A characterization theorem for the evolution semigroup generated by the sum of two unbounded operators

2004 ◽  
Vol 27 (6) ◽  
pp. 669-685 ◽  
Author(s):  
Giovanni Frosali ◽  
Cornelis V. M. van der Mee ◽  
Francesco Mugelli
Keyword(s):  
Characterization Theorem ◽  
Unbounded Operators ◽  
Evolution Semigroup

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.

Regularization of Some One-Dimensional Inverse Problems for Identification of Nonlinear Surface Phenomena

1995 ◽  
Author(s):  
C. W. Groetsch ◽  
Martin Hanke
Keyword(s):  
Inverse Problems ◽  
Model Identification ◽  
Surface Phenomena ◽  
Unbounded Operators ◽  
General Technique ◽  
Regularization Technique ◽  
One Dimensional ◽  
Data Errors ◽  
Ill Posed ◽  
Nonlinear Surface

Abstract A simple numerical method for some one-dimensional inverse problems of model identification type arising in nonlinear heat transfer is discussed. The essence of the method is to express the nonlinearity in terms of an integro-differential operator, the values of which are approximated by a linear spline technique. The inverse problems are mildly ill-posed and therefore call for regularization when data errors are present. A general technique for stabilization of unbounded operators may be applied to regularize the process and a specific regularization technique is illustrated on a model problem.

Functional Calculus for Unbounded Operators

1990 ◽  
pp. 323-340
Author(s):  
Israel Gohberg ◽  
Seymour Goldberg ◽  
Marinus A. Kaashoek
Keyword(s):  
Functional Calculus ◽  
Unbounded Operators

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.

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