Projection operator formalism and entropy

The entropy definition is deduced by means of (re)deriving the generalized non-linear Langevin equation using Zwanzig projector operator formalism. It is shown to be necessarily related to an invariant measure which, in classical mechanics, can always be taken to be the Liouville measure. It is not true that one is free to choose a ``relevant'' probability density independently as is done in other flavors of projection operator formalism. This observation induces an entropy expression which is valid also outside the thermodynamic limit and in far from equilibrium situations. The Zwanzig projection operator formalism therefore gives a deductive derivation of non-equilibrium, and equilibrium, thermodynamics. The entropy definition found is closely related to the (generalized) microcanonical Boltzmann-Planck definition but with some subtle differences. No ``shell thickness'' arguments are needed, nor desirable, for a rigorous definition. The entropy expression depends on the choice of macroscopic variables and does not exactly transform as a scalar quantity. The relation with expressions used in the GENERIC formalism are discussed

Scaling in the Bombay Stock Exchange Index

In this paper we study BSE Index financial time series for fractal and multifractal behaviour. We show that Bombay stock Exchange (BSE)Index time series is mono-fractal and can be represented by a fractional Brownian motion.Comment: 11 pages,3 figure

Dynamical aspects of inextensible chains

In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.Comment: 15 pages, LaTeX 2e + various packages, 3 figures. The title has been changed and three references have been added. A large part of the manuscript has been rewritten to improve readability. Chapter 4 has been added. It contains the construction of the generating functional without the shish-kebab approximation and a new derivation of the continuous limit of the freely jointed bar chai

Neutron knockout of 12Be populating neutron-unbound states in 11Be

Neutron-unbound resonant states of 11Be were populated in neutron knock-out reactions from 12Be and identified by 10Be-n coincidence measurements. A resonance in the decay-energy spectrum at 80(2) keV was attributed to a highly excited unbound state in 11Be at 3.949(2) MeV decaying to the 2+ excited state in 10Be. A knockout cross section of 15(3) mb was inferred for this 3.949(2) MeV state suggesting a spectroscopic factor near unity for this 0p3/2- level, consistent with the detailed shell model calculations.Comment: 5 pages, 2 figures \pacs{29.38.Db, 29.30.Hs, 24.50.+g, 21.10.Pc, 21.10.Hw, 27.20.+n} \keywords{neutron decay spectroscopy, neutron-unbound states in 11Be

Non-locality and Medium Effects in the Exclusive Photoproduction of Eta Mesons on Nuclei

A relativistic model for the quasifree exclusive photoproduction of $\eta$ mesons on nuclei is extended to include both non-local and medium effects. The reaction is assumed to proceed via the dominant contribution of the S$_{11}$(1535) resonance. The complicated integrals resulting from the non-locality are simplified using a modified version of a method given by Cooper and Maxwell. The non-locality effects are found to affect the magnitude of the cross section. Some possibilities reflecting the effects of the medium on the propagation and properties of the intermediate S$_{11}$ resonance are studied. The effects of allowing the S$_{11}$ to interact with the medium via mean field scalar and vector potentials are considered. Both broadening of width and reduction in mass of the resonance lead to a suppression of the calculated cross sections.Comment: 19 pages, 7 figure

Associations between mortality and air pollution in central Europe.

Increased mortality has been observed in association with elevated concentrations of air pollutants in European cities and in the United States. We reassessed the effects of particulate matter in Central Europe. Mortality and air pollution data were obtained for a highly polluted region of the Czech Republic and a rural region in Germany. Poisson regression analyses were conducted considering trend, season, meteorology, and influenza epidemics as confounders in both a parametric and a nonparametric approach. The Czech Republic had a 3.8% increase in mortality [95% confidence interval (CI), 0.8-6.9%] in association with 100 microg/m(3) total suspended particles (TSP) (lagged 2 days) for the time period 1982-1994. During the last 2 years of study, 68% of the TSP consisted of particulate matter [less than/equal to] 10 microm in aerodynamic diameter (PM(10)). An increase of 100 microg/m(3) TSP (lagged 1 day) was associated with a 9.5% increase in mortality (CI, 1.2-18.5%) and 100 microg/m(3) PM(10 )(lagged 1 day) showed a 9.8% increase in mortality (CI, 0.7-19.7%). We found no evidence for an association between mortality and particulate matter in the rural area in Germany at the Czech border. Data from the coal basin in the Czech Republic suggested an increase in mortality associated with the concentration of particulate matter in a highly polluted setting in Central Europe that is consistent with the associations observed in other western European cities and in the United States