To what extent do the Classical Equations of Motion Determine the Quantization Scheme?

A simple example of one particle moving in a (1+1) space-time is considered. As an example we take the harmonic oscillator. We confirm the statement that the classical Equations of Motion do not determine at all the quantization scheme. To this aim we use two inequivalent Lagrange functions, yielding Euler-Lagrange Equations, having the same set of solutions. We present in detail the calculations of both cases to emphasize the differences occuring between them.Comment: LaTeX 20 page

Parallel Temperatures in Supersonic Beams: Ultra Cooling of Light Atoms seeded in a Heavier Carrier Gas

We have found recently that, in a supersonic expansion of a mixture of two monoatomic gases, the parallel temperatures of the two gases can be very different. This effect is large if the seeded gas is highly diluted and if its atomic mass is considerably smaller than the one of the carrier gas. In the present paper, we present a complete derivation of our theoretical analysis of this effect. Our calculation is a natural extension of the existing theory of supersonic cooling to the case of a gas mixture, in the high dilution limit. Finally, we describe a set of temperature measurements made on a beam of lithium seeded in argon. Our experimental results are in very good agreement with the results of our calculation.Comment: 24 novembre 200

Scalar Representation and Conjugation of Set-Valued Functions

To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued functions is introduced and identified with the conjugates of the scalarizations. Using this conjugate, weak and strong duality results are proven.Comment: arXiv admin note: substantial text overlap with arXiv:1012.435

Effet des taches foliaires causées par le Phaeosphaeria nodorum inoculé à différents stades de développement sur le rendement du blé de printemps

Des études en serre ont été réalisées pour évaluer l'effet du Phaeosphaeria nodorum sur le rendement du blé de printemps (Triticum aestivum, cv. Laval 19). Les plants de blé étaient inoculés aux stades gonflement épiaison, pleine floraison et grain laiteux. L'essai a été réalisé au cours de l'hiver 1993 et répété au cours de l'hiver 1994. L'inoculation du champignon pathogène P. nodorum entraîne généralement une augmentation significative de la surface foliaire infectée et une réduction du rendement comparativement aux témoins non inoculés. La surface foliaire infectée mesurée uniquement sur la feuille étendard est similaire à celle mesurée sur la plante entière. Le stade phénologique a un effet significatif sur toutes les variables observées: surface foliaire infectée, poids des tiges et des feuilles, poids des épis, poids des grains, poids des biomasses végétative et totale et indice de récolte. L'inoculation du pathogène au stade grain laiteux, le plus tardif de l'étude, semble avoir provoqué moins d'effets négatifs sur le rendement du blé comparativement aux trois autres stades étudiés. Selon les résultats de cette étude et les observations réalisées au Québec au cours des 15 dernières années, il est peu probable que les taches foliaires causées par le P. nodorum provoquent des baisses appréciables de rendement du blé de printemps au Québec.Greenhouse studies were carried out to evaluate the effects of foliar leaf spots caused by P. nodorum on spring wheat (Triticum aestivum, cv. Laval 19) yield. Wheat plants were inoculated at booting, heading, flowering and milking growth stages. Experiments were first performed in winter 1993 and repeated in winter 1994. Inoculation of P. nodorum usually resulted in an increase of leaf spots and a decrease of yield compared to uninoculated plants. Foliar flag leaves spots were similar to total plant foliar leaf spots. All variables were significantly affected by inoculation stages : infected foliar area, biomass of straw and leaves, biomass of spikes, biomass of grains, vegetative biomass and harvest index. Inoculation at milking growth stage seemed to resul in the least negative impacts on yield compared to all other stages. From the results of this study and observations performed in Quebec during the 15 past years, leaf spots caused by P. nodorum should not resul in important spring wheat yield losses in Quebec

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

Kinetic Analysis of the Hydrocarbon Total Oxidation Using Individually Measured Adsorption Isotherms

Dedicated to Prof. Dr.-Ing. Andreas Seidel-Morgenstern on the occasion of his 60th birthda

Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in \Er^2

In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed