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中文
Table of Content
30 March 2008, Volume 23 Issue 1
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One Additive Diophantine Inequality with Mixed Powers 2 and 4
GONG Ke, LI Wei-ping
2008, 23(1): 1-7.
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In this paper, it is shown that: if λ
1
,…,λ
8
are nonzero real numbers, not all of the same sign, such that λ
1
/λ
2
is irrational, then for any real numberηandε>0 the inequality |λ
1
x
1
2
+λ
2
x
2
2
+λ
3
x
3
4
+…+λ
8
x
8
4
+η|<ε has infinitely many solutions in positive integers x
1
,…,x
8
.
Relative Strong F Compactness and Relative Ultra-F Compactness in L-topological Spaces
LI Yao-long
2008, 23(1): 8-15.
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ctness are defined in L-topological spaces for an arbitrary L-set.Properties of relative strong fuzzy sets and relative ultra-fuzzy compact sets are studied in detail and some characteristic theorems are given.Some examples are illustrated.
The Growth Orders of Meromorphic Solutions of Differential Equations
JIANG Xiu-hai, GAO Ling-yun
2008, 23(1): 16-20.
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By meas of the Nevanlinna theory of the value distribution of meromorphic functions,this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.
The Central Limit Theorem on SU(n,1)/S(U(n)×U(1))
2008, 23(1): 21-27.
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Periodic Solutions for a Kind of Second Order Differential Equation with a Deviating Argument
DU Bo, LU Shi-ping
2008, 23(1): 28-35.
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By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″(t)+f(x′(t))+ h(x(t))x′(t)+g(x(t-τ(t)))=p(t), some sufficient conditions on the existence of periodic solutions are obtained.
Weighted Bergman Spaces on Bounded Symmetric Domains
WANG Xiong-liang, LIU Tai-shun
2008, 23(1): 36-44.
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On bounded symmetric domainΩof C
n
, we investigate the properties of functions in weighted Bergman spaces A
p
(Ω,dv
s
) for 0<p≤+∞ and -1<s<+∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in
A
p
(Ω,dv
s
)
in terms of a class of linear operators D
α,β
. Making use of these characterizations, we ex- tend
A
p
(Ω,dv
s
) to the weighted Berg-man spaces A
p
α,β
(Ω,dv
s
) in a very natural way for 1≤p≤+∞and any real number s, that is, -∞<s<+∞.This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on
A
p
α,β
(Ω,dv
s
)
and the dual of
A
p
α,β
(Ω,dv
s
)
are given.
Blow Up of Periodic Solutions to a Class of Quasilinear Hyperbolic Systems in Diagonal Form
GE Ju
2008, 23(1): 45-55.
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In this paper,we discuss the blow-up of periodic solutions to a class of quasilinear hyperbolic systems in diagonal form,and make the accurate estimate of life-span.These results in this paper extend the conclusion [1～3].
A Note to the Objective Function for Centralized Case in Netessine and Rudi's Inventory Model
LI Xiao-shen, WANG Zhong-ying, GAO Ke-quan
2008, 23(1): 56-60.
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Netessine and Rudi(2003) consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition.They obtain analytically tractable solutions,establish concavity of the objective function,i.e.,the expected profit function generated by each product and uniqueness of the equilibrium for the decentralize case.For the centralized case,they indicate that the objective function,i.e., the expected profit function,might not be concave and not even quasiconcave.In this note we show,for the centralize case,that the objective function is submodular,and partially verify Netessine and Rudi’s observation that the objective function be unimodal in each of the decision variables for some case.
An Existence Theorem of Solution for a Singular Third-order Two-point Boundary Value Problem
YAO Qing-liu
2008, 23(1): 61-66.
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By constructing suitable Banach space,an existence theorem is established under a condition of linear growth for the third-order boundary value problem u′′′(t)+f(t,u(t),u′(t),u″(t))=0,0<t<1,u(O)=u′(0)=u′(1)=0, where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w) may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative.
Oscillation of Solutions for a Class of Nonlinear Neutral Partial Differential Equations with Continuous Distribution Delay
LUO Li-ping
2008, 23(1): 67-74.
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In this paper,some sufficient conditions are obtained for the oscillation of solu- tions for a class of second order nonlinear neutral partial differential equations with contin- uous distribution delay under Robin and Dirichlet’s boundary value conditions.
Global Attractors of Strong Solution for the Generalized Kuramoto-Sivashinsky Equation
WANG Su-yun, MU Lu-gui, ZHANG Yan-hong
2008, 23(1): 75-82.
