LocalH-theorem for the revised Enskog equation

A simple derivation of the local H-theorem for the revised Enskog equation is presented.On leave of absence from the Institute of Theoretical Physics, University of Warsaw, 00-681 Warsaw, Poland.     

Average trajectories and fluctuations from noisy,nonlinear maps

The average trajectories and fluctuations around them resulting from an ensemble of noisy, nonlinear maps are analyzed. The bifurcation diagram for the average value obtained from the computer simulation of noisy maps ensemble is discussed first. Then a deterministic average equation of motion describing in an approximate way the time evolution of the average value and of the variance is analyzed numerically. This equation predicts the existence of the bifurcation gap and of the exceptional attractors for special initial points. The scaling properties of the average value and of the variance are obtained with the help of this equation.On leave from Institute for Theoretical Physics, Warsaw University, 00-681 Warsaw, Hoza 69, Poland.     

Space echo

Residual effects of vanishing fields are shown to provide a formal analogue of the spin echo effect for the nonrelativistic spinless particle. The possible significance to the problem of nonlinear distributions is discussed.Supported by COSNET/SEP.On leave of absence from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

Null solutions of the Yang-Mills equations

We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays.Alexander von Humboldt Fellow. Address after 31 May 1986: Institute of Theoretical Physics, University of Warsaw, Hoa 69, 00-681 Warsaw, Poland.     

On a global existence theorem for the Enskog equation

In this note we prove global existence of mild solutions of the Enskog equation with small initial data.On leave from Department of Mathematics and Mechanics, University of Warsaw. Warsaw, Poland.     

A new proof of the propagation theorem forN-body quantum systems

A new proof of I. Sigal's and A. Soffer's propagation theorem is given. This theorem describes a large class of operators which are Kato-smooth with respect to anN-body Schrödinger operator.On leave from Division of Mathematical Methods in Physics, Warsaw University, Hoza 74, PL-00682 Warsaw, Poland     

The use of the Hurst exponent to predict changes in trends on the Warsaw Stock Exchange

The local properties of the time series of the evolution of share prices of 126 significant companies traded on the Warsaw Stock Exchange during the period between 1991-2008 have been investigated. The analysis was applied to daily financial returns. I have used the local DFA to obtain the Hurst exponent (diffusion coefficient) while searching for negative correlations by which changes of long-term trends would be effected. A certain evidence, proving that after the signature of anti-correlation-the drop in the Hurst exponent-the change in the trend and in the return rate of an investment is probable, was pointed out. Hence after further investigation this method may be useful as a part of an investment strategy. As the Warsaw Stock Exchange is relatively smaller and younger than other significant world Stock Exchanges-and as the developing market is less efficient-the generalization for others markets needs further investigation.     

Integrability of two interactingN-dimensional rigid bodies

A new class of integrable Euler equations on the Lie algebra so(2n) describing twon-dimensional interacting rigid bodies is found. A Lax representation of equations of motion which depends on a spectral parameter is given and complete integrability is proved. The double hamiltonian structure and the Lax representation of the general flow is discussed.On leave of absence from the Institute for Theoretical Physics of Warsaw University, ul. Hoza 69, PL-00-681 Warsaw, Poland     

Null strings and complex Einstein-Maxwell fields with cosmological constant

Previous results of two of us (J. P. and I. R.) concerning left-degenerate Einstein-flat complex space-times, and preliminary results concerning the electromagnetic field [1], are here generalized and worked out in some detail for the system of Einstein-Maxwell equations with a cosmological constant. On the assumption that there exists a congruence of totally null surfaces, the system is reduced to a pair of equations for two unknown functions.On leave of absence from the University of Warsaw, Warsaw, Poland.     

Electric charge in the Kruskal space-time and the Jeans conjecture

In 1928 Jeans conjectured that there might be regions in space such as for example centers of galaxies through which matter could be flowing into our universe from other universes. We investigate if this conjecture extended to charged matter could be realized within the framework of general relativity with the help of black and white holes. By studying a test electromagnetic field produced by a point charge in the maximally extended Schwarzschild space-time we show that an observer at infinity always can get an information on the value of the charge even if it is hidden inside a white hole. Therefore we conclude that the Jeans conjecture cannot be realized for charged matter by a white hole. This result can be generalized to include a test gravitational field produced by a test mass hidden inside a white hole, hole.On leave from Institute of Theoretical Physics, University of Warsaw, Warsaw, Poland.     

