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中文
Table of Content
30 December 2009, Volume 24 Issue 4
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The Latest Progress in Varying-coeffcient Models
LU Yi-qiang, LI Yu-ping
2009, 24(4): 475-484.
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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.
On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications
YU De-sheng
2009, 24(4): 485-490.
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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.
On Reverses of the Lp-petty Projection Inequality
WANG Wei-dong, WEI Dai-jun, XIANG Yu
2009, 24(4): 491-498.
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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.
On the Diophantine Equation
y
2
=px(x
2
+2)
WANG Xiao-Ying
2009, 24(4): 499-503.
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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 y
2
=px(x
2
+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.
Common Fixed Point Theorems for Sequences of Φ-type Contraction Set-valued Mappings
WU Jian-rong, LIU Hoi-yan
2009, 24(4): 504-510.
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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.
The Characteristic of W-complete (W*-complete) on LCS with the Axiom (T
0
)
Lina
2009, 24(4): 511-515.
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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.
The Explicit Solution to Equation AX+XB=C in Matrices
YOU Xing-hua, MA Sheng-rong, YAN Shi-jian
2009, 24(4): 516-524.
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At first one of g-inverses of AI
n
+I
m
B
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.
New Periodic Wave Solutions and Their Interaction for (2+1)-dimensional KdV Equation
GE Dong-jie, MA Hong-cai, YU Yao-dong
2009, 24(4): 525-536.
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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.
Remarks on Oscillation for Systems of High Order Partial Differential Equations of Neutral Type
LIN Wen-Tian
2009, 24(4): 537-542.
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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.
Optimality of Vector Optimization Involving Generalized Type-I Functions in Banach
QU He-mei, XUE Zhen-xia
2009, 24(4): 543-550.
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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.
On the Second Borel-Cantelli Lemma for a-mixing Sequences of Events
YUAN De-mei
2009, 24(4): 551-560.
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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.
The Discrete Horizontal Complex on Lattice Space
ZHOU Hui-qian, LIU Zhen, Ll Qi-sheng
2009, 24(4): 561-567.
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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.
A General Converse Comparison Theorem for Backward Stochastic Differential Equation with Non-lipschitz Coefficient
LU Min, WANG Zeng-wu
2009, 24(4): 568-573.
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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.
A Nonmonotone Trust Region Method for Solving Symmetric Nonlinear Equations
YUAN Gong-lin, WEI Zeng-cin , LU Xi-wen
2009, 24(4): 574-584.
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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.
Modified Formula for Cotes Rule with Fifths Derivatives of Endpoint
SUN Fan, HAN Ke-zhong
2009, 24(4): 585-589.
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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.
Additive Maps Preserving {1, 2, T}-inverses
RONC Jian-ying, YUE Qin, LIU Xu-qing
2009, 24(4): 590-597.
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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)
T
f(A), f(B)= f(B)f(A)
T
f(B) for any A,B∈M
mn
(F) with A=AB
T
A, B=BA
T
B. In this paper, we give the sufficient and necessary condition for f to be such a map.
Boundedness of a Kind of Oscillatory Singular Integral Operators
ZHAO Kai, WANG
2009, 24(4): 598-604.
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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
(R
n
)(1<p<∞) when-1<μ<αd(1/2)-|(1/p)-(1/2)|).
Some Kind of Equations Involving Euler's Function
Ll Yi-jun, Ll Yu-sheng
2009, 24(4): 605-608.
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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*-regular Families and Metrization Theorems
Ll Ke-dian, XU Hua-wei
2009, 24(4): 609-613.
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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].
Oscillation Criteria for Second-order Half-linear Impulsive Differential Equations with Damping
CHEN Xing-rong, PAN Li-jun
2009, 24(4): 614-620.
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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.
A Nonconforming Rectangular Finite Element Analysis for the Stokes Problem
XIAO Liu-chao, CHEN Shoo-chun
2009, 24(4): 621-627.
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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.
Some Conditions of Central Lie Ideal
HUANG Shu-liang, FU Shi-tai
2009, 24(4): 628-632.
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Let di(1≤i≤n), δ
1
,δ
2
,δ
3
be nonzero derivations of a prime ring R with charR≠2.Suppose that U is a Lie ideal such that u
2
∈U for all u∈U. In this paper, we prove that U Z(R) when one of the following holds: (1) d
1
(x
1
)d
2
(x
2
),...,d
n
(x
n
)∈Z(R)(2)δ
3
(y)δ
1
(x)=δ
2
(x)δ
3
(y). Further, if U is a Lie ideal and a subring then (3)δ
1
(x)δ
2
(y)+δ
2
(x)δ
1
(y)∈Z(R) for all x
i
,x,y∈U.
