On the problem of calculating the optical film parameters from the measured transmission spectra

The procedure for calculating the dispersion of the refractive and absorption indices and thickness of an optical film, based on measurements of spectral dependence of the transmittance, is described. The film parameters are calculated using a solution of the approximation problem. The effect of the film model on the calculated values of the refractive and absorption indices is analyzed.     

Studies on amine hydrothiocyanates. IV. Thermal decomposition studies using TG

The thermal decomposition of piperidine hydrothiocyanate, piperazine hydrothiocyanate, and the dihydrothiocyanates of ethylenediamine and 1,3-diaminopropane has been studied using TG. Piperidine hydrothiocyanate decomposes in a single step while the dihydrothiocyanates follow more complicated decomposition patterns yielding H₂S and half of the organic moiety first. The second step involves the loss of H₂S and the remainder of the organic moiety. In each case, complex polymeric materials result. Piperazine hydrothiocyanate also decomposes in two steps, the first involving the loss of half of the piperazine and the second involving the loss of piperazine and H₂S. Kinetic parameters have been determined for all these reactions.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.     

Characteristics of propagation of light beams in gyrotropic crystals

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 5, pp. 815–819, May, 1991.     

Charged Black Holes and Multidimensional Gravity

A multidimensional generalization of the Reissner-Nordström solution of general relativity is obtained for the case of n Ricci-flat internal spaces. A two-parameter family of black-hole solutions for an arbitrary dimensionality D is selected. Nontrivial black holes with D > 4 are shown to exist only with a nonzero electric charge. Observational consequences are discussed, in particular, a violation of Coulomb's law.     

Inverse and saturation theorems for linear combination of modified Baskakov operators

In this paper, we consider linear combinations of modified Baskakov operators. By use of several lemmas, we obtain the inverse theorem (Theorem 1.1) and the saturation (Theorem 1.2) for those linear combinations.     

Temperature dependence of corundum roentgenoluminescence and thermoluminescence

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 3, pp. 438–444, March, 1991.     

Kaplansky conjecture in the theory of quadratic forms

This article considers the splitting properties of finite-dimensional division rings over universal splitting fields of quadratic forms. An example of a field with u-invariant equal to 6 is constructed, which contradicts Kaplansky's conjecture concerning u-invariants.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im, V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 75–89, 1989.