A characterization of dimension-free hyperbolic geometry and the functional equation of 2-point invariants

2010 ◽  
Vol 80 (1-2) ◽  
pp. 5-11
Author(s):  
Walter Benz
Keyword(s):  
Functional Equation ◽  
Hyperbolic Geometry

scholarly journals Some results concerning the Cauchy functional equation in certain Banach algebras

1985 ◽  
Vol 31 (1) ◽  
pp. 137-144 ◽  
Author(s):  
J. Vukman
Keyword(s):  
Functional Equation ◽  
Hilbert Space ◽  
Identity Element ◽  
Banach Algebras ◽  
Cauchy Functional Equation

In this paper some results concerning the Cauchy functional equation, that is the functional equation f(x+y) = f(x) + f(y) in complex hermitian Banach *-algebras with an identity element are presented. As an application a generalization of Kurepa's extension of the Jordan-Neumann characterization of pre-Hilbert space is obtained.

Lifetime regression models based on a functional equation of physical nature

1987 ◽  
Vol 24 (01) ◽  
pp. 160-169 ◽  
Author(s):  
Enrique Castillo ◽  
Janos Galambos
Keyword(s):  
Functional Equation ◽  
Conditional Distribution ◽  
Regression Models ◽  
Practical Problem ◽  
Ad Hoc ◽  
Physical Nature ◽  
Value Theory ◽  
Complete Characterization ◽  
Lifetime Data

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.

scholarly journals On the general solution of a functional equation connected to sum form information measures on open domain—III

1986 ◽  
Vol 9 (3) ◽  
pp. 545-550 ◽  
Author(s):  
Pl. Kannappan ◽  
P. K. Sahoo
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Open Domain ◽  
Information Measures ◽  
Domain Iii ◽  
Weighted Entropy ◽  
Form Information

In this series, this paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degreeβ. Here, we find the general solution of the functional equation (2) on an open domain, without using0-probability and1-probability.

scholarly journals A functional equation related to generalized entropies and the modular group

2020 ◽  
Vol 94 (6) ◽  
pp. 1201-1212
Author(s):  
Daniel Bennequin ◽  
Juan Pablo Vigneaux
Keyword(s):  
Functional Equation ◽  
Modular Group ◽  
General Relation ◽  
Algebraic Characterization ◽  
Conditional Probabilities ◽  
Related System ◽  
System Of Functional Equations ◽  
Symmetry Of The Solution ◽  
Generalized Entropies

Abstract We solve a functional equation connected to the algebraic characterization of generalized information functions. To prove the symmetry of the solution, we study a related system of functional equations, which involves two homographies. These transformations generate the modular group, and this fact plays a crucial role in solving the system. The method suggests a more general relation between conditional probabilities and arithmetic.

A framework toward understanding the characterization of holomorphic dynamics

2014 ◽  
Author(s):  
Yunping Jiang
Keyword(s):  
Hyperbolic Geometry ◽  
Spherical Geometry ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Holomorphic Maps ◽  
Critical Set ◽  
Geometrically Finite ◽  
Infinite Degree ◽  
New Framework

This chapter reviews the characterization of geometrically finite rational maps and then outlines a framework for characterizing holomorphic maps. Whereas Thurston's methods are based on estimates of hyperbolic distortion in hyperbolic geometry, the framework suggested here is based on controlling conformal distortion in spherical geometry. The new framework enables one to relax two of Thurston's assumptions: first, that the iterated map has finite degree and, second, that its post-critical set is finite. Thus, it makes possible to characterize certain rational maps for which the post-critical set is not finite as well as certain classes of entire and meromorphic coverings for which the iterated map has infinite degree.

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