h analogue of Newton's binomial formula

In this letter, the $h$--analogue of Newton's binomial formula is obtained in the $h$--deformed quantum plane which does not have any $q$--analogue. For $h=0$, this is just the usual one as it should be. Furthermore, the binomial coefficients reduce to $\frac{n!}{(n-k)!}$ for $h=1$. \\ Some properties of the $h$--binomial coefficients are also given. \\ Finally, I hope that such results will contribute to an introduction of the $h$--analogue of the well--known functions, $h$--special functions and $h$--deformed analysis.Comment: 6 pages, latex Jounal-ref: J. Phys. A: Math. Gen. 31 (1998) L75

Casimir Effect in Hyperbolic Polygons

We derive a trace formula for the spectra of quantum mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two dimensional hyperboloid. Using this trace formula and the point splitting regularization method we calculate the Casimir energy for a scalar fields in such domains. The dependence of the vacuum energy on the number of vertexes is established.Comment: Latex, 1

Common European Sales Law (CESL) and Private International Law: Some Critical Remarks

This article is an updated and revised version of the contribution published by the author in XI Anuario Español de Derecho Internacional Privado, 2011, 25-61, under the title: “La Propuesta de Reglamento relativo a una normativa común de compraventa europea y el Derecho internacional privado”.La Propuesta de Reglamento del Parlamento Europeo y del Consejo relativo a una normativa común de compraventa europea de 11 de octubre de 2011 (PCESL) introduce una reglamentación material para algunas compraventas transfronterizas que no desplaza la aplicación de las normas de conflicto (en particular de las contenidas de los Reglamentos “Roma I” y “Roma II”). Al contrario, el instrumento opcional contenido en la Propuesta de Reglamento (CESL) presupone la aplicación de la ley de un Estado miembro, como lex contractus. Una vez escogida por las partes, la CESL desplaza a las normas internas cobre compraventa de la ley del Estado miembro. Esta opción del legislador comunitario plantea numerosos problemas e interrogantes acerca de las relaciones entre la CESL y las normas de Derecho internacional privado y en torno a su coexistencia con otros convenios internacionales y el propio acervo comunitario. El análisis de estas relaciones es el objeto del presente estudio, que permite concluir con una valoración negativa de la competitividad internacional de este nuevo instrumento comunitario.The Proposal for a Regulation of the European Parliament and of the Council on a Common European Sales Law of 11 October 2011 (PCESL) introduces a substantive regulation for some cross-border sales contracts that does not displace the application of conflict-of-laws rules (especially those included in “Rome I” and “Rome II” Regulations). On the contrary, the optional instrument included in the Proposal (CESL) presupposes the application of the law of a Member State as lex contractus. Once the parties have chosen the CESL, this regime prevails over the internal rules on sales contracts of the law of that Member State. The formula used by the European legislator gives rise to many concerns and questions about the relationships between the CESL and the conflict-of-laws rules and about its cohabitation with other international conventions and the European acquis itself. The analysis of these relationships is the subject of this article, which concludes with a negative assessment on the international competitiveness of the new European instrument

Lower limit on the neutralino mass in the general MSSM

We discuss constraints on SUSY models with non-unified gaugino masses and R_P conservation. We derive a lower bound on the neutralino mass combining the direct limits from LEP, the indirect limits from gmuon, bsgamma, Bsmumu and the relic density constraint from WMAP. The lightest neutralino (mneutralino=6GeV) is found in models with a light pseudoscalar with MA<200GeV and a large value for $tan\beta$. Models with heavy pseudoscalars lead to mneutralino>18(29)GeV for $\tan\beta=50(10)$. We show that even a very conservative bound from the muon anomalous magnetic moment can increase the lower bound on the neutralino mass in models with mu<0 and/or large values of $\tan\beta$. We then examine the potential of the Tevatron and the direct detection experiments to probe the SUSY models with the lightest neutralinos allowed in the context of light pseudoscalars with high $\tan\beta$. We also examine the potential of an e+e- collider of 500GeV to produce SUSY particles in all models with neutralinos lighter than the W. In contrast to the mSUGRA models, observation of at least one sparticle is not always guaranteed.Comment: 37 pages, LateX, 16 figures, paper with higher resolution figures available at http://wwwlapp.in2p3.fr/~boudjema/papers/bound-lsp/bound-lsp.htm