AN EXTENSION OF BROSOWSKI-MEINARDUS THEOREM ON INVARIANT APPROXIMATION

We obta(?) gener(?)ization of a fixed point th(?)of Dotson for nan-expansive mapptngs on star-sba p(?)sets and then(?)it to Prooe a unified Brosowski-M(?)us theorem on in(?)ariant approximatton in the setting,(?)fp-normed line(?)spaces.     

Intersections of homogeneous Cantor sets with their translations

We pursue the study on homogeneous Cantor sets with their translations. We get the fractal structure of intersection I（t）, and find that the Hausdorff measure of these sets forms a discrete spectrum whose non-zero values come only from shifting numbers with the coding of t. Concretely, a very brief calculation formula of the measure with the coding of t is given.     

Some results on topical functions and upward sets

The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets.We give characterizations of topical functions in terms of upward sets.     

Some remarks on Teichmüller spaces and modular groups

We study the fixed point sets of subgroups of modular groups acting on Teichmiiller spaces.     

Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain

We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.     

Harmonic functions with boundary values on Herz spaces

We discuss continuity of the Poisson transform on Herz spaces Bp as well as its action on weighted versions of these sets. We also consider Banach- valued versions of Herz spaces and study some of their properties.     

本原对称无环带号有向图的基指数与基指数集

In this paper,we study the bases and base sets of primitive symmetric loop-free (generalized)signed digraphs on n vertices.We obtain sharp upper bounds of the bases,and show that the base sets of the classes of such digraphs are{2,3,...,2n-1}.We also give a new proof of an important result obtained by Cheng and Liu.     

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.     

Theorems of Erdős-Ko-Rado type in geometrical settings

The original Erds-Ko-Rado problem has inspired much research. It started as a study on sets of pairwise intersecting k-subsets in an n-set, then it gave rise to research on sets of pairwise non-trivially intersecting k-dimensional vector spaces in the vector space V (n, q) of dimension n over the finite field of order q, and then research on sets of pairwise non-trivially intersecting generators and planes in finite classical polar spaces. We summarize the main results on the Erds-Ko-Rado problem in these three settings, mention the Erds-Ko-Rado problem in other related settings, and mention open problems for future research.     

THE HAUSDORFF CENTRED MEASURE OF THE SYMMETRY CANTOR SETS

Let 0<λ≤1/3,K(λ) be the attractor of an iterated function system {ψ1,ψ2} on the tine, whereλx, ψ2(x) = 1-λ+λx, x6 [0,1]. We call K(λ) the symmetry Cantor sets. In this paper, we obtained the exact Hausdorff Centred measure of K (A).     

γ-(α,β)-开集与γ-(α,β)-T_i空间（英文）

We introduce the concept of γ-(α, β)-open sets and the concepts of γ-(α, β)-T_i spaces(i = 0, 1, 2, 3, 4) based on the concept of(α, β)-open sets. We obtain some properties of γ-(α, β)-Tispaces. Furthermore, we study their essential characterization in topological space.     

GROWTH ESTIMATES FOR SINE-TYPE-FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS

We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem, of Bogmer, Horvath, Job and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riesz bases is desirable.     

Asymptotic quantization of probability distributions

We give a brief introduction to results on the asymptotics of quantizatlon errors. The topics discussed in-clude the quantization dimension, asymptotic distributions of sets of prototypes, asymptotically optimalquantizations, approximations and random quantizations.     

A NOTE ON THE JULIA SETS OF ENTIRE SOLUTIONS TO DELAY DIFFERENTIAL EQUATIONS

Let f be an entire solution of the Tumura-Clunie type non-linear delay differential equation.We mainly investigate the dynamical properties of Julia sets of f,and the lower bound estimates of the measure of related limiting directions is verified.     

FINDING PROJECTIONS ONTO THE INTERSECTION OF CONVEX SETS IN HILBERT SPACES. II.

We present a parallel iterative algorithm to find the shortest distance projection of a given point onto the intersection of a finite number of closed convex sets in a real Hilbert space ; the number of sets used at each iteration stept corresponding to the number of available processors, may be smaller than the total number of sets. The relaxation coefficient at each iteration step is determined by a geometrical condition in an associated Hilbert space, while for the weights mild conditions are given to assure norm convergence of the resulting sequence. These mild conditions leave enough flexibility to determine the weights more specifically in order to improve the speed of convergence.     

CLASSIFICATION OF GENERALIZED CARTAN MATRICES OF HYPERBOLIC TYPE

In this paper,the author gives all Dynkin diagrams of generalized Cartan matrices ofhyperbolic type,the order of hyperbolic generalized Carton matrix is less than or equal to10.All indefinite generalized Cartan matrices of order 2 are hyperbolic.The number ofDynkin diagrams of hyperbolic generalized Cartan matrices whose order is larger than 2 is238.Meanwhile,the author finds all Dynkin diagrams of strictly hyperbolic generalizedCartan matrices.     

ON A LEMMA OF BOWEN

We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen＇s result. An application is given to the level sets of Birkhoff average.     

GROWTH ESTIMATES FOR SINE—TYPE—FUNCTIONS AND APPLICATIONS TO RIESZ BASES OF EXPONENTIALS

We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets,thus obtaining explicit constants in a result of Levin.The estimates are then used to derive explicit lower bounds for exponential Riesz bases,as they arise in Avdonin‘s Theorem on 1/4 in the mean or in a Theorem of Bogmer,Horvath,Joo and Seip.An application is discussed,where knowledge of explicit lower bounds of exponential Riesz bases in desirable.     

On the complexity of expansive measures

We prove that the existence of positively expansive measures for continuous maps on compact metric spaces implies the existence of e 0 and a sequence of(m, e)-separated sets whose cardinalities go to infinite as m →∞. We then prove that maps exhibiting such a constant e and the positively expansive maps share some properties.     

EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHRDINGER SYSTEM

We study the existence and stability of the standing waves of two coupled Schrdinger equations with potentials |x|bi(bi ∈ R, i = 1, 2). Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the Schrdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1= b2= 2.