Strict Positivity of a Relativistic Hamiltonian Due to Brown and Ravenhall

1998 ◽  
Vol 30 (3) ◽  
pp. 283-290 ◽  
Author(s):  
C. Tix
Keyword(s):  
Strict Positivity ◽  
Brown And Ravenhall

BORN–OPPENHEIMER APPROXIMATION FOR THE BROWN–RAVENHALL EQUATION

2001 ◽  
Vol 13 (08) ◽  
pp. 921-951
Author(s):  
VANIA SORDONI
Keyword(s):  
Semiclassical Limit ◽  
Energy Levels ◽  
Mass Ratio ◽  
Nuclear Mass ◽  
Oppenheimer Approximation ◽  
Brown And Ravenhall

In this paper we study the pseudo-relativistic Hamiltonian proposed by Brown and Ravenhall in the semiclassical limit when the mass ratio h2 of electronic to nuclear mass tends to zero. We show that the relativistic contribution of the nuclei on WKB-type expansions of the first energy levels are of order o(h2), as h→0.

A central limit theorem for conditionally centred random fields with an application to Markov fields

1998 ◽  
Vol 35 (03) ◽  
pp. 608-621
Author(s):  
Francis Comets ◽  
Martin Janžura
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Markov Random Fields ◽  
Moment Condition ◽  
Markov Random ◽  
Pseudo Likelihood ◽  
Strict Positivity ◽  
Markov Fields

We prove a central limit theorem for conditionally centred random fields, under a moment condition and strict positivity of the empirical variance per observation. We use a random normalization, which fits non-stationary situations. The theorem applies directly to Markov random fields, including the cases of phase transition and lack of stationarity. One consequence is the asymptotic normality of the maximum pseudo-likelihood estimator for Markov fields in complete generality.

scholarly journals A Remark on the Strict Positivity of the Entropy Production

2006 ◽  
Vol 75 (1) ◽  
pp. 17-23 ◽  
Author(s):  
Walter H. Aschbacher ◽  
Herbert Spohn
Keyword(s):  
Entropy Production ◽  
Strict Positivity

scholarly journals Existence of collateral Equilibrium without survival assumption

2011 ◽  
Vol 41 (1) ◽  
pp. 7-24 ◽  
Author(s):  
Jaime Orrillo
Keyword(s):  
Quasi Equilibrium ◽  
Initial Endowment ◽  
Strict Positivity ◽  
Ex Post

This paper shows the existence of a collateral equilibrium without assuming any hypotheses on the strict positivity, be they individual initial endowments, including the ex post initial endowments, or aggregated initial endowments. Because of dropping the strict positivity of social initial endowment we fail to get an equilibrium. Instead, we get a quasi-equilibrium. Then, appealing to the concept of irreducibility (introduced by McKenzie in 1959) which is adapted to the collateral model, we show that the quasi-equilibrium is indeed a legitime equilibrium.

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