A Note on Property(ω)

In this note we study the property(ω),a variant of Weyl's theorem introduced by Rakoevic,by means of the new spectrum.We establish for a bounded linear operator defined on a Banach space a necessary and sufficient condition for which both property(ω) and approximate Weyl's theorem hold.As a consequence of the main result,we study the property(ω) and approximate Weyl's theorem for a class of operators which we call the λ-weak-H(p) operators.     

(α,β)-γ开集与(α,β)-γ-T_i空间（英文）

本文首先给出(α,β)-γ开集定义,获得了(α,β)-γ开集性质;然后引入了(α,β)-γ-Ti空间和(α,β)-γ-T*i空间概念(i=0,1/2,1,2,5/2),并得到它们更广泛的拓扑性质.     

A Note on μ(Z)-homeomorphisms

This paper is a continuation work of the authors on (z)-homeomorphisms. We establish similar relationships between quasisymmetric function and dilatation function as in quasiconformal mappings under (z)-homeomorphisms. Furthermore, a weighted quasiisometric inequality is presented.AMS Subject Classification (1991) 30C62 30C65     

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.     

(α,β)-fuzzy Subalgebras of Q-algebras

In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.     

A Note on Semigroups of Linear Operators

It is well known[l]that a closed linear operator A with dense domain in(an ordered)Banach space E senerates a C_O—semigroup if and only if the resolvent set p(A)contains(ω,+∞),andsup{‖(λ-ω)~nR(λ,A)~n‖:λ>ω,n∈N}<+∞(1)for someω.Sometimes,the condition(l)is not easy to verify.However,for the socalled resolvent positive operators(that is for someω,p(A)(?)(ω,+∞)and for allλ>ω,R(λ,A)=(λ-A)~1≥0),in[2],there are some easy-verified conditions.Here in thisnote,we establish another easy-verified condition.Let E_+be the positive cone of E,and     

A Note on Pseudo Ideals of Fields

Definition A subring A of a ring R is called a pseudo ideal, if for any r∈R and α∈A, r~2α∈A and αr~2∈A. The subring (R)~2={Σ±r_1~2…r_i~2|r_i∈R, t∈N} is called the square closed ring of R. Lemma The square closed ring of a division ring D is the intersection of all nontrivial pseudo ideals of D. Theorem Ⅰ If a simple ring R with a unit has a nontrivial pseudo ideal A containing an invertible element, R has characteristic p=2. In particular, the necessary condition for a division ring containing a nontrivial pseudo ideal is     

A Note on Stability of Multivariate Distributions

In this note,we give an elementary proof of a characterlzatlon for stabilityof nluuIvarlate dlstrlbutlons by considering a functional equatloll.     

A Note on Matchings of Bipartite Graphs

In this paper it is proved that let G(X,Y) be a bipartite graph with A(?)X and B(?)Y, and let k be an integer such that max{|A|, |B|}≤k≤min {|X|,|Y|}, then G contains a matching of k edges saturating both A and B iff for all S(?)X, (i) min{|N(S)| |X|-k, |N_B(S)| |X|-|B|}≥|S| and (ii) min{|N(S∩A)|,|N_B(S∩A)| k-|B|}≥|B∩A|, where N_B(S∩A)=N(S∩A∩B).It extends the theorems of Ore, Chen, Hoffman and Kuhn.     

A Note on Self-Mapping of the Interval

In this note we showed by construct a example that for, the con ditions and are not equivalent. Let, define by, for any We can construct a example as following: Let be identity, define by     

A Note on Topological Entropy of Maps

For a given collection of subsets of a compact metric space X which cover X,the entropies,hm(f)and hi(f),are introduced for a continuous map f of X to itseif. Also the concept of shadowing property with same end point (SPSEP for short) is introduced. The main results are,(1)H(f)≤hi(f)+hm(f)and,(2)h(f)=hm(f)whenever f has SPSEP,where h(f) is the topological entropy of f. Moreover,several corollaries are obtained.     

Note on the Paper “A Note on the SVD of Matrices”

Let F be a field, R be an F-algebra having SVD property['], R+ = {a e Rla = a}. In[2], we proved thatLemma 1 Let R be an F-algebra which having SVD proPerty Then R+ is a sub6e1d inF, R+ is a fOrmaIly rea1 6eId, and R+ is Pythagorean with no zerChdivisor.In the proof of Lernma 1 of [2], thereis this step: "FOr any a E R+ l clearly, there ekistsd E R+ n F such that a2 = ad = a', thus a = la E F, is fOllOws that R+ C F".Recently, paper [11 shows that "The proof of this step is no…     

Note on the Coradical Filtration of D(m,d, ξ)

In this note, the coradical filtration of the new class of Hopf algebras D(m, d, ξ) is determined. As consequences, the authors show that 1) D(m, d, ξ) is not pointed; 2) D(m, d, ξ) is a co-Frobenius Hopf algebra; 3) the coradical of D(m, d, ξ) is not a Hopf subalgebra.     

A Note on the Range of the Elementary Operator △_(AC)

ＡＮｏｔｅｏｎｔｈｅＲａｎｇｅｏｆｔｈｅＥｌｅｍｅｎｔａｒｙＯｐｅｒａｔｏｒ△_（ＡＣ）ＳｕｎＨｏｎｇｗｅｉ（孙宏伟）ＬｕＳｈｉｊｉｅ（鲁世杰）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｊｉａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚｈｏｕ，...     

A REMARK ON GENERAL COMPLEX(α,β)METRICS

In this paper,we give a characterization for the general complex(α,β)metrics to be strongly convex.As an application,we show that the well-known complex Randers...     

A Note of Regularity on Completely Distributive Lattices

ＡＮｏｔｅｏｆＲｅｇｕｌａｒｉｔｙｏｎＣｏｍｐｌｅｔｅｌｙＤｉｓｔｒｉｂｕｔｉｖｅＬａｔｔｉｃｅｓ￥ＣｈｅｎＹｉｘｉａｎｇ（ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｏｅｇｅ，２２１００９）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｎｏｔｅ，ｔｈｅａｕｔｈｏｒｇｉｖｅｓｓ...     

A Note on a Paper of Dickmeis etc

Let X be a Banach space, X~* be the class of all bounded and sublinear functionals T on X, i .e. (1) |T(f+g)|≤|T f|+|Tg|for all f, gX; (2) |T(af)|=|a||Tf|for all numbers a and f X; (3) ‖T‖_x~·=sup |T f|<∞. In[1] , W.Dickmeis, R.J.Nessel and E. van Wickeren proved the following theorem.