Estimates of flavoured scalar production in B - decays

Estimates are presented for the branching ratios of several two-particle B-meson decays into flavoured scalar mesons.Comment: 6 pages, Latex, no figures; small improvement

Equivariant Symplectic Geometry of Gauge Fixing in Yang-Mills Theory

The Faddeev-Popov gauge fixing in Yang-Mills theory is interpreted as equivariant localization. It is shown that the Faddeev-Popov procedure amounts to a construction of a symplectic manifold with a Hamiltonian group action. The BRST cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with Hamiltonian group action. The ghost operator is interpreted as a (pre)symplectic form and the gauge condition as the moment map corresponding to the Hamiltonian group action. This results in the identification of the gauge fixing action as a closed equivariant form, the sum of an equivariant symplectic form and a certain closed equivariant 4-form which ensures convergence. An almost complex structure compatible with the symplectic form is constructed. The equivariant localization principle is used to localize the path integrals onto the gauge slice. The Gribov problem is also discussed in the context of equivariant localization principle. As a simple illustration of the methods developed in the paper, the partition function of N=2 supersymmetric quantum mechanics is calculated by equivariant localizationComment: 46 pages, added remarks, typos and references correcte

Biological research of Grabia River - fifty years of activity

Grabia, a small still close to natural conditions lowland river, has been an object of special interest for Łódź hydrobiologists for more than 50 years. Over 100 scientific papers and over 100 master theses were produced in the Faculty of Biology and Environmental Protection University of Łódź. The initiator was Prof.L.K. Pawłowski who spent many years conducting research into the river. The ground and the first research objective was to recognize the fauna diversity. The checklist encompass almost 1000 invertebrate and 24 fish species. Taxonomy, biology and ecology of various taxa have made for many decades an essential trend of scientific activity. Special attention was dedicated to rotifers, leeches, branchiobdellids, snails and bivalves, gammarids and copepods as well as aquatic insects, fish and also diatoms. Some aspects of zoobenthos and Zooplankton communities ecology was the subject of 13 Ph.D.theses. The river with its rich animal and plant communities was also the subject of dynamics of river ecosystem research. The study on the structure of invertebrate assemblages on the background of habitat diversity has been recently conducted. The model may be treealed as a reference to the restoration of Europaean rivers and their valleys.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę

Charmless B decays into three charged track final states

Using a data sample of 10.5 1/fb collected by the Belle detector, three-body charmless decays B+ --> K+h+h- have been studied. The following branching fractions have been obtained: Br(B+ --> K+pi-pi+) = (64.8+-10.0+-7.0) x 10**-6 and Br(B+ --> K+K-K+) = (36.5+-6.1+-5.5) x 10**-6. The upper limits for other combinations of charged kaons and pions have been placed. Analysis of the intermediate two-body states gives evidence for production of scalar resonances in charmless B decays.Comment: 4 pages, Proceedings of the 4th International Conference on B Physics & CP Violation, Ise-Shima, Japan, February 19 - 23, 200

Random matrices: Universal properties of eigenvectors

The four moment theorem asserts, roughly speaking, that the joint distribution of a small number of eigenvalues of a Wigner random matrix (when measured at the scale of the mean eigenvalue spacing) depends only on the first four moments of the entries of the matrix. In this paper, we extend the four moment theorem to also cover the coefficients of the \emph{eigenvectors} of a Wigner random matrix. A similar result (with different hypotheses) has been proved recently by Knowles and Yin, using a different method. As an application, we prove some central limit theorems for these eigenvectors. In another application, we prove a universality result for the resolvent, up to the real axis. This implies universality of the inverse matrix.Comment: 25 pages, no figures, to appear, Random Matrices: Theory and applications. This is the final version, incorporating the referee's suggestion

The Lattice structure of Chip Firing Games and Related Models

In this paper, we study a famous discrete dynamical system, the Chip Firing Game, used as a model in physics, economics and computer science. We use order theory and show that the set of reachable states (i.e. the configuration space) of such a system started in any configuration is a lattice, which implies strong structural properties. The lattice structure of the configuration space of a dynamical system is of great interest since it implies convergence (and more) if the configuration space is finite. If it is infinite, this property implies another kind of convergence: all the configurations reachable from two given configurations are reachable from their infimum. In other words, there is a unique first configuration which is reachable from two given configurations. Moreover, the Chip Firing Game is a very general model, and we show how known models can be encoded as Chip Firing Games, and how some results about them can be deduced from this paper. Finally, we define a new model, which is a generalization of the Chip Firing Game, and about which many interesting questions arise.Comment: See http://www.liafa.jussieu.fr/~latap

Algorithmic Complexity of Power Law Networks

It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold. First, we define a deterministic condition for checking whether a graph has a power law degree distribution and experimentally validate it on real-world networks. This definition allows us to derive interesting properties of power law networks. We observe that for exponents of the degree distribution in the range $[1,2]$ such networks exhibit double power law phenomenon that was observed for several real-world networks. Our observation indicates that this phenomenon could be explained by just pure graph theoretical properties. The second aim of our work is to give a novel theoretical explanation why many algorithms run faster on real-world data than what is predicted by algorithmic worst-case analysis. We show how to exploit the power law degree distribution to design faster algorithms for a number of classical P-time problems including transitive closure, maximum matching, determinant, PageRank and matrix inverse. Moreover, we deal with the problems of counting triangles and finding maximum clique. Previously, it has been only shown that these problems can be solved very efficiently on power law graphs when these graphs are random, e.g., drawn at random from some distribution. However, it is unclear how to relate such a theoretical analysis to real-world graphs, which are fixed. Instead of that, we show that the randomness assumption can be replaced with a simple condition on the degrees of adjacent vertices, which can be used to obtain similar results. As a result, in some range of power law exponents, we are able to solve the maximum clique problem in polynomial time, although in general power law networks the problem is NP-complete