Equivalence and Singularity of Gaussian Measures on the Conic Sigma-Field

The alternative: equivalence-singularity on the conic sigma-field is established for a pair of centered Gaussian distributions and a corresponding criterion is given. The behavior of the logarithmic variation is established for the Radon–Nikodym derivative on the conic sigma-subfield. Bibliography: 6 titles.     

On modifications of random processes

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 194, pp. 150–169, 1992.     

A Ramsey‐type result for the hypercube

We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Q_n contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006     

Limit distribution “in the large” of linear functionals over a random process of the second order

An infinite-dimensional analogue of the theorem on the existence of an -typical distribution of linear functionals in a vector space of high dimension does not exist. There are given some additional conditions ensuring, nevertheless, the existence of a typical distribution of linear functionals in the infinite-dimensional case.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 97, pp. 199–202, 1980.The author is grateful to S. B. Makarov for pointing out and corresponding these errors.     

Linear quadrupoles with added octopole fields

Two methods of adding relatively small octopole fields to the main quadrupole field of quadrupoles and linear ion traps with cylindrical rods are investigated. The first, 'stretching' the quadrupole by moving two rods out from the axis, produces a combination of higher order fields with similar magnitudes in which the octopole field is not necessarily the greatest. The quadrupole field strength is changed significantly and a large potential appears on the axis. The second method uses rod pairs of different diameters. It adds octopole components of up to several percent while all other higher order fields remain small. An axis potential is also added, but it is only a few percent of the radio-frequency (RF) voltage and approximately equal to the strength of the octopole field. The axis potential can be removed by moving the larger rod pair out from the axis or applying unbalanced RF to the electrodes.     

Decomposition of vector-valued additive functions

From the additive nonnegative fonctions, defined on a - algebra of subsets, the property of countable additivity separates a class of regular objects, namely measures. Among additive Banach-valued functions, countable additivity is already not necessary for non-pathology. In the paper one isolates a class of regular vector-valued additive functions (measures) and one proves a theorem on the decomposition of a vector-valued additive function into the sum of a regular component (measure) and a purely pathological additive function, similar to a purely finitely additive measure.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 148–156, 1989.     

A remark on convergence in the limit theorem for the distribution of random functionals

Estimates are established which characterize the rate of convergence in a global limit theorem for random functionals.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 197–206, 1979.The author is grateful to L. N. Dovbysh for assistance and to I. A. Ibragimov for valuable consultations.     

Factor Model for the Study of Complex Processes

Doklady Mathematics - An original concept of building a factor model based on frames has been proposed. A method has been developed for calculating the values of factors by searching for the...     

Counterexample to the Conjecture on Monotonicity of a Gaussian Integral

It is shown that, for the Kantorovich metric on probability measures, the integral