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广
Using a new method developed in [5],we prove the existence of global attractors for the Generalized Kuramoto-Sivashinsky equation in Hper3(Ω) and Hper4(Ω).
The Lotka-Volterra Competition System with Discrete and Distributed Time Delays
ZHANG Jia-fang, ZHANG Zhi-ping
2008, 23(1): 83-88.
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In this paper,the Lotka-Volterra competition system with discrete and distrib- uted time delays is considered.By analyzing the characteristic equation of the linearized system,the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don’t effect the stability of the equilibrium in the delay system.Finally,we can conclude that the positive equilibrium is global asymptotically stable in the delay system.
On the Elliptic Equation "△u+K(x)e²
u
=0" with K(x) Positive Somewhere
WU San-cing, ZHANG Jing
2008, 23(1): 89-95.
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This paper considers the existence problem of an elliptic equation,which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is proved.In particular,K(x) is allowed to be unbounded above.
Existence of Travelling Wave Fronts to a Delayed Lattice Model for Population
SUN Feng-lan, TANG Yan-bin
2008, 23(1): 96-102.
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This paper considers the travelling wave fronts to a delayed lattice differential equation.The existence of the travelling wave solutions is proved by making use of the technique of the upper and lower solutions developed by J Wu and X Zou in [6].This work extends that of [4] in a general class of nonlinear terms.
Localization of Solutions of a Nonlinear Diffusion Problem
ZHOU Wen-shu, WEI Xiao-dan
2008, 23(1): 103-108.
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This paper concerns with properties of solutions of a nonlinear diffusion problem in non-divergence form.By constructing proper test functions,it is proved that solutions of the problem possess the property of localization.
A Characterization of Existence of Global Solutions for Some Fourth-order Wave Equations
CHEN Yong-ming, YANG Han
2008, 23(1): 109-114.
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The initial boundary value problem for the fourth-order wave equation u
tt
+△
2
u+u=|u|
p-1
u is considered. The existence and uniqueness of global weak solutions is obtained by using the Galerkin method and the concept of stable set due to Sattinger.
On the Smarandache LCM Sequence
XUE Xi-feng
2008, 23(1): 115-119.
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For any positive integer n,let L(n) = [1,2,...,n] be the least common multiple of the integers from 1 to n.Let k be any positive integer.The main purpose of this paper is to study the asymptotic property of L(n
k
), and give some interesting relevant results.
On the Braided Monoidal Categories of T-smash Products A
><
T
H
WANG Yong-zhong, LIU Rui-hua
2008, 23(1): 120-126.
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Let A and H be Hopf algebra,T-smash product A
><
T
H generalizes twisted smash product A * H.This paper shows a necessary and sufficient condition for T-smash product module category
A><TH
M to be braided monoidal category.
Approximation and Superconvergence Analysis for a New Higher Order Wilson Element to Sobolev Type Equations
SHI Dong-yang, HAO Xiao-bin
2008, 23(1): 127-134.
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In this paper,a new higher order Wilson element is presented,and the conver- gence is proved.Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
A Note of logA≥logB
GAO Fu-gen, YANG Chang-sen
2008, 23(1): 135-139.
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In this paper,firstly we shall show some equivalent conditions of A>B>0; secondly by using the results of ours we shah show some characterizations of the chaotic order(i.e.,logA≥log B) by norm inequalities.
Continuously Dependent on Boundary Value for Solution of Semi-liner Heat-conduction Equation
CAO Dian-li, WANG Jian-ping
2008, 23(1): 140-143.
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Reference [1] deals with the uniqueness of solution to problem (A) and solution of problem (A) is continuously dependent on free term and initial value under certain conditions. This paper discuss the solution of problem (A) is continuously dependent on boundary value on the basis of references [2] and [3].
Time Series of Random Macro-price and Application
GENG Xian-min
2008, 23(1): 144-155.
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This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series.By using the means of time series analysis, the input-output,Markov processes and the modern matrix analysis,the limiting problem of price balance and vibration in stochastic economic environment has been researched,and surprising conclusions obtained are as following:the probability that the economic collapse time is equal∞is 0.
The T Point of Meromorphic Functions in the Unit Disk
ZHANG Hong-kui, XIAO Ze-chang
2008, 23(1): 156-158.
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In this paper,the T points of meromorphic functions are defined and existence of the T points is showed in the Unit disk,we also prove T point must be J point.
