Explicit construction of elements of the ring S(n,r) of invariants of n-ary forms of degree r

Translated from Matematicheskie Zametki, Vol. 51, No. 2, pp. 139–143, February, 1992.     

Doping of solid solutions in liquid epitaxy. III. Tellurium in AlxGa1−xSb

A calculation is made of the dependences of the coefficient of the tellurium distribution K_Te and the electron concentration n in Al_xGa_1–xSb on the composition of the solid solution and the growth temperature. It is shown that K_Te must decrease with increasing x. The dependence of K_Te on the temperature is also determined by x. Experimental results were obtained on Al_xGa_1–x Sb (0 x 0.74) films grown by liquid epitaxy. The electron concentration in the films was measured through the thermoelectric power and the capacitance-voltage characteristics of Schottky barriers. Satisfactory agreement with the results of the calculation was obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 19–25, April, 1980.We thank G. K. Arbuzov for assistance in preparing the surface-barrier structures.     

Heuristic Methods for Large Centroid Clustering Problems

This article presents new heuristic methods for solving a class of hard centroid clustering problems including the p-median, the sum-of-squares clustering and the multi-source Weber problems. Centroid clustering is to partition a set of entities into a given number of subsets and to find the location of a centre for each subset in such a way that a dissimilarity measure between the entities and the centres is minimized. The first method proposed is a candidate list search that produces good solutions in a short amount of time if the number of centres in the problem is not too large. The second method is a general local optimization approach that finds very good solutions. The third method is designed for problems with a large number of centres; it decomposes the problem into subproblems that are solved independently. Numerical results show that these methods are efficient—dozens of best solutions known to problem instances of the literature have been improved—and fast, handling problem instances with more than 85,000 entities and 15,000 centres—much larger than those solved in the literature. The expected complexity of these new procedures is discussed and shown to be comparable to that of an existing method which is known to be very fast.     

Boundary-layer averaging for standard systems with lag

Thekth-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter 1, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to . We suggest another approach in which the step method is used onlyk times fort [0,k] and justify the asymptotic method.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10 pp. 1362–1368, October, 1994.     

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.     

Dynamic properties,scaling and related freezing criteria of two- and three-dimensional colloidal dispersions

The static and dynamic properties of 2- and 3-dimensional dispersions of strongly interacting colloidal spheres are examined. Quasi-2-dimensional dispersions of particles interacting by long range electrostatic and dipolar magnetic forces, respectively, are investigated using Brownian dynamics computer simulations with hydrodynamic interactions included. The dynamics of 3-dimensional bulk dispersions of charge-stabilized and neutral colloidal spheres is determined from a fully self-consistent mode-coupling scheme. For systems with long range repulsive interactions the dynamic correlation functions are shown to obey dynamic scaling in terms of a characteristic relaxation time related to the mean particle distance. Hydrodynamic interactions introduce a second characteristic length scale, and they lead to more restricted scaling behaviour with an enhancement of self-diffusion and, for 2-dimensional systems, to the divergence of the short-time collective diffusion coefficient. As a consequence of dynamic scaling, a dynamic criterion for the onset of colloidal freezing related to long-time self-diffusion is shown to be equivalent to a static freezing criterion related to the 2- and 3-dimensional static structure factors. Alternative freezing criteria are given in terms of the long-time and the mean collective diffusion coefficients.