Marked Schottky Groups and Representations of Surface Groups

We give a complete condition for any n elements of PSL(2, R)to generate a Fuchsian group which is a Schottky group on thatset of generators, and apply it to a question of Bowditch onrepresentations of surface groups into PSL(2, R). 2000 MathematicalSubject Classification: 20H10, 32G15.     

On Korovkin Type Theorem in the Space of Locally Integrable Functions

It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space L _p,w (loc) does not hold in all this space and is satisfied only on some subspace.     

Nonlinear Dynamics of a Two-Mode Wave Packet with Strong Linear Intermode

We investigate the dynamics of the wave packet formed by two codirected strongly interacting waves propagating in a medium with cubic nonlinearity. We obtain a soliton solution of the nonlinear Schrödinger equation in the degenerate case where the wave packet is described by a single partial momentum. In the nondegenerate case, we use the variational method to find the equation for the pulse duration, which turns out to be analogous to the equation for the coordinate in the Kepler problem. Solving it, we find the dependences of the pulse duration on the propagation distance in the cases of finite and infinite propagation regimes.     

A Theorem on Multiplicators in Nonhomogeneous Hölder Spaces and Some of Its Applications

In Sec. 2, sufficient conditions of the boundedness of convolution operators with kernel m in a nonhomogeneous Hölder space are given in terms of the Fourier-image of m. After that, the results of Sec. 2 are used to prove the solvability in a Hölder space of the Cauchy problem for linear systems of the hydrodynamic type. Bibliography: 6 titles.     

On the Twisted Cubic of PG(3, q)

In this paper we classify the lines of PG(3, q) whose points belong to imaginary chords of the twisted cubic of PG(3, q). Relying on this classification result, we obtain a complete classification of semiclassical spreads of the generalized hexagon H(q).     

Transient and steady state creep of Al-4.5 wt.% Mg during phase transformation

Transient and steady state creep of Al-4.5 wt. % Mg alloy was studied under various constant stresses ranging from 91 MPa to 117 MPa in the temperature range from 473 K to 553 K. The results of creep characteristics have shown two main deformation temperature regions (below 493 K and above 513 K as well as a transient region between these temperatures). Peak values of transient creep parametersB andn were obtained at 493 K. The transient creep parameterB was related to the steady state creep rate _st through the exponent which was found to range from 0.85 to 0.5. The stress exponentm of the steady state creep has been found to be minimum at the steady state strain peaks, which is characteristic of dislocation climb along the grain boundaries. Microstructural analysis confirmed that the above mentioned mechanism took place in the dissolution region of-phase.     

On the Pesin set of expansive geodesic flows in manifolds with no conjugate points

In this paper, we show that the Pesin set of an expansive geodesic flow in compact manifold with no conjugate points and bounded asymptote coincides a.e with an open and dense set of the unit tangent bundle. We also show that the set of hyperbolic periodic orbits is dense in the unit tangent bundle.     

Linear and nonlinear optical properties of CdSexS1−x microcrystallites

Microcrystals of CdSe_xS_1−x (x≈0.6) with nanometer dimensions have been investigated experimentally by a range of optical techniques. This system of ‘quantum dot’ consists of nanometer sized semiconductor particles embedded within an insulating glass matrix. The existence of microscopic CdSeS crystals within the glass matrix is demonstrated by the observation of Raman scattering from the ‘CdSe-like’ and ‘CdS-like’ LO phonons. The nature of the electronic states within these three dimensionally confined systems is investigated by linear absorption and photoluminescence spectroscopy. The photoluminescence spectra show features which are attributed to direct electron-hole recombination and recombination via states within the ‘blue shifted’ energy gap (which are possibly surface related). Carrier relaxation is also investigated by a pump-probe experiment whereby the absorption is partially bleached by a short pump pulse then probed some variable time later by a delayed probe pulse of much lower intensity. Fast and slow components in the carrier relaxation process are identified, and a relationship is suggested between the carrier relaxation and the features observed in the photoluminescence spectra. The well known ‘photodarkening’ properties of such materials are also investigated by the above techniques.