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.     

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.     

Investigation of the structure of a melt and molecular dynamics of ortho- and pyrophosphates by Raman spectroscopy

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 4, pp. 535–540, October, 1991.     

Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.