余拟三角弱Hopf群代数与辫子Monoidal范畴

In this paper, we first give the definitions of a crossed left π-H-comodules over a crossed weak Hopf π-algebra H, and show that the category of crossed left π-H-comodules is a monoidal category. Finally, we show that a family σ = {σα,β: Hα Hβ→ k}α,β∈πof k-linear maps is a coquasitriangular structure of a crossed weak Hopf π-algebra H if and only if the category of crossed left π-H-comodules over H is a braided monoidal category with braiding defined by σ.     

由双边群相关Hopf模诱导的Morita等价

Let H be a Hopf π-coalgebra over a commutative ring k with bijective antipode S, and A and B right π-H-comodulelike algebras. We show that the pair of adjoint functors （F3 = A  Bop A□ HBop -,G3 = （-）coH） between the categories A□HBopM and AMπB-H is a pair of inverse equivalences, when A is a faithfully flat π-H-Galois extension. Furthermore, the categories Moritaπ-H（A,B） and Morita □π-H（AcoH,BcoH） are equivalent, if A and B are faithfully flat π-H-Galois extensions.     

群Yetter-Drinfel''d范畴中的Hopf代数

In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel＇d category L^LyD（π） over a crossed Hopf group-coalgebra L, then its dual H^＊ is also a Hopf algebra in the category L^LyD（π）. Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD（π）.     

Weak Hopf Algebra in Yetter-Drinfeld Categories and Weak Biproducts

The Yetter-Drinfeld category of the Hopf algebra over a field is a pre braided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD. we prove that the weak biproducts of A and H is a weak Hopf algebra.     

Generalized braided Hopf algebras

The concept of （f, σ）-pair （B, H）is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category ^HM of left H-comodules through an （f, σ）-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel＇d category H^HYD by twisting the multiplication of B.     

广义Macaulay-Northcott模与Tor-群

Let （S,≤） be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups：Tori[[ RS,≤]]（[[MS,≤]],[NS,≤]）≌ s∈S ToriR （M,N）.     

On s-semipermutable subgroups of finite groups

Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.     

Characteristic modules and tensor products over quasi-hereditary algebras

Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.     

对偶的Hom型拟Hopf代数的余表示和范畴实现

In this paper, we introduce the dual Hom-quasi-Hopf algebra and prove that the comodules category of a(braided) dual Hom-quasi-bialgebra is a monoidal category. Finally,we give a categorical realization of dual Hom-quasi-Hopf algebras.     

L-模糊化拓扑空间中的Moore-Smith收敛理论

This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.     

ADDITIVE MAPS ON SOME OPERATOR ALGEBRAS BEHAVING LIKE(α, β)-DERIVATIONS OR GENERALIZED(α, β)-DERIVATIONS AT ZERO-PRODUCT ELEMENTS

Let A be a subalgebra of B(X) containing the identity operator I and an idempotent P. Suppose that α, β : A → A are ring epimorphisms and there exists some nest N on X such that α(P)(X) and β(P)(X) are non-trivial elements of N. Let A contain all rank one operators in AlgN and δ : A → B(X) be an additive mapping. It is shown that, if δ is(α, β)-derivable at zero point, then there exists an additive(α, β)-derivation τ : A → B(X)such that δ(A) = τ(A) + α(A)δ(I) for all A ∈ A. It is also shown that if δ is generalized(α, β)-derivable at zero point, then δ is an additive generalized(α, β)-derivation. Moreover,by use of this result, the additive maps(generalized)(α, β)-derivable at zero point on several nest algebras, are also characterized.     

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized(φ, ψ)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.     

The existence of nontrivial solutions to a semilinear elliptic system on without the ambrosetti-rabinowitz condition

In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.     

LIE IDEALS, MORITA CONTEXT AND GENERALIZED （α β）-DERIVATIONS

A classical problem in ring theory is to study conditions under which a ring is forced to become commutative. Stimulated from Jacobson＇s famous result, several tech- niques are developed to achieve this goal. In the present note, we use a pair of rings, which are the ingredients of a Morita context, and obtain that if one of the ring is prime with the generalized （α β）-derivations that satisfy certain conditions on the trace ideal of the ring, which by default is a Lie ideal, and the other ring is reduced, then the trace ideal of the reduced ring is contained in the center of the ring. As an outcome, in case of a semi-projective Morita context, the reduced ring becomes commutative.     

APPROXIMATING SOLUTION OF 0∈ T（x） FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

The purpose of this paper is to study the solution of 0 ∈ T (x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first pro...     

THE ACCELERATED SEARCH-EXTENSION METHOD FOR COMPUTING MULTIPLE SOLUTIONS OF SEMILINEAR PDEs

In this paper, we propose an accelerated search-extension method （ASEM） based on the interpolated coefficient finite element method, the search-extension method （SEM） and the two-grid method to obtain the multiple solutions for semilinear elliptic equations. This strategy is not only successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems, but also reduces the expensive computation greatly. The numerical results in I-D and 2-D cases will show the efficiency of our approach.     

WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERON-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.     

MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...     

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

Modifying the method of Ansari,we give some criteria for hypercyclicity of quasi-Mazur spaces.They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces.For some special locally convex spaces,for example,Ko¨the(LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces,we investigate their hypercyclicity.As we see,bounded biorthogonal systems play an important role in the construction of Ansari.Moreover,we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets,which are useful in judging the existence of bounded biorthogonal systems.     

Erds-Ko-Rado Theorem for Ladder Graphs

For a graph G and an integer r≥1,G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star(a family of independent r-sets containing some fixed vertex in G),and G is strictly r-EKR if every extremal intersecting family of independent r-sets is a star.Recently,Hurlbert and Kamat gave a preliminary result about EKR property of ladder graphs.They showed that a ladder graph with n rungs is 3-EKR for all n≥3.The present paper proves that this graph is r-EKR for all 1≤r≤n,and strictly r-EKR except for r=n-1.