数学季刊

贺福利

2014, 29(3): 317-324. doi:10.13371/j.cnki.chin.q.j.m.2014.03.001

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In this paper we consider several fundamental operators in complex Clifford algebra and show the close relationship of these operators. We also discuss a representation of the Lie algebra sl(2; C) and get several decompositions for Clifford algebra of even dimension under the action of these fundamental operators.

Tame Hecke代数的Hochschild同调

侯波

2014, 29(3): 325-334. doi:10.13371/j.cnki.chin.q.j.m.2014.03.002

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Let A be a tame Hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.

p-Laplacian型方程的多解性

陈自高

2014, 29(3): 335-343. doi:10.13371/j.cnki.chin.q.j.m.2014.03.003

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We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form（in particular, a p-Laplacian operator）, while the nonlinearity has a（p- 1）-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.

END随机变量的指数型不等式和完全收敛性

沈爱婷, 朱华炎, 张颖

2014, 29(3): 344-355. doi:10.13371/j.cnki.chin.q.j.m.2014.03.004

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Some exponential inequalities and complete convergence are established for extended negatively dependent（END） random variables. The inequalities extend and improve the results of Kim and Kim（On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22（2）: 315-321） and Nooghabi and Azarnoosh（Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50（2）: 419-428）. We also obtain the convergence rate O（n^-1/2ln^1/2n） for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.

线性移人——生灭过程及其统计推断

张术林, 魏正红, 毕秋香

2014, 29(3): 356-362. doi:10.13371/j.cnki.chin.q.j.m.2014.03.005

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In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death（IBD） model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.

对称锥互补问题的一类新的互补函数及其价值函数的水平有界性

张运胜

2014, 29(3): 363-372. doi:10.13371/j.cnki.chin.q.j.m.2014.03.006

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In this paper, we introduce a new class of two-parametric penalized function,which includes the penalized minimum function and the penalized Fischer-Burmeister function over symmetric cone complementarity problems. We propose that this class of function is a class of complementarity functions（C-function）. Moreover, its merit function has bounded level set under a weak condition.

Cⁿ中一类具有参数表示的映照族

邓未冰, 刘浩

2014, 29(3): 373-380. doi:10.13371/j.cnki.chin.q.j.m.2014.03.007

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In this paper, a kind of mappings with parametric representation is introduced,the growth theorem is set up.

格的粗糙直觉模糊理想(滤子)

贺鹏飞, 杨永伟, 辛小龙

2014, 29(3): 381-391. doi:10.13371/j.cnki.chin.q.j.m.2014.03.008

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In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).

部分线性单指标模型的变量选择

卢一强, 胡斌

2014, 29(3): 392-399. doi:10.13371/j.cnki.chin.q.j.m.2014.03.009

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In this article, we study the variable selection of partially linear single-index model（PLSIM）. Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

一类非线性分数阶泛函微分方程脉冲边值问题的解

韩仁基, 周先锋, 李翔, 蒋威

2014, 29(3): 400-411. doi:10.13371/j.cnki.chin.q.j.m.2014.03.010

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In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlinear fractional functional differential equation of mixed type. We obtain the existence results of solution by applying some well-known fixed point theorems. An example is given to illustrate the effectiveness of our result.

带中断风险和服务水平约束的库存模型

王全庆, 李振国, 李小申

2014, 29(3): 412-418. doi:10.13371/j.cnki.chin.q.j.m.2014.03.011

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We develop a newsvender model with service level constraint for oneproduct and multi-supplier system, where the supplies are susceptible to disruption risks. We prove the convexity of the programming problem,and provide the necessary and sufficient conditions for the optimal order quantities. Through analysis or numerical experiments we observe the effects of the disrupt risk and the service level constraint on the optimal policy. We propose some managerial insights in managing the multi-source supply chain with disruption risks.

M-亚正规权移位算子与可亚正规权移位算子的一些注记

葛斌, 周庆梅

2014, 29(3): 419-425. doi:10.13371/j.cnki.chin.q.j.m.2014.03.012

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Let {a_n}^∞_n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.

一类具有时滞和CTL免疫反应的病毒感染动力学模型的稳定性和Hopf分支

李晓童, 田晓红, 徐瑞

2014, 29(3): 426-437. doi:10.13371/j.cnki.chin.q.j.m.2014.03.013

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In this paper, a virus infection model with standard incidence rate and delayed CTL immune response is investigated. By analyzing corresponding characteristic equations,the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the CTL-activated infection equilibrium are established, respectively. By means of comparison arguments, it is verified that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio is less than unity. By using suitable Lyapunov functional and LaSalle’s invariance principle, it is shown that the CTL-inactivated infection equilibrium of the system is globally asymptotically stable if the immune response reproduction ratio is less than unity and the basic reproduction ratio is greater than unity. Numerical simulations are carried out to illustrate the theoretical result.

涉及不取零点的亚纯函数的正规族

邓炳茂, 刘丹, 王雪琴, 杨德贵

2014, 29(3): 438-446. doi:10.13371/j.cnki.chin.q.j.m.2014.03.014

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Let k, m be two positive integers with m ≤ k and let F be a family of zero-free meromorphic functions in a domain D, let h（z） ≡ 0 be a meromorphic function in D with all poles of h has multiplicity at most m. If, for each f ∈ F, f（k）（z） = h（z） has at most k- m distinct roots（ignoring multiplicity） in D, then F is normal in D. This extends the results due to Chang[1], Gu[3], Yang[11]and Deng[1]etc.

时间测度链上三阶时滞动力方程的振动性

杨甲山

2014, 29(3): 447-456. doi:10.13371/j.cnki.chin.q.j.m.2014.03.015

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This paper is concerned with the oscillatory behavior of a class of third-order nonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscillation criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.

带有第二声的一维热扩散系统解的整体吸引子

张明

2014, 29(3): 457-464. doi:10.13371/j.cnki.chin.q.j.m.2014.03.016

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In this paper we investigate the global attractors for the one-dimensional linear model of thermodiffusion with second sound. Using the method of contractive functions, we obtain the asymptotically compact of the semigroup and the existence of the global attractors

a-xy*的Moore-Penrose逆的表示的统一方法

杜法鹏, 薛以锋

2014, 29(3): 465-474. doi:10.13371/j.cnki.chin.q.j.m.2014.03.017

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Let A be an unital C*-algebra, a, x and y are elements in A. In this paper, we present a method how to calculate the Moore-Penrose inverse of a- xy*and investigate the expression for some new special cases of（a- xy*）.

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