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中文
Table of Content
30 June 2006, Volume 21 Issue 2
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Analysis on a Set of 12-parameter Rectangular Plate Element with High Accuracy
SHI Dong-yang, WANG Cai-xia
2006, 21(2): 159-165.
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It is proved that the so-called a set of 12-parameter rectangular plate elements with high accuracy constructed by using double set parameter method and undetermined method are, in fact, the same one; the real shape function space is nothing but the Adini’s element’s, which has nothing to do with the other high degree terms and leads to a new method for constructing the high accuracy plate elements. This fact has never been seen for other conventional and unconventional, conforming and nonconforming rectangular plate elements, such as Quasi-conforming elements, generalized conforming elements and other double set parameter finite elements. Moreover, such kind of rectangular elements can not be constructed by the conventional finite element methods.
The Study for Some Subclasses of Biholomorphic Mappings by an Unified Method
XU Qing-hua, LIU Tai-shun
2006, 21(2): 166-175.
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Let Ω∈C
n
be a bounded starlike circular domain with 0∈Ω. In this paper, we introduce a class of holomorphic mappings M
g
onΩ. Let f(z) be a normalized locally biholomorphic mapping onΩsuch that J
f
-1
(z)f(z)∈M
g
and z=0 is the zero of order k + 1 of f(z)-z. We obtain the growth and covering theorems for f(z). Especially, as corollaries, we unify and generalize many known results. Moreover, in view of proofs of corollaries, the essential relations among the subclasses of starlike mappings are shown.
Oscillation Criteria for Impulsive Hyperbolic Equations of Neutral Type
ZHU Xian-yang, LI Yong-kun, LU Ling-hong
2006, 21(2): 176-184.
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Oscillation properties of the solutions of impulsive hyperbolic equations are investigated by the method of differential inequalities.
Optimal Switching Control for Nonlinear Systems in A Finite Duration
MU Xiao-wu, LIU Hai-jun
2006, 21(2): 185-195.
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This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities(the appropriate generalization of the Hamilton-Jacobi equation in this context) and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.
Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but
X
1
X
2
X
3
X
4
LI Yi-jun
2006, 21(2): 196-201.
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To obtain a better Vinogradov’s bound, assistant function with two or three zeros and all Dirichlet’s characters has been evaluated. Assistant function g(X
1
,X
2
,X
3
,X
4
) with four zeros and all nonprincipal characters but X
1
X
2
X
3
X
4
is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.
Strong Consistency of Estimators of a Semiparametric Regression Model under Fixed Design
TIAN Ping, XUE Liu-gen
2006, 21(2): 202-209.
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In this paper, we consider the following semiparametric regression model under fixed design: y
i
=x
i
1
β+g(x
i
)+e
i
. The estimators of β, g(·) and σ
2
are obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.
A Class of the Geometric Inequalities Involving k-Brocard Distance
WEN Jia-jin, KE Rui, LV Tao
2006, 21(2): 210-219.
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Let P be an inner point of a convex N-gon Γ
N
:A
1
A
2
…A
N
A
1
(N≥3), and let di,k denote the distance from the point A
i+k
, to the line PA
i
(i=1,2,…,N,A
i
=A
j
i=j(modN)), which is called the k-Brocard distance for P of Γ
N
. We have proved the following double-inequality: If P∈Γ
N
, and then ... .
A New Hierarchy Soliton Equations Associated with a Schrdinger Type Spectral Problem and the Corresponding Finite-dimensional Integrable System
XING Xiu-zhi, WU Jing-zhu, GENG Xian-guo
2006, 21(2): 220-228.
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By introducing a Schrodinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.
Attractor for a Fourth-order Equation in the Whole Line
ZHAO Cai-di, LI Yong-sheng
2006, 21(2): 229-235.
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This paper studies the long time behavior of the following Cauchy problem The authors prove the existence of global attractor by showing the corresponding operator semigroup is asymptotically compact.
Construction of Finite Element Multiscaling Function with Three Coefficients
LI Rui
2006, 21(2): 236-241.
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The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.
Minimax Estimation of the Function of Parameters in Normal Distribution
MENG Hong-ling, KANG Jin-xuan, ZHANG Kai-guang
2006, 21(2): 242-245.
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The estimation of the functionθ=exp{αμ+bσ
2
} of parameters (μ,σ
2
) in normal distribution N(μ,σ
2
) is discussed. And when the prior distributions of μ and σ
2
are independent, under the loss function L(θ,δ)=(θ
-1
×δ-1)
2
, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.