A remark on compact matrix quantum groups

A simpler set of axioms of the theory of compact matrix quantum groups (pseudogroups) is found.Supported by Japan Society for Promoting Science. On leave from the Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoa 74, 00-682 Warsaw, Poland.     

Maximal indecomposable past sets and event horizons

The existence of maximal indecomposable past sets MIPs is demonstrated using the Kuratowski-Zorn lemma. A criterion for the existence of an absolute event horizon in space-time is given in terms of MIPs and a relation to black hole event horizon is shown.On leave of absence from the Institute of Theoretical Physics, Warsaw, Poland.     

Metric and Ricci tensors for a certain class of space-times ofD type

The class of space-times has been determined at the connection level, assuming the existence of some symmetrical relations between the Ricci rotation coefficients. It has been assumed, for instance, that at least two shear-free congruences of null geodesics exist. We have shown that onlyD type or conformally flat space-times can belong to this class. The theorem has been proved that a system of coordinates exists in which the metric tensor can depend on two coordinates, only. The metric tensor has been determined with an accuracy to two functions, each of which is a function of only one coordinate. Linear, second-order differential expressions have been found for these two functions. They determine the Ricci tensor. Several solutions of the Einstein-Maxwell equations with a cosmological constant are given.On leave from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.     

A kinetic model of dipole particles in curved space-time

A simple kinetic model of dipole particles moving in gravitational and electromagnetic fields is considered. Conservation of phase volume is proved. For stationary fields approximate expressions for the macroscopic energy-momentum and spin tensor of the system are obtained.This work was partly done during the author's stay at the C.R.M.A., Université de Montréal, under an exchange agreement with the University of Warsaw.     

On the measurement of polarization parameters of optical radar signals

The polarization parameters of optical radar signals, which are characterized by parameters resulting from entropy of partially polarized light waves, are discussed. It is shown that the properties of the signal can be represented by a factor which is a ratio of entropies, and by two parameters of the polarization ellipse. The proposed method using quasilinearly polarized signals of He-Ne laser at 632.8 nm was applied to the investigations of a number of typical materials.On leave from the Technical University of Warsaw, Warsaw Poland under Exchange Agreement between Poland and Austria. The address of the author: ul. Wieluska, 18 m.24 01 240, Warszawa. Poland.     

Approach to field-induced stationary state in a gas of hard rods

The Boltzmann equation describing one-dimensional motion of a charged hard rod in a neutral hard rod gas at temperatureT = 0 is solved. Under the action of a constant and uniform field the charged particle attains a stationary state. In the long time limit the velocity autocorrelation function decays via damped oscillations. In the reference system moving with the mean particle velocity the decay of fluctuations in the position space is governed (in the hydrodynamic limit) by the diffusion equation. Both the stationary current and the diffusion coefficient are proportional to the square root of the field. It is conjectured that this result also holds forT > 0 in a strong field limit.On leave from the Institute of Theoretical Physics, University of Warsaw, Hoza 69, 00-081 Warsaw, Poland.     

On the invariant mass conjecture in general relativity

An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, PolandSupported in part by the Polish Ministry of Science Research Project CPBP 01.2 and by the NSF Grant PHY8503072 to Yale University     

Generalized Euclidean stars with equation of state

This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013.     

A few properties of a certain class of degenerate space-times

The properties are studied of a class of space-times determined by assuming the shape of the metric formds ² including disposable coordinate functions. It has been found that this class includes degenerate space-times with geodetic, null, shear-free congruences with nonvanishing expansion. The theorem has been proved that this class of solutions of the Einstein equations can easily be expanded to solutions of Einstein-Maxwell equations with a fairly general electromagnetic field. For a selected subclass relations are given between the functions determining the metric form, and two new explicit solutions with arbitrary functions of the Einstein-Maxwell equations with a cosmological constant are found.On leave from the Institute of Theoretical Physics, Warsaw University, Warsaw, Poland.