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The Separation of Levels in Shcherba's Phonemic Theory
In: Canadian Slavonic papers: an interdisciplinary journal devoted to Central and Eastern Europe, Band 17, Heft 1, S. 126-142
ISSN: 2375-2475
A Generalized metric space for Electromagnetic Theory
In: Bulletin de la Classe des sciences, Band 51, Heft 1, S. 986-995
On étudie l'espace de configuration d'un point en mouvement dans un champ électromagnétique généralisé. Fonction de Lagrange L et Hamiltonienne H. Équations de mouvements. Interprétation géométrique des équations L = 1 et H = 1 .
Studies in medieval Arabic medicine: theory and practice
In: Collected studies series 204
Positive mass distribution in the non linear spinor theory
In: Bulletin de la Classe des sciences, Band 54, Heft 1, S. 1244-1261
Defining generalised functions products by analytic continuation, a two-point function whose mass distribution is positive may be used in the non linear spinor theory. As an application, we show that in an approximation where only strong interactions are considered — so that no imaginary parts have to be neglected, correct values for the π and η meson masses (and eventually, using enough parameters, for the meson nucleon coupling constants) may be obtained, in the first order of the new Tamm-Dancoff method, if the mass distribution is positive ; if not, it seems that the contribution of the negative part must be negligible.
Training Teachers to Use Piaget's Theory in Early Education
In: Enfance, Band 33, Heft 4, S. 319-320
ISSN: 1969-6981
On the formal developments in kinetic theory III : Applications
In: Bulletin de la Classe des sciences, Band 53, Heft 1, S. 1352-1364
In this final part we apply the formal techniques introduced in parts I and II to the Lorentz transformations of the asymptotic master equations. The different forms of the collision operator are also briefly discussed.
On the theory of hydrodynamic fluctuations in nonequilibrium systems
In: Bulletin de la Classe des Sciences de l'Académie Royale de Sciences, des Lettres et des Beaux-Arts de Belgique, Band 68, Heft 1, S. 124-140
Nonequilibrium fluctuating hydrodynamic equations are derived by a generalised Chapman-Enskog development applied to a previously de¬ duced nonlinear Langevin-Boltzmann equation. The long range character of the correlations in the hydrodynamic subspace is established.
One-boson Lee model and statistical-mechanical transformation theory
In: Bulletin de la Classe des sciences, Band 57, Heft 1, S. 325-337
The superoperator transformation theory developed by the Brussels school is applied to a simple quantum-mechanical system : the one-boson Lee model. The existence of a diagonalising transformation for this model permits the solution of dynamical problems such as that of induced emission and the construction of explicit matrix representations for asymptotic and dressing operators of the theory.
Transformation theory for a lattice model in a uniform field
In: Bulletin de la Classe des sciences, Band 61, Heft 1, S. 734-750
Abstract. — The collision operator is calculated for a system representing an infinite one-dimensional lattice in a uniform external field. Using its spectral properties we construct the unitary transformation which diago-nalizes the von Neumann operator. We follow the theory developed by the Brussels group in studying the dissipative properties of quantum systems.
Mathematical economics and game theory: essays in honor of Oskar Morgenstern
In: Lecture notes in economics and mathematical systems 141
Book Review: Action Theory and Social Science: Some Format Models
In: Philosophy of the social sciences: an international journal = Philosophie des sciences sociales, Band 13, Heft 1, S. 94-98
ISSN: 1552-7441
Mathematical foundations of non-equilibrium statistical mechanics. II. Perturbation theory
In: Bulletin de la Classe des sciences, Band 55, Heft 1, S. 1040-1054
Working within the formalism developed by Professor I. Prigogine and his coworkers, this paper examines both the perturbation series obtained by iterating the resolvent equation and the irreducible operators introduced by this means. It is shown that the series can be regarded as asymptotic in a certain sense but that this interpretation is not useful for long time behaviour. Instead of performing the usual resummation of the series it is shown that the irreducible operators can be defined in an entirely rigorous way independent of the series expansion. The advantages of this approach and its connection with the usual procedure are pointed out.
On the theory of unstable Plasmas in the ring approximation, I
In: Bulletin de la Classe des sciences, Band 53, Heft 1, S. 642-662
La forme générale de l'équation cinétique d'un plasma instable dans l'approximation des anneaux est donnée. Le calcul du terme des interactions est basé sur les propriétés des fonctions propres de l'opérateur de Vlassov linéarisé.
L'expression générale de la fonction de correlation de densité est calculée.
On the theory of brownian motion in a quantum bose fluid
In: Bulletin de la Classe des sciences, Band 52, Heft 1, S. 229-247
Résumé. — Nous appliquons la théorie générale des processus irréversibles développée par I. Prigogine et collaborateurs au problème particulier du mouvement d'une particule lourde chargée (masse M) dans un fluide de bosons (masse m ; γ = (m / M)1/2 ⩽ 1) sous l'influence d'un champ électrique extérieur. Nous obtenons des résultats similaires à ceux obtenus récemment par P. Résibois et H. T. Davis dans le cas classique : à l'ordre le plus bas en γ, la particule brownienne obéit à une équation de Fokker-Planck classique mais avec un coefficient de friction quantique.
Comme application de cette méthode, nous évaluons explicitement la constante de friction d'un ion lourd immergé dans un fluide dilué de Bose ; le résultat obtenu est en accord satisfaisant avec les expériences de I. Meyer et F. Reif sur l'He4 liquide.