Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure

2010 ◽  
Vol 80 (17-18) ◽  
pp. 1306-1312
Author(s):  
Pier Giovanni Bissiri
Keyword(s):  
Empirical Measure ◽  
Finite Dimensional ◽  
Exchangeable Sequence ◽  
The Law ◽  
Finite Exchangeable Sequence

On Vitali's Theorem for Groups of Motions of Euclidean Space

1999 ◽  
Vol 6 (4) ◽  
pp. 323-334
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Some inequalities for moments and coefficients of variation for a large class of probability functions

1979 ◽  
Vol 16 (3) ◽  
pp. 665-670 ◽  
Author(s):  
Burt V. Bronk
Keyword(s):  
Large Class ◽  
Average Molecular Weight ◽  
Empirical Measure ◽  
Number Average Molecular Weight ◽  
Positive Real ◽  
Coefficients Of Variation ◽  
Probability Densities ◽  
Rigorous Bounds ◽  
Illustrative Application

Some inequalities for moments and coefficients of variation of probability densities over the positive real line are obtained by means of simple geometrical relationships. As an illustrative application rigorous bounds are obtained for the ratio of weight average to number average molecular weight for a large class of distributions of macromolecules, giving a more precise characterization of this empirical measure of heterogeneity.

Spectral synthesis and residually finite-dimensional algebras

2017 ◽  
Vol 16 (10) ◽  
pp. 1750200 ◽  
Author(s):  
László Székelyhidi ◽  
Bettina Wilkens
Keyword(s):  
Spectral Analysis ◽  
Abelian Group ◽  
Theoretical Approach ◽  
Abelian Groups ◽  
Spectral Synthesis ◽  
Residually Finite ◽  
Finite Dimensional ◽  
Analysis And Synthesis ◽  
Spectral Analysis And Synthesis

In 2004, a counterexample was given for a 1965 result of R. J. Elliott claiming that discrete spectral synthesis holds on every Abelian group. Since then the investigation of discrete spectral analysis and synthesis has gained traction. Characterizations of the Abelian groups that possess spectral analysis and spectral synthesis, respectively, were published in 2005. A characterization of the varieties on discrete Abelian groups enjoying spectral synthesis is still missing. We present a ring theoretical approach to the issue. In particular, we provide a generalization of the Principal Ideal Theorem on discrete Abelian groups.

scholarly journals Auerbach Bases and Minimal Volume Sufficient Enlargements

2011 ◽  
Vol 54 (4) ◽  
pp. 726-738
Author(s):  
M. I. Ostrovskii
Keyword(s):  
Linear Space ◽  
Isometric Embedding ◽  
Normed Linear Space ◽  
Convex Set ◽  
Linear Projection ◽  
Minimal Volume ◽  
Finite Dimensional ◽  
Dimensional Normed Space ◽  
Closed Convex Set

AbstractLet BY denote the unit ball of a normed linear space Y. A symmetric, bounded, closed, convex set A in a finite dimensional normed linear space X is called a sufficient enlargement for X if, for an arbitrary isometric embedding of X into a Banach space Y, there exists a linear projection P: Y → X such that P(BY ) ⊂ A. Each finite dimensional normed space has a minimal-volume sufficient enlargement that is a parallelepiped; some spaces have “exotic” minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having “exotic” minimal-volume sufficient enlargements in terms of Auerbach bases.

scholarly journals Generating infinite monoids of cellular automata

2021 ◽  
pp. 2250215
Author(s):  
Alonso Castillo-Ramirez
Keyword(s):  
Cellular Automata ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Residually Finite ◽  
Residually Finite Group ◽  
Group Of Units ◽  
Finite Dimensional ◽  
Index Condition ◽  
Indicable Group

For a group [Formula: see text] and a set [Formula: see text], let [Formula: see text] be the monoid of all cellular automata over [Formula: see text], and let [Formula: see text] be its group of units. By establishing a characterization of surjunctive groups in terms of the monoid [Formula: see text], we prove that the rank of [Formula: see text] (i.e. the smallest cardinality of a generating set) is equal to the rank of [Formula: see text] plus the relative rank of [Formula: see text] in [Formula: see text], and that the latter is infinite when [Formula: see text] has an infinite decreasing chain of normal subgroups of finite index, condition which is satisfied, for example, for any infinite residually finite group. Moreover, when [Formula: see text] is a vector space over a field [Formula: see text], we study the monoid [Formula: see text] of all linear cellular automata over [Formula: see text] and its group of units [Formula: see text]. We show that if [Formula: see text] is an indicable group and [Formula: see text] is finite-dimensional, then [Formula: see text] is not finitely generated; however, for any finitely generated indicable group [Formula: see text], the group [Formula: see text] is finitely generated if and only if [Formula: see text] is finite.

An Analogue of Longo's Canonical Endomorphism for Bimodule Theory and Its Application to Asymptotic Inclusions

1997 ◽  
Vol 08 (02) ◽  
pp. 249-265 ◽  
Author(s):  
Toshihiko Masuda
Keyword(s):  
Finite System ◽  
Type Ii ◽  
Type Iii ◽  
Finite Dimensional ◽  
Parallel Construction

We give an analogous characterization of Longo's canonical endomorphism in the bimodule theory, and by using this, we construct an inclusion of factors of type II 1 from a finite system of bimodules as a parallel construction to that of Longo–Rehren in a type III setting. When the original factors are approximately finite dimensional, we prove this new inclusion is isomorphic to the asymptotic inclusion in the sense of Ocneanu. This solves a conjecture of Longo–Rehren.

La zone économique exclusive dans la pratique des États

1998 ◽  
Vol 35 ◽  
pp. 3-55 ◽  
Author(s):  
Francis Rigaldies
Keyword(s):  
United Nations ◽  
Scientific Research ◽  
Law Of The Sea ◽  
Basic Principles ◽  
Judicial Decisions ◽  
State Practice ◽  
United Nations Convention ◽  
The United Nations ◽  
The Law

SummaryThe use of the concept of an exclusive Economie zone has increased since the adoption of the United Nations Convention on the Law of the Sea. However, the characterization of this zone varies greatly between States. This article presents an exhaustive survey of the concept of an exclusive Economie zone. The author discusses the types of jurisdiction exercised by States in their uses of an exclusive Economie zone. Disparity exists between the provisions of the Convention and State practice in some specific areas: for example, the provisions on the environment and on scientific research. Despite these exceptions, the author maintains that the basic tenets of the Convention are respected in State practice. State declarations as well as arbitral and judicial decisions show that the Convention and State practice are together evolving to reinforce the basic principles of the concept of an exclusive Economie zone.

scholarly journals A characterization of the law of Lotka in terms of sampling

2005 ◽  
Vol 62 (3) ◽  
pp. 321-328 ◽  
Author(s):  
Leo Egghe
Keyword(s):  
The Law
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