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.     

Preparation and semiconducting properties of Th3As4

The resistivity, thermoelectric power and Hall constant in the temperature range of 78–830 K were determined for polycrystalline Th₃As₄ samples obtained by annealing thin thorium slabs in arsenic vapour. The samples examined were n-type semiconductors with a carrier concentration ranging from 1.0 × 10¹⁸cm^?3 to 2.8 × 10¹⁸ cm^?3 for which the effective mass was found to be equal to 0.55–0.76m₀. The Hall mobility, about 450cm²V^?1s^?1 at room temperature, obeys a $\text{T}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ law at high temperatures. On the basis of the electrical measurements the forbidden gap of Th₃As₄ was found to be equal to 0.43 eV.     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

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.     

Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

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.     

On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Plasma-driven inflation

The possibility of inflation without any genuine scalar is discussed. It is suggested that drops of primordial plasma may drive inflation. The model, although naive, is consistent with observational data.