Hybrid fixed point result for lipschitz homomorphisms on quasi-Banach algebras

We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.     

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.     

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.     

Existence of unbiased estimate of regression parameters in simple linear EV models

It is well known that for one-dimensional normal EV regression model X = x u,Y =α βx e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and βare not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and βunder some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and βexist, and the form of the MVUE of a and βare also given.     

On a class of two-dimensional Finsler manifolds of isotropic S-curvature

For an(α, β)-metric(non-Randers type) of isotropic S-curvature on an n-dimensional manifold with non-constant norm ‖β‖α, we first show that n = 2, and then we characterize such a class of two-dimensional(α, β)-manifolds with some PDEs, and also construct some examples for such a class.     

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.     

ABSOLUTE RETRACTIVITY OF SOME SETS TO TWO-VARIABLES MULTIFUNCTIONS

In this paper,by providing some different conditions respect to another works,we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F:X × X → P b,cl (X),on complete metric spaces.     

On Growth and Covering Theorem for Almost Spiallike Mapping of Type β with Order α

Let f(x) be an almost spirallike mapping of type β with order α on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f(x), we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.     

COMPLETE ACCUMULATION POINTS AND COMPACTNESS OF FUZZY SETS

Let A be a fuzzy set in a fuzzy topological space (X,τ) and β∈(0, 1]. We denote by ζ_x~a the fuzzy point defined by ζ_x~a(x)=a and ζ_x~a(y)=0 for eaoh y≠x, where a is called the height of ζ_x~a. A subfamily u of τ is called an open β-cover of A if each fuzzy point in A with height β is quasi-coincident with ([1]) some member of u. By a β-subcover of the open β-cover u of A is meant any subfamily of u that is also an open β-cover of A. A is called β-compact in (X, τ) if every open β-cover     

对偶的Hom-型拟Hopf代数的Monoidal范畴解释（英文）

In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.     

论附属于某种连续映像的不等式及其在纤维空间中的应用

<正> §1. 设 X,Y 为拓扑空间,又设 f:X→Y 为连续映像.J.H.C.Whitehead 证明 X,Y 为 CW 丛而 f 能导出基本群及上同调群间的同模对应时,f 为同伦对等映像.映像 f 是否存在,不仅与 X,Y 的基本群及上同调群的构造有关,而与 X,Y 内在的几何结构有密切的关系.连续照像 f 导出 X,Y 之间上同调群的准同模对应 f,那末 f 能与某些准同模对应相交换,由此 J.H.C.Whitehead 指出正则准同模的观念.由[4]可知正则同模论供应我们许多同伦不变量,它们是直接可以计算的东西,并且对于 X,Y 间连续映像的分类问题,应该有密切的关系.     

Definability of Completely Decomposable Torsion-Free Abelian Groups by Endomorphism Semigroups and Homomorphism Groups

Mathematical Notes - Let C be an Abelian group. A class X of Abelian groups is called a CE?H-class if, for every groups A, B ∈ X, the isomorphisms E?(A) ? E?(B) and...     

Isomorphisms of geodesic flows on quadrics

We consider several well-known isomorphisms between Jacobi’s geodesic problem and some integrable cases from rigid body dynamics (the cases of Clebsch and Brun). A relationship between these isomorphisms is indicated. The problem of compactification for geodesic flows on noncompact surfaces is stated. This problem is hypothesized to be intimately connected with the property of integrability.     

The Triangulated Hopf Category n +SL(2)

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.     

同伦群和同调群的关系及其应用

<正> 最近几年来,关于同伦群的研究,特别是球面同化群的计算有很大的进步,但是关于更一般的空间的同伦群的计算,就作者所知道的文献来说,似乎没有相应的进展,在这一方面的工作,最早也是最主要的是 Hurewicz 定理,Serre 在[15]中利用所谓 C同构的概念,把 Hurewicz 定理推广到所谓(n-1)维 C 连通空间中,但是也和 Hure-wicz 定理一样,只能讨论 n 维同伦群和 n 维同调群的关系.张素诚,Hilton 及 Barrat     

The constructive theory of preference relations on a locally compact space

This paper, which is written within a rigorously constructive framework, deals with preference relations (strict weak orders) on a locally compact space X, and with the representation of such relations by continuous utility functions (order isomorphisms) from X into ℝ. Necessary conditions are given for finding the values of a utility function algorithmically in terms of the parameters when X is a locally compact, convex subset of R^N. These conditions single out the class of admissible preference relations, which are investigated in some detail. The paper concludes with some results on the algorithmic continuity of the process which assigns utility functions to admissible preference relations.The work of this paper can be regarded as a recursive development of preference and utility theory.     

Multirectangular invariants for power Köthe spaces

Using some new linear topological invariants, isomorphisms and quasidiagonal isomorphisms are investigated on the class of first type power Köthe spaces [Proceedings of 7th Winter School in Drogobych, 1976, pp. 101-126; Turkish J. Math. 20 (1996) 237-289; Linear Topol. Spaces Complex Anal. 2 (1995) 35-44]. This is the smallest class of Köthe spaces containing all Cartesian and projective tensor products of power series spaces and closed with respect to taking of basic subspaces (closed linear hulls of subsets of the canonical basis). As an application, it is shown that isomorphic spaces from this class have, up to quasidiagonal isomorphisms, the same basic subspaces of finite (infinite) type.     

Representations and categorical realization of Hom-quasi-Hopf algebras

We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.     

Surrogate duality for vector optimization

Using our theorems (of [12]) on separation of convex sets by linear operators, in the sense of the lexi-cographical order on Rⁿ, we prove some theorems of surrogate duality for vector optimization problems with convex constraints (but no regularity assumption), where the surrogate constraint sets are generalized half-spaces and the surrogate multipliers are linear operators, or isomorphisms, or isometries. In the cae of inequality constraints, we prove that the surrogate multipliers can be taken lexicographically non-negative isometries or non-negative (in the usual order) linear isomorphisms.