scholarly journals On the class gamma and related classes of functions

2013 ◽  
Vol 93 (107) ◽  
pp. 1-18 ◽  
Author(s):  
Edward Omey
Keyword(s):  
Uniform Convergence ◽  
Auxiliary Function ◽  
Higher Order ◽  
Representation Theorems ◽  
Order Relations ◽  
Measurable Functions ◽  
Local Uniform Convergence

The gamma class ??(g) consists of positive and measurable functions that satisfy f(x + yg(x))/f(x) ? exp(?y). In most cases the auxiliary function g is Beurling varying and self-neglecting, i.e., g(x)/x ? 0 and g??0(g). Taking h = log f, we find that h?E??(g, 1), where E??(g, a) is the class of positive and measurable functions that satisfy (f(x + yg(x))? f(x))/a(x) ? ?y. In this paper we discuss local uniform convergence for functions in the classes ??(g) and E??(g, a). From this, we obtain several representation theorems. We also prove some higher order relations for functions in the class ??(g) and related classes. Two applications are given.

Personality and psychopathology: Higher order relations between the five factor model of personality and the MMPI-2 Restructured Form

2013 ◽  
Vol 47 (5) ◽  
pp. 572-579 ◽  
Author(s):  
Paul T. van der Heijden ◽  
Gina M.P. Rossi ◽  
William M. van der Veld ◽  
Jan J.L. Derksen ◽  
Jos I.M. Egger
Keyword(s):  
Factor Model ◽  
Five Factor Model ◽  
Higher Order ◽  
Order Relations

General coalescence conditions for the exact wave functions. II. Higher-order relations for many-particle systems

2014 ◽  
Vol 140 (21) ◽  
pp. 214103 ◽  
Author(s):  
Yusaku I. Kurokawa ◽  
Hiroyuki Nakashima ◽  
Hiroshi Nakatsuji
Keyword(s):  
Higher Order ◽  
Particle Systems ◽  
Wave Functions ◽  
Order Relations

scholarly journals MAXIMUM PRINCIPLES FOR SOME HIGHER-ORDER SEMILINEAR ELLIPTIC EQUATIONS

2010 ◽  
Vol 53 (2) ◽  
pp. 313-320 ◽  
Author(s):  
A. MARENO
Keyword(s):  
Elliptic Equations ◽  
Auxiliary Function ◽  
Higher Order ◽  
Semilinear Elliptic Equations ◽  
Maximum Principles ◽  
Eighth Order ◽  
Analyse Math ◽  
Semilinear Elliptic

AbstractWe deduce maximum principles for fourth-, sixth- and eighth-order elliptic equations by modifying an auxiliary function introduced by Payne (J. Analyse Math. 30 (1976), 421–433). Integral bounds on various gradients of the solutions of these equations are obtained.

scholarly journals Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming

2018 ◽  
Vol 2 (POPL) ◽  
pp. 1-28 ◽  
Author(s):  
Thomas Ehrhard ◽  
Michele Pagani ◽  
Christine Tasson
Keyword(s):  
Higher Order ◽  
Measurable Functions

scholarly journals LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250065 ◽  
Author(s):  
JÓN I. MAGNÚSSON ◽  
ALEXANDER RASHKOVSKII ◽  
RAGNAR SIGURDSSON ◽  
PASCAL J. THOMAS
Keyword(s):  
Green Function ◽  
Uniform Convergence ◽  
Complete Intersection ◽  
Green Functions ◽  
Ideal Formula ◽  
Vanishing Ideal ◽  
Pluricomplex Green Function ◽  
Samuel Multiplicity ◽  
Hyperconvex Domain ◽  
Local Uniform Convergence

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing ideal [Formula: see text] and pluricomplex Green function [Formula: see text]. Suppose that, as ε tends to 0, [Formula: see text] converges to [Formula: see text] (local uniform convergence), and that (Gε)ε converges to G, locally uniformly away from 0; then [Formula: see text]. If the Hilbert–Samuel multiplicity of [Formula: see text] is strictly larger than its length (codimension, equal to N here), then (Gε)ε cannot converge to [Formula: see text]. Conversely, if [Formula: see text] is a complete intersection ideal, then (Gε)ε converges to [Formula: see text]. We work out the case of three poles.

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