Ont ∞ quasi-similarity of linear systems

Summary Conti defined t similarity of systems (1)x=tA(t)xand (2)y=B(t)y, and showed that it is an equivalence relation which preserves uniform and strict stability. Here the definition is weakened by imposing less stringent integrability conditions, some in terms of perhaps conditionally convergent improper integrals, on the matrix function relating A and B. The extended relation, t quasi-similarity, is not symmetric or transitive; however, it is shown that if (2) is t quasi-similar to (1)and (1)is uniformly, uniformly asymptotically, or strictly stable, then so is (2).Results are also given concerning linear asymptotic equilibrium of (2)in the case where (1)is stricly stable or has linear asymptotic equilibrium.     

Automorphic functions on SL(m,ℝ)

One presents a method for the expansion of functions F:SL(m,)^h that are automorphic with respect ot the congruence subgroup in SL(m,). For m=2 the method gives the usual expansion into Fourier series. One gives a comparison with the expansion presented previously by the author in the paper: The expansion of automorphic functions, J. Sov. Math.,26, No. 3 (1984).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 129, pp. 164–176, 1983.     

Polymer-Supported dicyanoketene acetal as a pi-acid catalyst: monothioacetalization and carbon-carbon bond formation of acetals

Polymeric dicyanoketene acetals (DCKA) were synthesized by copolymerization of styrene and divinylbenzene or ethylene glycol dimethacrylate. These novel polymers could be used successfully as recyclable pi-acid catalysts in monothioacetalization or carbon-carbon bond forming reaction of acetals.     

Effect of flashlamp diameter on luminescent coolants for a solid-state laser

Reducing the diameter of the flashlamp was found to increase the percent improvement in output of a solid-state laser caused by using luminescent coolants. However, this change in diameter also reduced the effectiveness of the flashlamp in producing long (150 s) laser pulses so that an overall decrease in laser output was observed. In the formation of short (40 s) laser pulses, on the other hand, larger absolute values were obtained using the smaller diameter flashlamp.     

Resonant generation of even-order harmonics in metal vapors

Generation of the second- and fourth-order harmonics of laser radiation is reported in Mg vapor at the forbidden 3s ²¹ S _o–4s ¹ S _o transition. The conversion efficiency for the second-order harmonics has been measured to be 10^–2% and for the fourth one 10^–8%.     

Calculation of excited molecular states taking account of partial relaxation of the core

Effects of electron-core relaxation in the excitation of atomic systems are considered. A new approach to the consideration of relaxation is proposed, and the corresponding equations are obtained. In the -electron approximation, the first excited states of some organic molecules are calculated by the V^(N–1)-potential method, the Morokuma-Iwata method, and a method proposed in the present work.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 55–59, October, 1985.     

Synthesis of o- and m-Carborane-substituted Porphyrins of the Natural Type

Basing on protoporphyrin IX, its monobenzyl ester, deuteroporphyrin IX, 9-hydroxymethyl-m- and 9-hydroxymethyl-p-carboranes, mono- and dicarborane-containing porphyrins were prepared.