Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove the both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte

Production of light nuclei, hypernuclei and their antiparticles in relativistic nuclear collisions

We present, using the statistical model, an analysis of the production of light nuclei, hypernuclei and their antiparticles in central collisions of heavy nuclei. Based on these studies we provide predictions for the production yields of multiply-strange light nuclei.Comment: 9 pages, 6 figues; v2: final versions accepted for publication (Phys. Lett. B

The thermal model on the verge of the ultimate test: particle production in Pb-Pb collisions at the LHC

We investigate the production of hadrons in nuclear collisions within the framework of the thermal (or statistical hadronization) model. We discuss both the ligh-quark hadrons as well as charmonium and provide predictions for the LHC energy. Even as its exact magnitude is dependent on the charm production cross section, not yet measured in Pb-Pb collisions, we can confidently predict that at the LHC the nuclear modification factor of charmonium as a function of centrality is larger than that observed at RHIC and compare the experimental results to these predictions.Comment: 4 pages, 3 figures; proceedings of QM201

Heavy quark(onium) at LHC: the statistical hadronization case

We discuss the production of charmonium in nuclear collisions within the framework of the statistical hadronization model. We demonstrate that the model reproduces very well the availble data at RHIC. We provide predictions for the LHC energy where, dependently on the charm production cross section, a dramatically different behaviour of charmonium production as a function of centrality might be expected. We discuss also the case in elementary collisions, where clearly the statistical model does not reproduce the measurements.Comment: 8 pages, 5 figures; proceeding of SQM09, Buzios, Brazil, to be published in J. Phys.

Measurement of the space-time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line

Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the simplified context of two-dimensional flat space-time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signals. We present a generalization of this measurement procedure applicable to all three types of space-time intervals between two events in space-times of any number of dimensions. We also present some preliminary observations on an alternative measurement procedure that can be applied taking into account the gravitational field of the measuring apparatus, and briefly discuss quantum limitations of measurability in this context.Comment: 17 page

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Predictions of hadron abundances in pp collisions at the LHC

Based on the statistical hadronization model, we obtain quantitative predictions for the relative abundances of hadron species in pp collisions at the LHC. By using the parameters of the model determined at sqrt s = 200 GeV, and extrapolating the overall normalization from ppbar collisions at the SPS and Tevatron, we find that the expected rapidity densities are almost grand-canonical. Therefore, at LHC the ratios between different species become essentially energy-independent, provided that the hadronization temperature T_H and the strangeness suppression factor gamma_S retain the stable values observed in the presently explored range of pp and ppbar collisions.Comment: 4 pages. Final version published in JP

Production of Strange Clusters and Strange Matter in Nucleus-Nucleus Collisions at the AGS

Production probabilities for strange clusters and strange matter in Au+Au collisions at AGS energy are obtained in the thermal fireball model. The only parameters of the model, the baryon chemical potential and temperature, were determined from a description of the rather complete set of hadron yields from Si+nucleus collisions at the AGS. For the production of light nuclear fragments and strange clusters the results are similar to recent coalescence model calculations. Strange matter production with baryon number larger than 10 is predicted to be much smaller than any current experimental sensitivities.Comment: 9 Pages (no figures

The PreAmplifier ShAper for the ALICE TPC-Detector

In this paper the PreAmplifier ShAper (PASA) for the Time Projection Chamber (TPC) of the ALICE experiment at LHC is presented. The ALICE TPC PASA is an ASIC that integrates 16 identical channels, each consisting of Charge Sensitive Amplifiers (CSA) followed by a Pole-Zero network, self-adaptive bias network, two second-order bridged-T filters, two non-inverting level shifters and a start-up circuit. The circuit is optimized for a detector capacitance of 18-25 pF. For an input capacitance of 25 pF, the PASA features a conversion gain of 12.74 mV/fC, a peaking time of 160 ns, a FWHM of 190 ns, a power consumption of 11.65 mW/ch and an equivalent noise charge of 244e + 17e/pF. The circuit recovers smoothly to the baseline in about 600 ns. An integral non-linearity of 0.19% with an output swing of about 2.1 V is also achieved. The total area of the chip is 18 mm$^2$ and is implemented in AMS's C35B3C1 0.35 micron CMOS technology. Detailed characterization test were performed on about 48000 PASA circuits before mounting them on the ALICE TPC front-end cards. After more than two years of operation of the ALICE TPC with p-p and Pb-Pb collisions, the PASA has demonstrated to fulfill all requirements