A Characterization Theorem for Weak Records

1994 ◽  
Vol 38 (4) ◽  
pp. 762-764 ◽  
Author(s):  
A. V. Stepanov
Keyword(s):  
Characterization Theorem ◽  
Weak Records

scholarly journals Probability logic: A model-theoretic perspective

2020 ◽  
Author(s):  
M Pourmahdian ◽  
R Zoghifard
Keyword(s):  
Characterization Theorem ◽  
Expressive Power ◽  
Probability Logic ◽  
Theoretic Analysis ◽  
Compactness Property ◽  
Probability Models ◽  
Finitely Additive Probability ◽  
Additive Probability ◽  
Basic Probability ◽  
Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

Area properties associated with a convex plane curve

2017 ◽  
Vol 24 (3) ◽  
pp. 429-437
Author(s):  
Dong-Soo Kim ◽  
Young Ho Kim ◽  
Hyeong-Kwan Ju ◽  
Kyu-Chul Shim
Keyword(s):  
Characteristic Property ◽  
Plane Curve ◽  
Characterization Theorem ◽  
Convex Curve ◽  
Convex Plane ◽  
Convex Curves ◽  
Necessary And Sufficient ◽  
Locally Convex

AbstractArchimedes knew that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area of the region bounded by the parabola X and chord AB is four thirds of the area of the triangle {\bigtriangleup ABP}. Recently, the first two authors have proved that this fact is the characteristic property of parabolas.In this paper, we study strictly locally convex curves in the plane {{\mathbb{R}}^{2}}. As a result, generalizing the above mentioned characterization theorem for parabolas, we present two conditions, which are necessary and sufficient, for a strictly locally convex curve in the plane to be an open arc of a parabola.

scholarly journals Categorical Abstract Algebraic Logic: Equivalential π-Institutions

2008 ◽  
Vol 6 ◽  
Author(s):  
George Voutsadakis
Keyword(s):  
Matrix Theory ◽  
Algebraic Logic ◽  
Characterization Theorem ◽  
Abstract Algebraic Logic ◽  
Transfer Theorem ◽  
Deductive Systems

The theory of equivalential deductive systems, as introduced by Prucnal and Wrónski and further developed by Czelakowski, is abstracted to cover the case of logical systems formalized as π-institutions. More precisely, the notion of an N-equivalence system for a given π-institution is introduced. A characterization theorem for N-equivalence systems, previously proven for N-parameterized equivalence systems, is revisited and a “transfer theorem” for N-equivalence systems is proven. For a π-institution I having an N-equivalence system, the maximum such system is singled out and, then, an analog of Herrmann’s Test, characterizing those N-protoalgebraic π-institutions having an N-equivalence system, is formulated. Finally, some of the rudiments of matrix theory are revisited in the context of π-institutions, as they relate to the existence of N-equivalence systems.

scholarly journals A characterization theorem for matrix variances

2014 ◽  
Vol 80 (34) ◽  
pp. 681-687
Author(s):  
Dénes Petz ◽  
Dániel Virosztek
Keyword(s):  
Characterization Theorem
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