On the volume of the convex hull of two convex bodies

In this note we examine the volume of the convex hull of two congruent copies of a convex body in Euclidean $n$-space, under some subsets of the isometry group of the space. We prove inequalities for this volume if the two bodies are translates, or reflected copies of each other about a common point or a hyperplane containing it. In particular, we give a proof of a related conjecture of Rogers and Shephard.Comment: 9 pages, 3 figure

Development of the Information Society in Czech Republic, Poland and Slovakia

The article is presenting facts about the politics carried on the EU concerning development of the information society in Czech Republic, Poland and Slovakia - countries that in 2004 became members of the EU. Enlargement of the EU structures allowed for more dynamic development of these countries in the information society context. The situation of each country was presented by indicators describing the household and the community situation in information society. Indicators was gained from Eurostat system. The universality of these indicators lets to the assessment of the level and dynamics of development in relation to the EU average. Comparison of Poland and its southern neighbors allows also to observe changes that occur and may allow better progress in this field.Artykul prezentuje dane na temat prowadzonej w UE polityki w zakresie rozwoju spoleczeństwa informacyjnego w Czechach, Polsce i Slowacji, które staly się czlonkami UE w 2004 roku. Rozszerzenie struktur unijnych pozwolilo na zdynamizowanie rozwoju tych krajów w zakresie spoleczeństwa informacyjnego. Sytuację poszczególnych krajów zaprezentowano przy pomocy wskażników opisujących gospodarstwa domowe oraz spoleczność pochodzące z Eurostatu. Powszechność tych wskażników pozwala na ocenę dynamiki rozwoju oraz poziomu tego rozwoju w odniesieniu do wartości średniej w UE. Porównanie Polski oraz jej poludniowych sąsiadów pozwolić ma również na dostrzeżenie przemian, które zachodzą i mogą pozwolić na lepszy postęp w tej dziedzinie

Quantum corrections of Abelian Duality Transformations

A modification of the Abelian Duality transformations is proposed guaranteeing that a (not necessarily conformally invariant) $\sigma$-model be quantum equivalent (at least up to two loops in perturbation theory) to its dual. This requires a somewhat non standard perturbative treatment of the {\sl dual} $\sigma$-model. Explicit formulae of the modified duality transformation are presented for a special class of block diagonal purely metric $\sigma$-models.Comment: Latex 11 pages; remarks on a free model and references adde

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi Witten string in the light cone gauge are reviewed.Comment: 21 pages, Plain Tex, to appear in the E.P. Wigner memorial volume of Acta Physica Hungaric

Factor analysis of the long gamma-ray bursts

We study statistically 197 long gamma-ray bursts, detected and measured in detail by the BATSE instrument of the Compton Gamma-Ray Observatory. In the sample 10 variables, describing for any burst the time behavior of the spectra and other quantities, are collected. The factor analysis method is used to find the latent random variables describing the temporal and spectral properties of GRBs. The application of this particular method to this sample indicates that five factors and the \REpk spectral variable (the ratio of peak energies in the spectrum) describe the sample satisfactorily. Both the pseudo-redshifts inferred from the variability, and the Amati-relation in its original form, are disfavored.Comment: 5 pages, acceptod to A&

Exotic plasma as classical Hall Liquid

A non-relativistic plasma model endowed with an ``exotic'' structure associated with the two-parameter central extension of the planar Galilei group is constructed. Introducing a Chern-Simons statistical gauge field provides us with a self-consistent system; when the magnetic field takes a critical value determined by the extension parameters, the fluid becomes incompressible and moves collectively, according to the Hall law.Comment: 11 pages, LaTex, no figures. Revised version: Some details better explained. To appear in Int. Journ. Mod. Phys.