Characterizations of Certain Congruences on Orthodox Semigroups

In this paper, we intrnduce the notation pmin,pmin p^min and p^min, by which we describe the trace classes and the kernel classes of general congruence p on orthodox semigronps.Then we have given and proved some equivalent characterizations of special congruences by mean of kernels and traces. On the basis of above-mentioned congruences, we further investigate theirrelations. Some results shout congruences on iverse semigroups are generalized to orthodox semigroups.     

Trotter—Kato Theorems for an α—times Integrated Semigroups

In this paper,we discuss on the convergence and approximation of an α-times integrated semigroups. The Trotter-kato theorems for an α-times integrated semigroups are obtained.     

POINTWISE SATURATION THEOREM FOR PROBABILISTIC REPRESENTATIONS OF （C0） OPERATOR SEMIGROUPS

In this paper, the saturation theorem of probabilistic represntations of (C0) operator semigroups on G(M,ω) are obtain.     

带恰当断面的拟-型$\delta$半群

In this paper,some properties of quasi-type δ semigroups with an adequate transversal are explored.In particular,abundant semigroups with a cancellative transversal are character-ized.Our results generalize and enrich Saito＇s results on quasi-orthodox semigroups with an inverse transversal.     

逆周期的交换半群生成的簇的子簇

In this paper, all subvarieties of the varieties Ak （k ∈N） generated by aperiodic commutative semigroups are characterized. Based on this characterization, the structure of lattice of subvarieties of Ak is investigated.     

A Class of Left E-adequate Semigroups

In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^＋（μ^＊,μ ） abundant semigroups and type μ^＋left E-adequate semigroups. In fact, regular semigroups are type μ^＋abundant semigroups and inverse semigroups are type μ^＋left E-adequate semigroups. Next, we construct a special kind of algebras called E^＋-product. It is proved that every E^＋-product is a type μ^＋left E-adequate semigroup, and every type μ^＋left E-adequate semigroup is isomorphic to an E^＋-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^＋-product of a Clifford semigroup by a fundamental inverse semigroup.     

关于具有$Q$-逆断面的正则半群的同余格

In this paper, a complete congruence on the congruence lattice of regular semigroups with Q-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.     

Ideals in Morita Rings and Morita Semigroups

We characterize the lattice of all ideals of a Morita ring （semigroup） when the corresponding pair of rings （semigroups） in the Morita context are Morita equivalent s-unital （like-unitv） rings （semigroups）.     

左C-wrpp 半群的左$\Delta$-积

We study another structure of so-called left C-wrpp semigroups. In particular, the concept of left △-product is extended and enriched. The aim of this paper is to give a construction of left C-wrpp semigroups by a left regular band and a strong semilattice of left-R cancellative monoids. Properties of left C-wrpp semigroups endowed with left △-products are particularly investigated.     

The structure of superabundant semigroups

A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.