On the Creative Contribution of V. S. Korolyuk to the Development of Probability Theory

We present a brief survey of the main results obtained by V. S. Korolyuk in probability theory and mathematical statistics.     

A new strategy for asymmetric synthesis of aminophosphonic acid derivatives: the first enantioselective catalytic reduction of C-phosphorylated imines

The first highly enantioselective catalytic reduction of 1-imino-2,2,2-trifluoroethylphosphonates and the synthesis of enantiomerically enriched biorelevant phosphonotrifluoroalanine is reported.     

On singularity and fine spectral structure of random continued fractions

We study properties of the distribution of a random variable of the continued fraction form where are independent and not necessarily identically distributed random variables. We prove the singularity of and study the fine spectral structure of such measures.     

Modification of the lie‐algebraic scheme and approximation error estimations

A new modification of the the Lie‐algebraic scheme for solving partial differential equations with initial and boundary conditions based on constructing quasirepresentations of the Heisenberg‐Weyl algebra operators involving boundary conditions is proposed. Approximation errors for the modified scheme are evaluated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theory and practice of long-period gratings: when a loss becomes a gain

Losses of cladding modes are part of the mechanism of operation of a long-period grating (LPG) when it is used as an optical filter. We present a LPG computer simulation that accounts for these losses. On the basis of this simulation, we show that losses result in qualitatively different LPG spectral behavior. There is an optimal loss value that provides sidelobe-free, 100% power transfer from the core to the cladding mode for a uniform LPG. We obtained a simple equation that relates this optimum lose value to the LPG length and the cross-coupling coefficient. Based on the results, we propose new approaches to LPG design in a fiber as well as in waveguide platforms for fiber-optic communication and sensor applications. A design of a LPG reconfigurable filter is suggested.     

Partial actions and an embedding theorem for inverse semigroups

Periodica Mathematica Hungarica - We give a simple construction involving partial actions which permits us to obtain an easy proof of a weakened version of L. O’Carroll’s...     

Size of the jump and behavior of the absolute maximum for processes with independent increments

For a process with independent increments and negative mean one investigates the asymptotic behavior of the distribution of the absolute maximum and the size of the jump over a positive level. Necessary and sufficient conditions for the existence of a proper distribution of the size of a jump over an infinite level are found.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 451–458, April, 1990.