Hyperbolic evolution groups and dichotomic evolution families

Recently, Ben-Artzi and Gohberg [2] used the concept ofC ₀-semigroups in order to characterize the existence of dichotomies for nonautonomous differential equations on _n. A similar task was performed by Latushkin and Stepin [11] for dichotomies of linear skew-product flows. In this paper we will useC _o-semigroups to characterize existence of dichotomies for strongly continuous evolution families (U(t,s)) _t.s on Hilbert and Banach spaces. Under an exponential growth condition we show that the concepts of hyperbolic evolution groups and exponentially dichotomic evolution families are equivalent.     

MAXIMAL ELEMENTS FOR G_B-MAJORIZED MAPPINGS IN PRODUCT G_CONVEX SPACES AND APPLICATIONS (Ⅱ)

IntroductionThispaperisacontinuumoftheprecedingpaperofauthor[1] .Fortheconceptsandnotationsofgeneralizedconvex (orG_convex)space ,CG_convexspace,theclassB(Y ,X)ofbetteradmissiblemappings ,GB_mappings,GB_majorizedmappingsandtherelatednotions,thereadermayconsultRef.[1].Themainaimofthispaperistogivesomeapplicationsoftheexistencetheoremsofmaximalelementsobtainedbyauthor[1] .ByapplyingourresultsinRef.[1],wegivesomecomponentversionofcoincidencetheoremandFan_Browdertypefixedpointtheorems .Somee…     

关于分担值的正规定则

定义了半纯函数族的限制值和分担值，证明若在区域Ｄ内有３个限制值或３个分担值，则为在Ｄ内正规．本定理以著名的Ｍｂｎｔｅｌ定则为特例．     

Theorems on unions ofU-sets

The properties of families of subsets of topological spaces that make it possible to separate out the common core of the proofs of theorems on unions of sets of uniqueness for series in various systems of functions are considered. As a consequence of the results obtained, it is proved, in particular, that the countable union of closed sets of uniqueness for the trigonometric series is a set of uniqueness for the Abel-Poisson summation method. Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 778–787, May, 2000.     

Riesz basis for strongly continuous groups

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (counted with multiplicity) can be grouped into subsets of at most K elements, and the distance between the groups is (uniformly) bounded away from zero, then the spectral projections associated to the groups form a Riesz family. This implies that if in every range of the spectral projection we construct an orthonormal basis, then the union of these bases is a Riesz basis in the Hilbert space.     

Zalcman引理在随机迭代函数族动力系统中的应用

本文根据Schwick的思想,利用Zalcman引理讨论了随机迭代函数族动力系统,指出了函数族随机迭代动力系统的Fatou集和函数族衍生半群动力系统的Fatou集定义差别明显但却等价.并获得了如下正规定则,设F={f_i|f_i为C（C）上的非线性解析函数,i ∈ M},其中M为非空指标集,Σ_M={（j₁,j₂,…,j_n,…）|j_i ∈ M,i ∈ N},若对任意的指标序列σ=（j₁,j₂,…,j_n,…）∈ Σ_M,迭代序列{W_σⁿ=f_jn º f_jn-1 º … ºf_j1（z）|n ∈ N}在点z处正规,则函数族F本身在点z处正规.     

The Roper-Suffridge extension operator and classes of biholomorphic mappings Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs) and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.     

Birmbaum信息与多个测验分数的最佳组合法

本文用现代教育、心理测量的ＩＲＴ（项目反应理论）中的Ｂｉｒｍｂａｕｍ信息函数，对经典教育、心理测量（ＣＴＴ）中的真实分数模型Ｘ＝Ｔ＋ｅ给出了一种多个测量分数的最佳组合法。该组合获得最大信息，并突破了ＩＲＴ和ＣＴＴ的局限性。     

Estimating a model through the conditional MLE

The estimation problem of a model through the conditional maximum likelihood estimator (MLE) is explored. The estimated model is compared using the two dual Kullback-Leibler losses with that through the unconditional MLE. The former is found to be superior to the latter under familiar models. This result is applicable to the model selection problem. These suggest a novel extensive use of the conditional likelihood, since the traditional use of the conditional likelihood was restricted only on inference for the structural parameter.     

I族函数的反函数系数的精确上界

本文得出导数具有正实部的解折函数族的反函数的系数的精确上界。