Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction

The uniqueness and the global Markov property for the regular Gibbs measure corresponding to the interaction $$U_\Lambda (\varphi ): = \lambda \int\limits_\Lambda {d_2 x\int {d\varrho (\alpha ):e^{\alpha \varphi } :_0 (x)} } $$ [forλ>0,d?(α) a probability measure with support in \(( - 2\sqrt {\pi ,} 2\sqrt \pi )\) ] is proved.     

The thermoelastic behaviour of the orientationally disordered ionic crystals in two dimensions

The anomalous temperature dependence of the elastic constantsc ₁₁ andc ₆₆ and the elastic instability temperatureT _c are obtained in the two-dimensional microscopic model of the alkali cyanides crystals. It has been found, by means of the Michel and Naudts' theory of the translation rotation coupling, that the orientational disorder in the high-temperature phase leads to the critical softening of the shear elastic constantc ₆₆.     

Vibrations of parametrically excited systems

The paper is concerned with a set of linear differential equations with time-dependent parameters given by trigonometrical series. Derived formulas make it possible to examine stability, to find boundaries of the regions of instability and to estimate the steady state response amplitude of forced vibrations.     

Instability of the motion of a beam of periodically varying length

The parametric instability of the motion of a cantilever beam of periodically varying length is investigated. The boundaries of the instability regions are found and plotted.     

One-dimensional model with rotational and liquid-crystalline phase transitions

A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water.     

Discriminant versus rough sets approach to vague data analysis

This paper presents a comparative study of the use of two different methods of data analysis on a common set of data. The first is a method based on rough sets theory and the second is the location model method from the field of discriminant analysis. To investigate the comparative performance of these methods, a set of real medical data has been used. The data considered are of both discrete and continuous character. During the comparison, particular attention is paid to data reduction and to the derivation of decision rules and classification functions from the reduced set.     

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.     

Optical absorption of 1-phenyl-3-methyl-1H-pyrazolo[3,4-b]quinoline derivatives: Molecular dynamics modeling

Paper deals with quantum chemical modeling of the optical absorption spectra of 6-fluoro, 7-trifluoromethyl, 6-cyano, 6-carboethoxy and 6-tert-butyl derivatives of 1-phenyl-3-methyl-1H-pyrazolo[3,4-b]quinoline. The calculations are performed by means of the semiempirical quantum chemical methods (AM1 or PM3) applied to the equilibrium molecular conformation in vacuo (T = 0 K) or molecular dynamic (MD) trajectories as obtained within fragmental or total MD simulations at T = 300 K. The results of these calculations are compared with the measured spectra of optical absorption. The quantum chemical analysis show that the dynamics of the methyl, trifluoromethyl, carboethoxy and tert-butyl groups practically does not influence the absorption spectra whereas the strongest their modifications are found to be related with dynamics of the aromatic group. The semiempirical method AM1 in combination with MD simulations gives for all dyes the best agreement between the calculated and measured spectral positions of absorption bands. In most cases the quantum chemical calculations describe properly the trends of their changes depending on the lateral substituent.