Optical determination of interface roughness in multilayered semiconductor structures

Received: 20 September 1998     

On the maximum in hall coefficient temperature dependence in medium-doped n-GaAs

Hall coefficient and conductivity are measured in a wide temperature interval from 14.5 to 295 K in order to characterize n-type GaAs bulk monocrystals with moderate donor concentration 10¹⁷–10¹⁸ cm^–3. The weak temperature dependence of the Hall coefficient, showing a slight maximum at 120 K, is analyzed for the first time in terms of the model developed by Klotynsh and Bariss of discrete local levels degenerate with the continuum. For that purpose the presence of a discrete donor level degenerate with the conduction band is supposed and its energy position is calculated using the model. The concentration and the degeneracy factor of this level are determined by fitting the theoretical temperature dependence of the free electron concentration to the experimental one, the former being calculated using the charge neutrality equation. In addition, a qualitative interpretation of the Hall mobility temperature dependence is given.     

Surjectivity and fixed points of relaxed dissipative multifunctions. Differential inclusions approach

One from the most important properties of accretive and monotone operators is the existence of zeros and surjectivity. In the paper we introduce relaxed variants of dissipative, accretive and monotone operators. Using essentially the properties of the solution set of appropriate differential inclusions we study the existence of zeros of such operators. As corollaries the existence of fixed points of relaxed contractive and relaxed nonexpansive multifunctions are obtained.     

Nonemptiness of viability kernels for infinite-dimensional differential inclusions

We investigate infinite-dimensional differential inclusions. Sufficient conditions for nonemptiness of the viability kernels of such systems are obtained.     

An example of optimal switching between a wiener process and a deterministic motion with a non-zero switching cost

The optimal policy and the value function of a problem of optimal switching between a Wiener process and a deterministic motion on a segment are found in the present article. The speed of the motion is equal to 1 and it is in direction to the nearest end of the segment. For every switching a positive payment has to be paid. The problem is to minimize the sum of the first exit time of the process and the total payment. It turns out that there exist four different optimal rules depending on the length of the segment and the switching cost.     

Features of magnetization reversal in LCMO/YBCO heterostructures

The change in the magnetic domain structure due to the proximity of a superconductor has been experimentally investigated for the first time. The complex character of magnetization reversal at temperatures below critical, caused by the mutual long-range effect of a superconductor and a magnet, has been shown. In particular, it is found that even magnetization reversal of the heterostructure by an in-plane field leads to the formation of Abrikosov vortices in the superconductor, carrying a flux perpendicularly to the film plane. It is shown that this is a consequence of the transformation of narrow domain walls into wide stripes due to the interaction with scattering fields from the superconductor. In turn, after penetration of the magnetic flux into the superconductor at some depth, the scattering fields cause backward magnetization reversal of the external film edge, as a result of which vortices with oppositely directed fluxes enter the crystal and propagate in the superconductor bulk in the form of chains along twins, as in the case of magnetization by a perpendicular magnetic field. Thus, at longitudinal magnetization, the flux enters the superconducting film in the form of wide stripes with alternating perpendicular induction, which is explained by the long-range interaction of the scattering fields of the superconductor with the manganite magnetization.     

Voltammetric monitoring of laccase-catalysed mediated reactions

Six different compounds capable of mediating laccase-catalysed reactions have been tested by cyclic voltammetry. They exhibited quasi-reversible electrodic behaviour with formal redox potentials ranging from 150 to 800 mV (E(0)' vs. SCE). The immersion of a laccase-coated glassy carbon electrode (GCE) in mediator solutions generated large cathodic catalytic currents easily recorded by cyclic voltammetry at low-potential scan rates. This current showed two well-defined pH profiles, which correlated with the variation of the mediator redox potentials at the pH range tested. The relevant effect of temperature on the activity of laccase has been assessed here. Likewise, it was shown that the current record varied with the substrate concentration. This trend fitted Michaelis-Menten kinetics, which allowed us to give an estimation of the affinity of the fungal laccase for the different mediators.     

Discrete Approximation of Impulsive Differential Inclusions

The article deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is strongly connected to [11 T. Donchev ( 2008 ). Approximation of the solution set of impulsive systems . In Lecture Notes in Comput. Sci . ( et al. . eds.). Vol. 4818 , Springer-Verlag , Berlin , pp. 309 – 316 . [Google Scholar]] and is its continuation. We achieve order of convergence 1 for the Euler approximation under Lipschitz assumptions on the set-valued right-hand side and on the functions describing the jump surfaces and jumps themselves. Another criterion prevents the beating phenomena and generalizes available conditions. Several test examples illustrate the conditions and the practical evaluation of the jump conditions.     

One-sided Perron Differential Inclusions

The main qualitative properties of the solution set of almost lower (upper) semicontinuous one-sided Perron differential inclusion with state constraints in finite dimensional spaces are studied. Using the technique introduced by Veliov (Nonlinear Anal 23:1027–1038, 1994) we give sufficient conditions for the solution map of the above state constrained differential inclusion to be continuous in the sense of Hausdorff metric. An application on the propagation of the continuity of the state constrained minimum time function associated with the nonautonomous differential inclusion and the target zero is given. Some relaxation theorems are proved, which are used afterward to derive necessary and sufficient conditions for invariance.     

Filippov–Pliss lemma and m-dissipative differential inclusions

In the paper we prove a variant of the well known Filippov–Pliss lemma for evolution inclusions given by multivalued perturbations of m-dissipative differential equations in Banach spaces with uniformly convex dual. The perturbations are assumed to be almost upper hemicontinuous with convex weakly compact values and to satisfy one-sided Peron condition. The result is then applied to prove the connectedness of the solution set of evolution inclusions without compactness and afterward the existence of attractor of autonomous evolution inclusion when the perturbations are one-sided Lipschitz with negative constant.