๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the unimodality of power transformations of positive stable densities

โœ Scribed by Thomas Simon

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
141 KB
Volume
285
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Abstract

Let Z~ฮฑ~ be a positive ฮฑโ€stable random variable and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$r\in {\mathbb {R}}.$\end{document} We show the existence of an unbounded open domain D in [1/2, 1] ร— ( โˆ’ โˆž, โˆ’1/2] with a cusp at (1/2, โˆ’1/2), characterized by the complete monotonicity of the function \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$F_{\alpha ,r}(\lambda ) = (\alpha \lambda ^\alpha -r)e^{-\lambda ^\alpha }!! ,$\end{document} such that \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$Z_\alpha ^r$\end{document} is unimodal if and only if (ฮฑ, r)โˆ‰D.

๐Ÿ“œ SIMILAR VOLUMES

On the Approximation of Positive Functio
On the Approximation of Positive Functions by Power
โœ U. Schmid ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 124 KB

The problem to be studied goes back to a question of Erdรถs and Kรถvari, concerning functions \(M(x), x \in R_{0}{ }^{+}\), which are positive and logarithmically convex in \(\ln x\). The question to find necessary and sufficient conditions for the existence of a power series \[ N(x)=\sum c_{n} x^{n}

On the Approximation of Positive Functio
On the Approximation of Positive Functions by Power Series, II
โœ Ulrich Schmid ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 242 KB

We consider positive functions h=h(x) defined for x # R + 0 . Conditions for the existence of a power series N(x)= c n x n , c n 0, with the property x 0, for some constants d 1 , d 2 # R + , are investigated in [J. Clunie and T. Ko vari,

Influence of the power density on the ki
Influence of the power density on the kinetics of photopolymerization and properties of dental composites
โœ A. D. Neves; J. A. C. Discacciati; R. L. Orรฉfice; M. I. Yoshida ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 249 KB ๐Ÿ‘ 1 views

## Abstract Polymer shrinkage during photopolymerization of dimethacrylate monomers, used for many years to produce materials for dental restoration, can induce either the formation of toothโ€restoration gaps or the production of residual stress depending on the quality of adhesion between tooth and