Table of Content

30 June 2004, Volume 19 Issue 2

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Weighted Composition Operators between Hardy Spaces on the Unit Ball

XU Hui-ming, LIU Tai-shun

2004, 19(2):  111-119. 

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We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H¹ to H¹ is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.








Eigenvalues of Spin^c Dirac Operator

FENG Xiu-fang, LAN She-yun, DING Lu, ZHENG Zhu-jun

2004, 19(2):  120-125. 

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In this paper we research the lower bound of the eigenvalue of Spinc Dirac operator on the Spinc manifold. By the Weisenbock formula, we get an estimate of it, then following the idea of Th Friedrich [2] and X Zhang [6]. We get a finer estimate of it. As an application, we give a condition when the Seiberg-Witten equation only has 0 solution.


Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-II Censoring

WANG Rong-hua, FEI He-liang

2004, 19(2):  126-132. 

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In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.

Chromatic Uniqueness of the Complement of T_m（l, 4, m - 6）

ZHANG Shu-min

2004, 19(2):  133-141. 

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In the paper, we prove that the complement of Tm(1,4,m - 6)(m > 10) is chromatically unique if and only if m ≠5k(k ≥ 2).



Convergence Analysis on a Class of Nonmonotone Conjugate Gradient Methods without Sufficient Decrease Condition

DU Shou-qiang, CHEN Yuan-yuan

2004, 19(2):  142-145. 

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In [3] Liu et al. investigated global convergence of conjugate gradient methods. In that paper they allowed βκ to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.





Geometric Properties of AR(q) Nonlinear Regression Models

LIU Ying-an, WEI Bo-cheng

2004, 19(2):  146-154. 

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This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988) [1,2] and Seber & Wild(1989) [3].


On the Sum of Two Piatetski-Shapiro Primes

MENG Xian-meng

2004, 19(2):  155-159. 

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In this paper, we study the binary Goldbach problem in the set of the Piatetski-Shapiro primes. We obtain that for all most all large even integer n, the equationn = p1+p2, pi∈Pγi, i = 1, 2has solutions, where 0 < γ1,γ2 ≤ 1 are fixed real numbers, such that 73(1 - γ2) < 9, 73(1 - γ1) + 43(1 - γ2) < 9.


A Robin Problem for Quasi-linear System

OUYANG Cheng

2004, 19(2):  160-163. 

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 In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.





The Almost Periodic Solution on a Lienard Equation

ZHU Huan-ran

2004, 19(2):  164-171. 

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By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.



Constructing Pandiagonal Snowflake Magic Squares of Odd Order

ZHANG Shi-de, HU Qing-wen, WANG Ji-zhao

2004, 19(2):  172-185. 

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The constructional methods of pandiagonal snowflake magic squares of orders 4m are established in paper [3]. In this paper, the constructional methods of pandiagonal snowflake magic squares of odd orders n are established with n = 6m+l, 6m+5 and 6m+3, m is an odd positive integer and m is an even positive integer 9|6m + 3. It is seen that the number sets for constructing pandiagonal snowflake magic squares can be extended to the matrices with symmetric partial difference in each direction for orders 6m + 1 , 6m + 5; to the trisection matrices with symmetric partial difference in each direction for order 6m + 3.


On the Asymptotic Behavior of Certain Second Order Differential Equations

XU Zhi-ting, XIA Yong

2004, 19(2):  186-187. 

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Two criteria for asymptotic behavior of certain second order differential equations are obtained. The results extend and improve Feng’s theorem.





Notes on the Scaling Function

2004, 19(2):  188-191. 

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Two properties are given in this paper about the scaling function: suppose V_j; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a₁,b₁]∪[a₂,b₂](b₁ < a₂,0 < a₂), then we havea1 ≤ 0, 0 < b₁, a₁ < b₂/2 ≤ b₁, 2π < b₂ - a₁ ≤ 8π.


Regularity of Solution for a Class Zakharov-Kuznestov Equation

MA Yun-xin, GUO Tian-fen

2004, 19(2):  192-197. 

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Global Convergence of a New Conjugate Gradient Methods with a Modification of the Curry-Altman Step-size Rule

CAO Li-hua, SUN Qing-ying

2004, 19(2):  198-204. 

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Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman’s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property. Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method. 

Boundedness of Multiplication Operators on α-Bloch Spaces

GUO Ji-dong, LOU Zeng-jian

2004, 19(2):  205-208. 

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In this note we study and give a full characterization of the boundeness of multiplication operators on α-Bloch spaces.



The Jacobson Radical of (R（G]）^G

HU Chang-liu, WANG Yuan-zheng

2004, 19(2):  209-212. 

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 In this paper,the Jacobson radical of (R[G])G, the fixed point subring of a group ring (R[G]) is studied. Some related properties of (R[G])^G are discussed.


Some Results Concerning a Singular Interga

QIAO Jian-wei, LING Feng-cai, ZHANG Zhen-feng

2004, 19(2):  213-217. 

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 In this note, we present some detail estimates for the integral with general integer k, as well as a singular integral formed from it, which would be useful for some nonlinear additive problems of primes.



The Loeb Algebras of Absolutely Continuous Measure

CHEN Dong-li, YUAN Wen-fa

2004, 19(2):  218-220. 

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It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).