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中文
Table of Content
30 December 2006, Volume 21 Issue 4
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Open Manifolds with Nonnegative Ricci Curvature and Large Volume Growth
XU Sen-lin, SONG Bing-yu
2006, 21(4): 475-481.
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In this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature,large volume growth has finite topological type provided that ...
for some constant ε＞0.We also prove that a complete Riemannian manifold with nonnegative kth-Ricci curvature and under some pinching conditions is diffeomorphic to R
n
.
Some Coordinate Polynomials in Three Variables
GONG Sheng-jun, LI Shang-zhi
2006, 21(4): 482-487.
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In this paper,we introduce a polynomial sequence in K[x],in which two neigh- bor polynomials satisfy a wonderful property.Using that,we give partial answer of an open problem: if φ(x,y,z)=(f(x,y),g(x,y,z),z),which sends every linear coordinate to a coor-dinate,thenφis an automorphism of K[x,y,z].As a byproduct,we give an easy proof of the welt-known Jung’s Theorem.
On Growth and Covering Theorem for a Kind of Spiral-like Mappings
LIU Hao, CUI Hong-yu, LIU Ai-chao
2006, 21(4): 488-492.
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In this paper,we deduce growth and covering theorem for f(x) by the other means,where f(x) is strongly spiral-like mapping of typeβwith orderαdefined on Unit Ball B of complex Banach space,and still give growth upper bound and distortion upper bound for subordinate mapping.
The Relationship of Between Fuzzy Power Groups and Fuzzy Quotient Groups
YAN Guang-xia, MI Hong-hail, SHI Ya-ting
2006, 21(4): 493-496.
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In this paper,we extend the concept of fuzzy quotient groups.The structures of fuzzy power groups and fuzzy quotient groups are discussed.The relationship between fuzzy power groups and fuzzy quotient groups are considered.
A Generalization of Cuccia's Theorem
XU Ying-wu, LI Shi-rong
2006, 21(4): 497-502.
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For a finite group G,let S(G)be the set of minimal subgroups of odd order of G which are complemented in G.It is proved that if every minimal subgroup X of odd order of G which does not belong to S(G),CG(X)is either subnormal or abnormal in G.Then G solvable.
Oscillation of Nonlinear Partial Difference Equations with Continuous Variables
YANG Jun, WANG Chun-yan, GUAN Xin-ping
2006, 21(4): 503-510.
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This paper is concerned with the oscillation of nonlinear partial difference equa- tions with continuous variables and the corresponding dual equations.Several sufficient conditions are obtained for the oscillation of these equations.
On p-mean Curvature Operator with Critical Exponent
FU Hong-zhuo, SHEN Yao-tian, YANG Jun
2006, 21(4): 511-521.
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This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: ...
is a bounded domain in R
N
(N＞p＞1)with smooth boundary Ω,2＜=p＜=q＜=P*,P*=(Np)/(N-p),λ,P＞0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator.
Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients
ZHANG Ling-yuan, ZHANG Jin-liang, WANG Ming-liang
2006, 21(4): 522-528.
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By using the homogeneous balance principle(HBP),we derive a Backlund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.
Global Attractivity for a Differential Delay Model
LILin, WANG Bing-shun
2006, 21(4): 529-537.
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This paper considers the scalar differential delay equation x(t)=-μx(t)-f(x(t-τ)),where f(x)is a decreasing continuous function.By proving that all solutions will be ultimately in some interval,we give the conditions under which the unique equilibrium point of the differential delay equation is globally attractive.
Global Well-posedness of the Generalized Long-short Wave Equations
ZHANG Rui-feng, LIANG Hong-wei
2006, 21(4): 538-544.
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In the present paper,we investigate the well-posedness of the global solution for the Cauchy problem of generalized long-short wave equations.Applying Kato’s method for abstract quasi-linear evolution equations and a priori estimates of solution,we get the existence of globally smooth solution.
Analysis of an Epidemic Model with Age of Vaccination
GUO Shu-li, DING Feng-xia
2006, 21(4): 545-552.
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A simple SI epidemic model with age of vaccination is discussed in this paper. Both varing birth rate,the mortality rate caused by disease and vaccine waning rate are considered in this model.We prove that the global dynamics is completely determined by the basic reproductive number R(Ψ)(Ψdenotes per capita vaccination rate).If R(0)＜1, the disease-free equilibrium is a global attractor;If R(Ψ)＜1,the disease-free equilibrium is locally asymptotically stable;If R(Ψ)＞1,an unique endemic equilibrium exists and is locally asymptotically stable under certain condition.
The Optimal Conditions of the Linear Fractional Programming Problem with Constraint
SUN Jian-she, YE Liu-qing
2006, 21(4): 553-556.
