数学学报杂志 北大期刊 CSCD期刊 统计源期刊

Lacunary Measures and Self-similar Probability Measuresin Function Spaces

作者：HansTRIEBEL 刊期：2004年第04期

The paper deals with multifractal quantities for some types of Radon measures, especially self-similar probability measures, and their relations to Besov spaces.

Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow

作者：ZeJunWANG 刊期：2004年第04期

In this paper, we study a kind of 2-dimensional axi-symmetrical piston problem in compressible flow. The corresponding mathematical model is the well-known Euler system. With the Newton iteration procedure and energy estimate, we give the local existence of the shock front solution to this problem.

Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

作者：XiangYuZHOU; WeiMingLIU 刊期：2004年第04期

Let X be a Hopf manifolds with an Abelian fundamental group, E is a holomorphic vector bundle of rank r with trivial pull-back to W = C^n - {0}. We prove the existence of a non-vanishing section of L (О× E for some line bundle on X and study the vector bundles filtration structure of E.These generalize the results of...

Some Characterizations of the Properties LB^-∞ and LB∞

作者：ThuanQuangTHAI 刊期：2004年第04期

The aim of this paper is to give some properties of the linear topological invariant LB^-∞ Using these results we show that a nuclear Fréchet space F has the property LB∞ if and only if every separately holomorphic function on an open subset U × V of E × F^* has a local Dirichlet representation,where E is a nuclear...

Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

作者：J.C.ROSALES; P.A.GARCíA-SANCHEZ; J.I.GARCíA-GARCíA; J.A.JIMENEZMADRID 刊期：2004年第04期

For a numerical semigroup, we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup. The semigroup is fully determined by its multiplicity and these gaps.We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a nu...

Uniqueness of Limit Cycle for the Quadratic Systems with Weak Saddle and Focus

作者：ShenQiZHAO; PingGuangZHANG 刊期：2004年第04期

It is proved that the quadratic system with a weak saddle has at most one limit cycle, and that if this system has a separatrix cycle passing through the weak saddle, then the stability of the separatrix cycle is contrary to that of the singular point surrounded by it.

On the Characterizability of the Automorphism Groups of Sporadic Simple Groups by Their Element Orders

作者：A.R.MOGHADDAMFAR; A.R.ZOKAYI; M.R.DARAFSHEH 刊期：2004年第04期

Cauchy Problem of Some Doubly Degenerate Parabolic Equations with Initial Datum a Measure

作者：HuiJunFAN 刊期：2004年第04期

This paper discusses the Cauchy problem of the equation ut=↓△·（|↓△u^m|^p-2↓△u^m)-u^q with initial datum a measure. Under the assumption of the parameters, one proves the existence and non-existence of the non-negative generalized solution.

Modular Lie Superalgebras of H-type

作者：YongZhengZHANG 刊期：2004年第04期

In this article the Z-graded transitive modular Lie superalgebra О+i≥-1 Li, whose representation of Lo in L-1 is isomorphic to the natural representation of osp(L-1), is determined.

Remarks on the Regularity to 3-D IdealMagnetohydrodynamic Equations

作者：QuanSenJIU; ChengHE 刊期：2004年第04期

In this paper we are interested in the sufficient conditions which guarantee the regularity of solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T]. Five sufficient conditions are given. Our results are motivated by two main ideas: one is to control the accumulation of vorticity a...

Definition of Measure-theoretic Pressure Using Spanning Sets

作者：LianFaHE; JinFengLV; LiNaZHOU 刊期：2004年第04期

We introduce a new definition of measure-theoretic pressure for ergodic measures of continuous maps on a compact metric space. This definition is similar to those of topological pressure involving spanning sets. As an application, for C^1+α(α > O) diffeomorphisms of a compact manifold,we study the relationship betwee...

Quasi-sure Limit Theorem of Parabolic StochasticPartial Differential Equations

作者：XiChengZHANG 刊期：2004年第04期

In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions, by the way, we obtain the quasi-sure continuity of the solution.

Disk-like Tiles Derived from Complex Bases

作者：JunLUO; ZuoLingZHOU 刊期：2004年第04期

For each positive integer k, the radix representation of the complex numbers in the base-κ + i gives rise to a lattice self-atone tile Tκ in the plane, which consists of all the complex numbersthat can be expressed in the form ∑j>1 dj(-κ + i)^-j, where dj ∈ {0, 1,2 , κ^2}. We prove that Tκ is homeomorphic to the cl...

Viscosity Solutions of Monotonic Functional Parabolic PDE

作者：WeiAnLIU; GangLU 刊期：2004年第04期

In this paper, by the technique of coupled solutions, the notion of viscosity solution is extended to quasi-monotonic fully nonlinear parabolic equations with delay, which involves many models arising from optimal control theory, economy and finance, biology etc. The comparison, existence and uniqueness are proved, A...

Asymtotics of M-estmation in Non-linear Regression

作者：YingYANG 刊期：2004年第04期

Consider the standard non-linear regression model yi = g(xi, θo) +εi, i = 1,..., n where g(x.θ) is a continuous function on a bounded closed region X × О-, θ00 is the unknown parameter vector in О- C R^p, {x1, x2 …… xn} is a deterministic design of experiment and {ε1, ε2 …… εn} is a sequence of independent random...