Local Sβ-compactness of L-topological Spaces

In this paper,the notion of local Sβ-compactness of L-topological spaces is introduced.It is proved that the local Sβ-compactness is an L-good extension,which is inherited by a closed subspace,multiplicative and invariable under the continuous open surjective L-valued Zadeh function.     

随机游动局部时的某些极限性质

Let X,X1,X2,...be i.i.d.random variables with EX2 δ<∞(for some δ>0).Consider a one-dimensional random walk S={Sn}n≥0,starting from S0=0.Let ξk]=x}.A strong approximation of ξ*(n) by the local time for Wiener process is presented and the limsup-type and liminf-type laws of iterated logarithm of the maximum local time ξ*(n) are obtained.Furthermore,the precise asymptotics in the law of iterated logarithm of ξ*(n) is proved.     

On Levi-fiat hypersurfaces with given boundary in C~n

Let S■C~n be a compact connected 2-codimensional submanifold.If n≥3,essentially local conditions and the assumption:every complex point of S is elliptic imply the existence of a projection in C~n of a Levi-flat(2n-1)-subvariety whose boundary is S(Dolbeault,Tomassini,Zaitsev, 2005).We extend the result when S is homeomorphic to a sphere and has one hyperbolic point. For n=2 many results are known since the 1980's and a new result with a very technical hypothesis is announced.     

Growth Theorem and Distortion Theorem for a Sub class of Parab olic Starlike Mappings

In this article, we firstly introduce a subclass of parabolic starlike mappings writen as P S (β;ρ). Secondly, the growth theorem for P S (β;ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of P S (β;ρ), the distortion theorem along a unit direction is also established.     

TWO WEIGHT CHARACTERIZATIONS FOR THE MULTILINEAR LOCAL MAXIMAL OPERATORS

Let 0<β<1 andΩbe a proper open and non-empty subset of Rⁿ.In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_β((f))(x)=sup_Q(∈xQ∈Fβ)Π_i=1^m1/|Q|∫_Q|f_i(y_i)|dy_i,where F_β={Q(x,l):x∈Ω,l<βd(x,Ω^c)},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_βare obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.     

The discrete logarithm problem from a local duality perspective

The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).     

Robust Nonparametric Function Estimation for Errors-in-variables Models

This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.     

Stability of the Equilibrium to the Boltzmann Equation with Large Potential Force

The Boltzmann equation with external potential force exists a unique equilibrium—local Maxwellian. The author constructs the nonlinear stability of the equilibrium when the initial datum is a small perturbation of the local Maxwellian in the whole space R~3. Compared with the previous result [Ukai, S., Yang, T. and Zhao, H.-J.,Global solutions to the Boltzmann equation with external forces, Anal. Appl.(Singap.), 3,2005, 157–193], no smallness condition on the Sobolev norm H~1 of the potential is needed in our arguments. The proof is based on the entropy-energy inequality and the L~2-L~∞ estimates.     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. shown that{∪- αεY＇ Gα, [ Y＇ ε P（Y）} is the set of all closed subsemigroups of It is a Clifford semigroup S = {Y; Gα; Фα,β}, where Y＇- denotes the suhsemilattice of Y generated by Y＇. In particular, G is the only dosed subsemigroup of itself for a group G and each one of subsemilattiees of a semilattiee is closed. Also, it is shown that the semiring P（S） is isomorphic to the semiring P（Y） for a Clifford semigroup S = [Y; Gα; Фα,β].     

DYNAMICS OF RELATIVISTIC FLUID FOR COMPRESSIBLE GAS

In this paper the relativistic fluid dynamics for compressible gas is studied.We show that the strict convexity of the negative thermodynamical entropy preserves invariant under the Lorentz transformation if and only if the local speed of sound in this gas is strictly less than that of light in the vacuum.A symmetric form for the equations of relativistic hydrodynamics is presented,and thus the local classical solutions to these equations can be deduced.At last,the non-relativistic limits of these local cla...     

