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2009年 第24卷 第4期    刊出日期：2009-12-30

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变系数模型的最新进展

卢一强, 李玉萍

2009, 24(4):  475-484. 

摘要 ( 20 )   PDF (620KB) ( 8 )  

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Varying-coefficient models are a useful extension of classical linear model. They are widely applied to economics, biomedicine, epidemiology, and so on. There are extensive studies on them in the latest three decade years. In this paper, many of models related to varying-coefficient models are gathered up. All kinds of the estimation procedures and theory of hypothesis test on the varying-coefficients model are summarized. From my opinion, some aspects waiting to study are proposed.



二次曲线外切多边形中有向面积的定值定理及其应用

喻德生

2009, 24(4):  485-490. 

摘要 ( 19 )   PDF (353KB) ( 14 )  

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Using polar equations for conic sections, we research conic circumscribed n-sided polygons(n≥4) deeply on the basis of papers. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n(n-3) concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons(n≥4). So the results of papers are unified.



关于Lp-petty投影不等式的逆

王卫东, 魏代俊, 向宇

2009, 24(4):  491-498. 

摘要 ( 21 )   PDF (434KB) ( 6 )  

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Lutwak, Yang and Zhang established the Lp-petty projection inequality. In this paper, the several reverses of the Lp-petty projection inequality are shown.



关于丢番图方程y²=px(x²+2)

王晓瑛

2009, 24(4):  499-503. 

摘要 ( 18 )   PDF (235KB) ( 9 )  

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For any fixed odd prime p, let N(p) denote the number of positive integer solutions (x,y) of the equation y²=px(x²+2). In this paper, using some properties of binary quartic Diophantine equations, we prove that if p≡5 or 7(mod 8), then N(p)=0; ifp≡1(mod 8), then N(p)≤1; ifp>3 and p≡3(mod 8), then N(p)≤2.



Φ型压缩集值映射列的公共不动点定理

吴健荣, 柳海燕

2009, 24(4):  504-510. 

摘要 ( 16 )   PDF (409KB) ( 10 )  

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In complete metric spaces, the common fixed point theorems for sequences of Φ-type contraction set-valued mappings are established, and the corresponding random common fixed point theorems for set-valued mappings are also obtained.





关于具(T₀)公理的局部凸空间弱完备(弱完备)的特征性质

丽娜

2009, 24(4):  511-515. 

摘要 ( 16 )   PDF (261KB) ( 16 )  

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In this paper, it is shown that if a local convex space is weakly complete, then it is complete. Moreover, it shows that a local convex space with the axiom(To) is weakly complete(or weakly* complete) if and only if it is finite dimensional.


矩阵方程AX+XB=C的显式解

尤兴华, 马圣容, 颜世建

2009, 24(4):  516-524. 

摘要 ( 23 )   PDF (434KB) ( 23 )  

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At first one of g-inverses of AI_n+I_mB^T is given out, then the explicit solution to matrix equation AX+XB=C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.


(2+1)维KdV方程的新周期波之间的相互作用

葛东杰, 马红彩, 耀东

2009, 24(4):  525-536. 

摘要 ( 27 )   PDF (2454KB) ( 19 )  

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A class of new doubly periodic wave solutions for(2+1)-dimensional KdV equation are obtained by introducing appropriate Jacobi elliptic functions and Weierstrass elliptic functions in the general solution(contains two arbitrary functions) got by means of multilinear variable separation approach for(2+1)-dimensional KdV equation. Limiting cases are considered and some localized excitations are derived, such as dromion, multidromions, dromion-antidromion, multidromions-antidromions,and so on. Some solutions of the dromion-antidromion and multidromions-antidromions are periodic in one direction but localized in the other direction. The interaction properties of these solutions, which are numerically studied, reveal that some of them are nonelastic and some are completely elastic. Furthermore, these results are visualized.


一类高阶中立型偏微分方程系统振动性的注记

林文贤

2009, 24(4):  537-542. 

摘要 ( 16 )   PDF (281KB) ( 5 )  

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In this paper, some sufficient conditions are obtained for the oscillation for solutions of systems of high order partial differential equations of neutral type.



Banach空间中广义型-Ⅰ向量优化的最优性条件

曲贺梅, 薛贞霞

2009, 24(4):  543-550. 

摘要 ( 17 )   PDF (461KB) ( 12 )  

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In this note, new classes of generalized type-I functions are introduced for functions between Banach spaces. These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.



关于α混合事件序列的第二Borel-Cantelli引理

袁德美

2009, 24(4):  551-560. 

摘要 ( 8 )   PDF (516KB) ( 29 )  

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In this paper, we give some conditions on diverging rate of series of the probabilities and converging rate of series of theα-mixing coefficients for sequences of events, under which the conclusion of the Second Borel-Cantelli Lemma holds. As corollaries, some moment conditions are obtained, under which the strong law of large numbers holds for sequences of identically distributed random variables.



格点空间上的离散水平复形

周慧倩, 刘震, 李起升

2009, 24(4):  561-567. 

