An Overview of Scheduling Problems Arising in Satellite Communications

Satellite communications, like batches of work in a job shop, need to be scheduled in order to use their resources as efficiently as possible. The most common satellite communications system in use today is known as Time Division Multiple Access (TDMA), in which data from earth stations is buffered before being transmitted to the appropriate receiver on a satellite. Cycles of transmission are fixed for all stations. Since the same satellite will be used for routeing data in several different ways, a schedule must be devised to use the receivers, repeaters and transmitters on board to minimize the time needed for completion of a batch of work. This paper is a survey of current scheduling algorithms used for optimizing satellite communications resources. Apart from telecommunications, the methods presented here could be applied to more general scheduling problems with renewable resources but without precedence constraints.     

Minimizing Maximum Weighted Error for Imprecise Computation Tasks

We consider the problem of preemptively scheduling a set of imprecise computation tasks on m ≥ 1 identical processors, with each task T_i having two weights, w_i and w′_i. Two performance metrics are considered: (1) the maximum w′-weighted error; (2) the total w-weighted error subject to the constraint that the maximum w′-weighted error is minimized. For the problem of minimizing the maximum w′-weighted error, we give an algorithm which runs in O(n³ log²n) time for multiprocessors and O(n²) time for a single processor. For the problem of minimizing the total w-weighted error subject to the constraint that the maximum w′-weighted error is minimized, we give an algorithm which also has the same time complexity.     

On formal integration in composition rings of polynomials

This author wants to express his thanks to the School of Information Engineering at Teesside Polytechnic, Middlesbrough, England, for its support and hospitality during a visiting appointment of 3 months in 1989, when this paper was written.     

Properties of neodymium-doped aluminophosphate laser glasses

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 90–95, January, 1992.     

Application of Novel Focusing Mirrors in Gyrotron Transmission Lines

A novel focusing mirror based on the shifting of the beam phase according to the Gaussian beam optics enabled us to realize a focusing elements with different focal lengths in different directions and to convert the gyrotron output into a Gaussian-like beam. In this paper, we compare the quality of beams produced by the new system (which includes novel mirrors) and a conventional system consisting of a quasi-optical antenna, an ellipsoidal mirror and two parabolic cylinder mirrors.     

A generalization of Lomonosov's inequality and its applications to invariant subspaces

In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.

     

Analysis of semiconducting materials by high-resolution radiofrequency glow discharge mass spectrometry

The analytical capabilities of a high-resolution mass spectrometer in combination with a 13.56 MHz glow discharge ion source for the analysis of semiconducting materials (silicon carbide and gallium arsenide) were studied. It was shown that single positively charged ions of sample material have about 10 eV higher average energy than the ions of the discharge and residual gas. Therefore effective energy separation of the ions of analyte from the ions of the discharge and residual gas was achieved by adjusting the ion transfer optics (breadth and position of energy slit), which improves the analytical capabilities of the developed method.Some analytical applications are presented to illustrate the performance of r.f. GDMS for the bulk analysis of semiconducting materials. The results of the trace element analysis of gallium arsenide and silicon carbide samples are compared with data of independent methods (LIMS, ICP-AES, SIMS).Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthdayOn leave from the Institute of Inorganic Chemistry, 630090 Novosibirsk, Russia     

Variational aspects of Faddeev calculations

We examine differences between³H binding energies obtained by solving the Faddeev equations using standard partial-wave expansion procedures and results from solving the Schrödinger equation by means of the coupled-rearrangement-channel variational method. Variational bounds generated from Faddeev solutions for several contemporary, realistic potential models are presented as a function of the number of partial waves retained in the potential expansion. We demonstrate that the Faddeev wave function yields an optimal variational bound for the partial-wave truncated potential from which it is generated, but it does not yield optimal bounds for the full Hamiltonian or when the potential is partial-wave truncated at a different level. Finally, qualitative differences between³H solutions for static models such as the AV14 and RSC potentials and for momentum-dependent models such as the Nijmegen soft-core and Paris potentials are explored, and comparison is made with solutions for the RSC/TM two-body-force plus three-body-force model.