On a diophantine problem of P. Erdös

Research supported in part by Grant 4055 from the Hungarian National Foundation for Scientific Research and by Kereskedelmi és Hitelbank Rt. Universitas Foundation.     

Critical thickness and stress relaxation in YBaCuO (123) strained epitaxial layers and YBaCuO based strained superlattices

An energy model has been used to calculate the critical thickness h _c of YBaCuO thin films and YBaCuO based superlattices within an isotropic or anisotropic approximation. The critical thickness of single layers calculated from the anisotropic model (16 nm) is in good agreement with the previously published experimental values which are spread out from 4 to 20 nm. In the case of superlattices, relaxation appears to be governed by the critical thickness of the elementary sub-layers and is then better evaluated through the calculation performed for YBaCuO single layers. XRD measurements on YBa₂Cu₃O₇/PrBa₂Cu_3?xGa_xO₇ superlattices grown on {100{ SrTiO₃ have evidenced a tetragonal stress in the YBaCuO ab plane which remains expanded when the YBaCuO elementary layer thickness is lower than 4.8 nm (4 YBaCuO cells). However the critical temperature of the shortest period superlattices is only slightly affected by this expanded stress in contrast to the effect of an elastic stress externally applied along the ab plane of YBaCuO thin films.     

Study of perfection of layers of AlGaSb(AS) solid solution

Studies have been carried out on the perfection of then-Al_xGa_1–xSb_1–yAs_y (0.12x0.26) layer grown on GaSb substrates under different conditions of lattice matching. During the relaxation of the mechanical stresses at first a system of tilt dislocations with a density of up to 5 · 10⁵ cm^–2 is formed while in thick layers (h 20 m) a network of misfit dislocations parallel to the heteroboundary is formed. The time required to dissolve a weighed amount of GaAs in the melt is shown to be of major importance for obtaining layers of a solid solution that are isoperiodic with the substrate. The entry of arsenic only in the initial portion of the epitaxial layer can reduce the dislocation density in the layer without decreasing the measured value of Aa. Dissolution of a weighed amount of GaAs in a Ga + Sb melt for two hours at T=730–750°C is sufficient to obtain layers of Al_xGa_1–xSb_1–yAs_y solid solution that are isoperiodic with the substrate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 84–89, January, 1988.In conclusion, we thank L. V. Druzhinina for useful discussions as well as Z. V. Korotchenko, L. S. Khludkova, and F. S. Kim for assistance in the performance of the experiments.     

Coherence of synchrotron radiation

Gal'tsov et al. [Vestn. Mosk. Gos. Univ., Fiz., Astron.,14, No. 5, 614 (1973)] studied the radiation spectrum of N equally spaced charges moving along a circle. In particular, it was shown that as N the intensity of the radiation from the system of charges vanishes. The present study will consider the radiation spectrum of N charges moving along an arbitrary closed curve, randomly distributed in the vicinity of equally spaced points. The coherency factor will be found for the assumption that: a) the distributions of individual charges are not intercorrelated; b) the charge distribution is such that in the vicinity of a given point only one charge is found. It will be shown that as N the radiation intensity tends to a finite limit.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 8–11, March, 1988.     

Density estimation and adaptive control of markov processes: Average and discounted criteria

We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ^d i.i.d. disturbances with unknown distribution . Under mild semi-continuity and compactness conditions, and assuming that is absolutely continuous with respect to Lebesgue measure, we establish the existence of adaptive control policies which are (1) optimal for the average-reward criterion, and (2) asymptotically optimal in the discounted case. Our results are obtained by taking advantage of some well-known facts in the theory of density estimation. This approach allows us to avoid restrictive conditions on the state space and/or on the system's transition law imposed in recent works, and on the other hand, it clearly shows the way to other applications of nonparametric (density) estimation to adaptive control.Research partially supported by The Third World Academy of Sciences under Research Grant No. MP 898-152.     

Comparative analysis of (p,d), (d,t) and (3He, α) reactions on13C nucleus

The angular distributions of the (p, d), (d, t) and(³He, ) reactions on¹³C have been analysed within the framework of DWBA in which additional information on nuclear vertex constants was introduced. Although all these reactions seem to be similar single nucleon transfer, their mechanism is shown to be quite different and so is the information extracted thereof. While from the (p, d) reactions spectroscopic factors may be extracted unambiguously, from the (d, t) reactions it is possible to obtain directly the values of vertex constants only, which in turn are consistent with those determined by extrapolation of the experimental cross sections of the (p, d) reactions to the pole.In the case of (³He, ) reactions, however, the analysis indicates inadequacy of the DWBA concerning the calculations of central partial amplitudes. For a more reliable extraction of structural information, besides the correct normalization of peripheral amplitudes, a contribution of more complex mechanisms must be taken into account.