摘要 ( 13 )   PDF (394KB) ( 7 )  

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We define discrete total differential forms on lattice space by changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.



非Lipschitz条件下倒向随同微分方程解的反比较定理

陆敏, 王增武

2009, 24(4):  568-573. 

摘要 ( 23 )   PDF (324KB) ( 9 )  

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In this article, we first introduce g-expectation via the solution of backward stochastic differential equation(BSDE in short) with non-Lipschitz coefficient, and give the properties of g-expectation, then we establish a general converse comparison theorem for backward stochastic differential equation with non-Lipschitz coefficient.



一个求解非线性对称方程组的非单调信赖域方法

袁功林, 韦增欣, 鲁习文

2009, 24(4):  574-584. 

摘要 ( 17 )   PDF (614KB) ( 40 )  

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A trust region method combining with nonmonotone technique is proposed for solving symmetric nonlinear equations. The global convergence of the given method will be established under suitable conditions. Numerical results show that the method is interesting for the given problems.



带端点5阶导数的Cotes修正公式

孙帆, 韩可众

2009, 24(4):  585-589. 

摘要 ( 16 )   PDF (296KB) ( 16 )  

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This paper presents a Modified Formula for Cotes rule with fifths derivatives of endpoint and its truncation error. It also displays an analysis on convergence order of compound formula. Though compound modified formula for Cotes rule with endpoint derivatives just calculates a newly-added fifths derivative of the two endpoints for each time compared with compound Cotes formula calculation, there are 2 more ranks of the convergence order in this modified formula. Examples of numerical calculation have validated theoretical analysis. 


保持{1,2,T}-逆的加法映射

荣建英, 岳勤, 刘绪庆

2009, 24(4):  590-597. 

摘要 ( 16 )   PDF (427KB) ( 15 )  

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Let F be a field of characteristic not 2 and 3.Let f: M_mn(F)→M_mn(F) be an additive map preserving {1,2,T}-inverse, i.e. f(A)=f(A)f(B)^Tf(A), f(B)= f(B)f(A)^Tf(B) for any A,B∈M_mn(F) with A=AB^TA, B=BA^TB. In this paper, we give the sufficient and necessary condition for f to be such a map.



一类振荡奇异积分算子的有界性

赵凯, 王磊

2009, 24(4):  598-604. 

摘要 ( 19 )   PDF (383KB) ( 18 )  

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In this paper, we study a kind of oscillatory singular integral operator T with Calderon-Zygrnund kernel, which had been studied by Ricci and Stein in[6], and extend their result. We get that T is bounded on L^p(Rⁿ)(1<p<∞) when-1<μ<αd(1/2)-|(1/p)-(1/2)|).



一类包含欧拉函数的方程

李怡君, 李育生

2009, 24(4):  605-608. 

摘要 ( 12 )   PDF (190KB) ( 28 )  

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For any given positive integer n≥1, the Euler function φ(n) is defined to be the number of positive integers not exceeding n which are relatively prime to n. ω(n) is defined to be the number of different prime divisors of n. Some kind of equations involving Euler’s function is studied in the paper.



cs*-正则族与度量化定理

李克典, 徐华伟

2009, 24(4):  609-613. 

摘要 ( 23 )   PDF (312KB) ( 10 )  

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In this paper, we proved that a sequential space has a cs*-regular cs*-network (or a cs*-regular weak base) is metrizable, which generalized related results in [6], [12] and [14].



带阻尼的二阶半线性脉冲微分方程的振动准则

陈星荣, 潘立军

2009, 24(4):  614-620. 

摘要 ( 16 )   PDF (369KB) ( 8 )  

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By employing the inequality of [8] and a positive continuous function g(t), t∈[t_o,+∞), oscillation criteria for the second-order half-linear impulsive differential equ-ations with damping are established. Our results generalize and improve some known ones.



Stokes问题的一个非协调矩形有限元分析

肖留超, 陈绍春

2009, 24(4):  621-627. 

摘要 ( 15 )   PDF (373KB) ( 21 )  

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A nonconforming rectangular finite element is presented, which satisfies the discrete B-B condition for the Stokes problem. And the element has two order convergence rate for the velocity and pressure.



中心李理想的若干条件

黄述亮, 傅士太

2009, 24(4):  628-632. 

摘要 ( 15 )   PDF (291KB) ( 27 )  

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Let di(1≤i≤n), δ₁,δ₂,δ₃ be nonzero derivations of a prime ring R with charR≠2.Suppose that U is a Lie ideal such that u²∈U for all u∈U. In this paper, we prove that U Z(R) when one of the following holds: (1) d₁(x₁)d₂(x₂),...,d_n(x_n)∈Z(R)(2)δ₃(y)δ₁(x)=δ₂(x)δ₃(y). Further, if U is a Lie ideal and a subring then (3)δ₁(x)δ₂(y)+δ₂(x)δ₁(y)∈Z(R) for all x_i,x,y∈U.