边值问题的正解

宋常修

2012, 27(3): 337-343.

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In this paper, the author studies the following nonlinear dynamic equation {x△(t) = r(t)x(σ(t)) + f(t, x(σ(t))), t ∈ [0, T ], x(0) = x(σ(T )). By applying and improving the generalized form of Leggett-Williams fixed point theorem, sufficient conditions are established for the existence of positive solutions.

关于一些解析函数空间的系数乘子

岳修奎

2012, 27(3): 344-351.

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In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (H_α, H_β) and (A^p,α), A^q,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (H_α, H_β) = H_β-α with 0 < α < β < ∞.

F(p,q,s)空间到Block型空间的复合积分型算子

吕小芬, 应少鸿

2012, 27(3): 352-356.

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This paper deals with the boundedness and compactness of the compositionintegral type operators T g, from F (p, q, s) spaces to(little) Bloch-type spaces in the unit ball of C n , where Tg,φf(z) =∫01fφ(tz)Rg(tz)(dt)/t , z ∈ B, g ∈ H(B) and φ∈H(B, B).

单位圆内代数体函数的唯一性

张晓梅, 孙道椿

2012, 27(3): 357-363.

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In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.

广义凸空间上的重合点和几乎相似重合点及其应用

朴勇杰, 石仁淑

2012, 27(3): 364-370.

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We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.

耦合KdV和Schwarzian KdV方程的显式行波解

李灵晓, 李二强

2012, 27(3): 371-374.

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In this paper the (G’/G)-expansion method is used to find exact travelling wave solutions for a combined KdV and Schwarzian KdV equation. As a result, multiple travelling wave solutions with arbitrary parameters are obtained, which are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are derived from the travelling waves. The (G’/G)-expansion method presents a wider applicability for handling nonlinear wave equations.

k-拟-*-A(ｎ)算子的性质

左飞, 申俊丽

2012, 27(3): 375-381.

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An operator T is called k-quasi-*-A(n) operator, if T^*k|T¹⁺ⁿ|^2/(1+n)T^k≥T^*k|T^*|²T^k, k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum.

带有记忆的热弹盘问题解的整体存在性

马志勇, 张凌瑞

2012, 27(3): 382-388.

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In this paper, we shall establish some global existence results for the higherdimensional nonhomogeneous, linear, semilinear and nonlinear Thermoelastic plates with memory respectively by using semigroup approach. The existence and decay of solutions of homogeneous linear problem has been solved by Romero [1].

关于强n-Corenstein投射模，内射模和平坦模的注记

尚文亮

2012, 27(3): 389-396.

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In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.3

LINEX损失函数下的信度模型

温利民, 张先坤, 郑丹, 方婧

2012, 27(3): 397-402.

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LINEX(linear and exponential) loss function is a useful asymmetric loss function. The purpose of using a LINEX loss function in credibility models is to solve the problem of very high premium by suing a symmetric quadratic loss function in most of classical credibility models. The Bayes premium and the credibility premium are derived under LINEX loss function. The consistency of Bayes premium and credibility premium were also checked. Finally, the simulation was introduced to show the differences between the credibility estimator we derived and the classical one.

一类临界情况的广义非线性奇摄动时滞模型近似解析解

汪娜

2012, 27(3): 403-408.

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Based on the boundary layer corrective method, a class of generalized nonlinear perturbed model in the critical case is studied. The asymptotic solution for the original equation is constructed. And the method is of significance to seek approximate solutions to other nonlinear models.

(V,ρ)_h,φ-Ⅰ 型多目标规划的最优性充分条件

张庆祥, 姜艳, 康瑞瑞

2012, 27(3): 409-416.

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New classes of functions namely (V, ρ)_h,φ-type I, quasi (V, ρ)_h,φ-type I and pseudo (V, ρ)_h,φ-type I functions are defined for multiobjective programming problem by using BenTal’s generalized algebraic operation. The examples of (V, ρ)_h,φ-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.

两个素数和一个素数平方和的丢番图逼近

李伟平, 王天泽

2012, 27(3): 417-423.

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We show that if λ₁, λ₂, λ₃ are non-zero real numbers, not all of the same sign, η is real and λ₁/λ₂ is irrational, then there are infinitely many ordered triples of primes (p₁, p₂, p₃) for which |λ₁p₁+λ₂p₂+λ₃p²₃₊η| < (maxp_j )- 1/40 (logmaxp_j)⁴.

具有随机区间收益的效用优化分析

尤苏蓉, 彭玉争, 赵菲菲

2012, 27(3): 424-431.

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This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor’s subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets’ prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.

常曲率空间中伪脐2-调和子流形

独力, 张娟

2012, 27(3): 432-438.

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The conjecture [1] asserts that any biharmonic submanifold in sphere has constant mean curvature. In this paper, we first prove that this conjecture is true for pseudo-umbilical biharmonic submanifolds M n in constant curvature spaces S n+p (c)(c > 0), generalizing the result in [1]. Secondly, some sufficient conditions for pseudo-umbilical proper biharmonic submanifolds M n to be totally umbilical ones are obtained.

求解广义线性互补问题的光滑牛顿法

唐嘉, 马昌凤

2012, 27(3): 439-446.

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The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.

函数空间中的AP性质

沈荣鑫

2012, 27(3): 447-451.

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In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C_α(X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C_α(X) is an AP-space which has countable tightness, then C_α(X) is discretely generated.

Banach空间中推广的Roper-Suffridge算子

王晓凤, 阮林要, 张芳芳

2012, 27(3): 452-457.

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In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.

二阶微分方程三点边值问题变号解的存在性

李春燕, 苏亚娟

2012, 27(3): 458-466.

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In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ’’(t) + f(y) = 0, t ∈ [0, 1], y’ (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.

具有非单调出生函数的周期反应扩散模型的渐近传播速度

黄业辉, 翁佩萱

2012, 27(3): 467-474.

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A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.

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