Grunwald-Wang theorem,an effective version

The main purpose of this article is to establish an effective version of the Grunwald-Wang theorem,which asserts that given a family of local characters χvof K *vof exponent m, where v ∈ S for a finite set S of primes of K, there exists a global character χ of the idele class group CK of exponent m(unless some special case occurs, when it is 2m) whose local component at v is χv. The effectiveness problem for this theorem is to bound the norm N(χ) of the conductor of χ in terms of K, m, S and N(χv)(v ∈ S). The Kummer case(when K contains μm) is easy since it is almost an application of the Chinese remainder theorem. In this paper, we solve this problem completely in general case, and give three versions of bound, one is with GRH, and the other two are unconditional bounds. These effective results have some interesting applications in concrete situations. To give a simple example, if we fix p and l, one gets a good least upper bound for N such that p is not an l-th power mod N. One also gets the least upper bound for N such that lr| φ(N) and p is not an l-th power mod N.Some part of this article is adopted(with some revision) from the unpublished thesis by Wang(2001).     

Two-stage local M-estimation of additive models

This paper studies local M-estimation of the nonparametric components of additive models.A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives.Under very mild conditions,the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known.The established asymptotic results also hold for two particular local M-estimations:the local least squares and least absolute deviation estimations.However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions,its implementation is time-consuming.To reduce the computational burden,one-step approximations to the two-stage local M-estimators are developed.The one-step estimators are shown to achieve the same effciency as the fully iterative two-stage local M-estimators,which makes the two-stage local M-estimation more feasible in practice.The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers.In addition,the practical implementation of the proposed estimation is considered in details.Simulations demonstrate the merits of the two-stage local M-estimation,and a real example illustrates the performance of the methodology.     

全聚点集与(?)α-紧性

In this paper we introduce the concept for the set of complete cluster point and (?)_α-cormpactness in the metric space. We have proved several primitive properties relatedto the complete cluster point and set of complete cluster point. We have discussed the relationship among some kinds of (?)_α-compactness; and analysed the relationship among the (?)_α-compactness and the general compactness. We have found that the (?)_α-compactness and the general compactness are eqivalent to each other in the metric space.     

Limsup deviations on trees

The vertices of an infinite locally finite tree T are labelled by a collection of i.i.d. real random variables {Xσ}σ∈T which defines a tree indexed walk Sσ = ∑θ＜r≤σXr. We introduce and study the oscillations of the walk:Exact Hausdorff dimension of the set of such ξ 's is calculated. An application is given to study the local variation of Brownian motion. A general limsup deviation problem on trees is also studied.     

DEGREE 3 ALGEBRAIC MINIMAL SURFACES IN THE 3-SPHERE

We give a local analytic characterization that a minimal surface in the 3-sphere S3 R4 defined by an irreducible cubic polynomial is one of the Lawson’s minimal tori.This provides an alternative proof of the result by Perdomo(Characterization of order 3 algebraic immersed minimal surfaces of S3,Geom.Dedicata 129(2007),23-34).     

On multifractal of Cantor dust

We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust, The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure, Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self- similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.     

一类具有交叉扩散效应的三种群诱饵-捕食系统整体解的存在性（英文）

The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤ ∞.By obtaining the bounds of W21-norms of the local solution independent of T,it is established the global existence of the solution.     

次线性泛函与分离定理

In this note, we consider a family of functional S={p_V|V∈U} , where U is a local base of a locally convex topological linear space (E,T) consisting of all convex neighbourhoods of θ, p_V is the Minkowski's functional of V. It is proved that the family S can distinguishes compact convex set and bounded closed convex set. In the sequel, an elementary proof of H. Bauer's maximality principle and Krein-Milman theorem are given. Some other interesting properties of s are given also.     

SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK

Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.     

LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION

The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt+ut=uxx V’(u) on R.The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut=uxxV’(u).Whereas a lot is known about the local stability of travelling fronts in parabolic systems,for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type.However,for the combustion or monostable type of V,the problem is much more complicated.In this paper,a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established.And then,the result is extended to the damped wave equation with a case of monostable pushed front.