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In this article,the authors discuss the optimal conditions of the linear fractional programming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution with constraint condition.
Nonconforming Finite Element Approximation on Anisotropic Meshes with Numerical Quadrature
YANG Qiao, SHI Dong-yang
2006, 21(4): 557-560.
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In this paper we mainly discuss the nonconforming finite element method for second order elliptic boundary value problems on anisotropic meshes.By changing the discretization form(i.e.,by use of numerical quadrature in the procedure of computing the left load),we obtain the optimal estimate O(h),which is as same as in the traditional finite element analysis when the load f∈H
1
(Ω)∩C
0
(Ω)which is weaker than the previous studies.The results obtained in this paper are also valid to the conforming triangular element and nonconforming Carey’s element.
Positive Periodic Solutions for Nonautonomous Differential Equations with Delay
PENG Shi-guo
2006, 21(4): 561-566.
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By utilizing a fixed point theorem on cone,some new results on the existence of positive periodic solutions for nonautonomous differential equations with delay are derived.
Algebraic Independence Measures for the Values of Mahler Type Functions
WANG Tian-qin, LIU Hua-ke
2006, 21(4): 567-576.
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In this paper,we give the algebraic independence measures for the values of Mahler type functions in complex number field and p-adic number field,respectively.
On Normal Criterion of Meromorphic Functions
Zhang Wen-hua
2006, 21(4): 577-580.
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We proved:Let F be a family of meromorphic functions in a domain D and a≠0,b∈C.If f′(z)-a(f(z))2≠b,f≠0 and the poles of f(z) are of multiplicity＞=3 for each f(z)∈F, then F is normal in D.
On the Smarandache Pseudo Number Sequence
LIU Yan-ni
2006, 21(4): 581-584.
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The main purpose of this paper is to study the mean value properties of the second Smarandache pseudo-odd number sequence and pseudo-even number sequence,and give some interesting asymptotic formula for them.
An Upper Bound for the Number of Normalized Latin Square
DUAN Lian
2006, 21(4): 585-589.
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In this note,the author find an upper bound formula for the number of the p×p normalized Latin Square,the first row and column of which are both standard order 1,2,...,p.
On Global Boundedness of Solutions for the Drift-diffusion Semiconductor Equations
GUO Xiu-lan, ZHANG Yu-lan, LI Gong-sheng
2006, 21(4): 590-596.
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This paper is devoted to the mixed initial-boundary value problem for the semi- conductor equations.Using Stampacchia recurrence method,we prove that the solutions are globally bounded and positive.
Two Sequences of Operator Monotone Functions and Strictly Chaotic Order
ZHANG Lei, JIANG Jian-fei
2006, 21(4): 597-607.
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In this paper we introduce two sequences of operator functions and their dual functions: ...
defined on (0,+∞). We find that they are all operator monotone functions with respect to the strictly chaotic order and some ordinary orders among positive invertible operators. Indeed, we extend the results of the operator monotone function (tlog t -t+1)/(log
2
t) which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics [1].
The Construction of a Class of Compactly Supported Orthogonal Matrix-valued Wavelets
CHEN Qing-jiang, CHENG Chuan-ru, CHENG Zheng-xing
2006, 21(4): 608-616.
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In this paper,we introduce matrix-valued multiresolution analysis and orthogonal matrix-valued wavelets.We obtain a necessary and sufficient condition on the existence of orthogonal matrix-valued wavelets by means of paraunitary vector filter bank theory.A method for constructing a class of compactly supported orthogonal matrix-valued wavelets is proposed by using multiresolution analysis method and matrix theory.
Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models
WU Xin-qian, TIAN Zheng, JU Yan-wei
2006, 21(4): 617-622.
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Consider the model Y
t
=βY
t-1
+g(Y
t-2
)+ε
t
for 3＜=t＜=T. Here g is an unknown function,βis an unknown parameter, vε
t
are i.i.d,random errors with mean 0 and varianceσ2 and the fourth moment α
4,
andεt are independent of Y
s
for all t＞=3 and s=1,2. Pseudo-LS estimators ...
distribution to N(0,1). The result can be used to establish large sample interval estimates of σ
2
or to make large sample tests for σ
2
.
On Computation Formula for a Series
YANG Qian-li, LI Hai-long
2006, 21(4): 623-628.
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It is one of the most interesting problems in number theory to compute some especial series by using Zeta and Gamma functions,and results have been obtained for some especial series.In this paper,we give an important formula which is proved also by using Zeta and Gamma functions.
Covering Theorems on Two Classes of Quasi-conformal Mappings
LIAO Mao-xin, GAO Chun-yi, WANG Zhi-gang
2006, 21(4): 629-632.
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In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.
