Laser fluorescence-absorption analysis of iodine-129 and nitrogen dioxide impurities in a special atmosphere

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 116–121, January, 1992.     

On Beneš' bang-bang control problem

This paper treats Bene' bang-bang control problem. We present a proof of the optimality of a specific control function which differs from those proofs known in the literature and which appears to be useful for other problems too. The idea is to discretize the problem, solve the latter by means of dynamic programming and then to go to the limit.This work was supported by the Sonderforschungsbereiche 21 and 72, University of Bonn, Bonn, West Germany     

Homotopy properties of algebraic sets

In this paper there are announced several homotopy theorems on algebraic subsets of complex projective spaces. Some of the theorems generalize and refine results of the preceding note of the author (RZhMat, 1978, 5A531). It is also asserted that any -dimensional complex affine algebraic set has the homotopy type of a finite -dimensional cellular space. A generalization is given, in two versions, of a theorem of Bart-Larsen (RZhMat, 1973, 7A587).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 83, pp. 67–72, 1979.     

Spectrum generating algebras and a closed form expression forr k -radial coulomb matrix elements

The explicit expressions forr ^k -radial Coulomb matrix elements are given.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Symmetric random walks in random environments

We consider a random walk on thed-dimensional lattice ^d where the transition probabilitiesp(x,y) are symmetric,p(x,y)=p(y,x), different from zero only ify–x belongs to a finite symmetric set including the origin and are random. We prove the convergence of the finite-dimensional probability distributions of normalized random paths to the finite-dimensional probability distributions of a Wiener process and find our an explicit expression for the diffusion matrix.     

Elastic constants of the alloys Cd1−x Zn x (x<0.3%) and their temperature dependence

The temperature dependence of elastic constants of Cd_1–x Zn _x alloys, havingx=0.021, 0·042 and 0·233 at.%, has been measured in the temperature range from 4·2 to 300 K by the pulse-echo-overlap ultrasonic method. The adiabatic compressibilities and the Debye temperatures have been calculated. All elastic constants with the exception ofc ₄₄ increase slightly with the growing concentration of Zn.The summary of this paper was presented on the 7^th Conference on Ultrasonic Methods in ilina, September 11^th–13^th, 1980.     

Ergodic properties of a system in contact with a heat bath: A one dimensional model

We consider a one-dimensional model of a system in contact with a heat bath: A particle (the system ormolecule) of massM, confined to the unit interval [0, 1], is surrounded by an infinite ideal gas (thebath of atoms) of point particles of massm with which it interacts via elastic collisions. The atoms are not affected by the walls at 0 and at 1. We obtain convergence to equilibrium for the molecule, from essentially any initial distribution on its position and velocity. The infinite composite system of molecule and bath has very good ergodic properties: it is a Bernoulli system.Supported in part by NSF Grants PHY 78-03816 and PHY 78-15920     

Classical and quantum limitations on energy consumption in computation

Fundamental limitations on the energy dissipated during one elementary logical operation are discussed. A model of a real physical device (parametric quantron) based on the Josephson effect in superconductors is used throughout the discussion. This device is shown to be physically reversible, and moreover it can serve as the clementary cell of a logically reversible computer, both these properties being necessary to achieve the fundamental limits of energy dissipation. These limits due to classical and quantum statistics are shown to lie well below the earlier estimates,k _B T and , respectively.     

Configurationally and conformationally homogeneous cyclic n-aryl sulfimides—IV : Synthesis,configuration and stereochemistry of the rearrangement of 1,3-di-thiane-1-N-p-chlorophenylimides

1,3-Dithiane-1-N-p-chlorophenylimides (1,4-9) were prepared and their configuration and conformation was determined by ¹H and ¹³C NMR. The compounds were rearranged to the corresponding 2-(2'-amino-5'-chlorophenyl)-1, 3-dithianes (1U,4U,9U). The rearrangement reactions took place with ?95% stereospecifity. The mechanism of the reaction was investigated with the aid of analogs specifically deuterated at C-2.