L-fuzzy Lattice Implication Algebra
SONG Qing-long, LI Chun-rui, ZHAO Guang-feng
2006, 21(2): 246-251.
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This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.
A Note on 0-F-inverse Semigroups
CHEN Li-min
2006, 21(2): 252-254.
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In this paper, we introduce 0-F-inverse semigroups and characterize 0-F-inverse categorical semigroups by using their minimal primitive congruenceβ.
The Properties Analysis for Generalized Abstract Evolutionary Algorithm
XUE Ming-zhi, MA Yun-ling
2006, 21(2): 255-260.
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There has been a growing interest in mathematical models to character the evo- lutionary algorithms.The best-known one of such models is the axiomatic model called the abstract evolutionary algorithm(AEA),which unifies most of the currently known evolu- tionary algorithms and describes the evolution as an abstract stochastic process composed of two fundamental abstract operators:abstract selection and evolution operators.In this paper,we first introduce the definitions of the generalized abstract selection and evolution operators.Then we discuss the characterizatlon of some parameters related to generalized abstract selection and evolution operators.Based on these operators,we finally give the
strong convergence of the generalized abstract evolutionary algorithm.
The present work provides a big step toward the establishment of a unified theory of evolutionary computa- tion.
An Equation of Stirling Numbers of the Second Kind
DU Chun-yu, ZHANG Jian-guo
2006, 21(2): 261-263.
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In this paper, we propose and prove the following equation, where is a Stirling number of the second kind, when n≥3 is given.
Total Chromatic Number of the Join of K
m,n
and C
n
LI Guang-rong, ZHANG Li-min
2006, 21(2): 264-270.
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The total chromatic number XT(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no adjacent or incident pair of elements receive the same color. G is called Type 1 if XT(G)=Δ(G) + 1. In this paper we prove that the join of a complete bipartite graph K
m,n
and a cycle C
n
is of Type 1.
Oscillation of Second Order Delay Differential Equations with Nonlinear Neutral Term
XU Zhi-ting, JIN Chu-hua
2006, 21(2): 271-277.
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By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.
A Note on the Variation of Permanents
HOU Qian-min, LIU Xiu-sheng
2006, 21(2): 278-282.
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It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖
F
max(‖A‖
F
,‖B‖
F
)
n-1
or ... holds for where A
H
denotes the conjuagte transpose of the matrix A=(a
ij
)
n×n
.
Stability Analysis for Switching of Discrete Linear Singular Systems
GUO Xiao-li, LI Wei, MU Xiao-wu
2006, 21(2): 283-287.
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In this paper, we study the stability of discrete linear singular systems by switching controller. Using some recent results on multiple-Lyapunov function technique, we obtain two sufficient conditions of linear singular systems.
The Boundedness of a Class of Singular Integrals and Their Commutators on Generalized Morrey Spaces
WANG Yue-shan, WANG Xue-min
2006, 21(2): 288-292.
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The generalized Morrey spaces are introduced under the hypothesis that Rn is endowed with the general parabolic metric , and the boundedness properties are established in generalized Morrey spaces for a class of singular integral operators, which include Calderon-Zygmund singular integrals and their commutators with BMO.
The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist
ZENG Chao-yi
2006, 21(2): 293-296.
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The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1):S
i
(x)=a
i
x+b
i
,x∈[0,1], i=1, 2,…,m, where 0<a
i
< 1, i=1, 2,…, m; b
i
+a
i
>0, i=1, 2,…, m-1, b1=0 and a
m
+b
m
=1. Providing the sufficient and necessary conditions of its existence Hausdorff measure.
Value Distribution of Differential Polynomials in Meromorphic Functions
LIU Xiao-shu
2006, 21(2): 297-300.
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Let f(z) be a meromorphic function and Ψ be the differential polynomial of f which satisfies the condition of N(r, f) + N (r, 1/f) = S(r, f). We obtain several results about the zero point of the Ψ and those results extend and improve the results of Yang and Yi in this paper.
Syntactic Extension of Lattice-valued Propositional Logic LP(X)
ZHENG Feng-bin, LI Qing-yu, WANG Xue-fang, XU Yang
2006, 21(2): 301-308.
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We have given a semantic extension of lattice-valued propositional logic LP(X) in [6]. In this paper, we investigate its corresponding syntactic extension of LP(X) and give the relations between these two extensions.
A Model-calibration Approach to Using Complete Auxiliary Information from Stratified Sampling Survey Data
WU Chang-chun, ZHANG Run-chu
2006, 21(2): 309-316.
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In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).
