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- Alexey Kuznetsov
- 2009

In this paper we introduce a ten-parameter family of Lévy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by… (More)

The purpose of this review article is to give an up to date account of the theory and applications of scale functions for spectrally negative Lévy processes. Our review also includes the first extensive overview of how to work numerically with scale functions. Aside from being well acquainted with the general theory of probability, the reader is assumed to… (More)

- Alexey Kuznetsov
- 2005

In this article we consider some increasing trees, the number of which is equal to the number of alternating (updown) permutations, that is, permutations of the form σ(1) < σ(2) > σ(3) < ... . It turns out that there are several such classes of increasing trees, each of which is interesting in itself. Special attention is paid to the study of various… (More)

- Alexey Kuznetsov
- 2010

In this article we study in detail the expansion of the Riemann Ξ function in MeixnerPollaczek polynomials. We obtain explicit formulas, recurrence relation and asymptotic expansion for the coefficients and investigate the zeros of the partial sums. ∗To appear in the Canadian Mathematical Bulletin †Research supported by the Natural Sciences and Engineering… (More)

- Alexey Kuznetsov
- SIAM J. Matrix Analysis Applications
- 2015

The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions – the eigenfunctions of the continuous Fourier transform. This eigenbasis should also have some degree of analytical tractability and… (More)

- Bartlomiej Dyda, Alexey Kuznetsov, Mateusz Kwasnicki
- J. London Math. Society
- 2017

- Iu I Potapov, Evgeny D. Volkov, Alexey Kuznetsov
- Physical review. E, Statistical, nonlinear, and…
- 2011

Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network.… (More)

- Mourad E. H. Ismail, Linda Perez-Rodriguez, +16 authors George Andrews
- 2015

In this talk, I will discuss Hankel determinant generated by a Laguerre weight multiplied by exp(−t/x), t > 0, inducing an infinitely fast 0 at the origin. For finite n, the Hankel determinant, is expressed in terms a finite n Painleve III. Under double scaling where n→∞ and t→ 0, such that s := 2nt is finite, the original PIII becomes a lesser PIII. The… (More)

- Alexey Kuznetsov, Alexander A. Bush, Viktor B. Rybakov, Eugene V. Babaev
- Molecules
- 2005

Various 2-substituted indolizines can be directly and selectively lithiated in the 5 position and subsequent reactions with different electrophiles lead to some novel classes of indolizines. In particular, previously unknown 5-formyl- and 5-iodoindolizine have been prepared by this way and the molecular structure of 5-formyl-2- phenylindolizine was… (More)

We investigate analytical properties of free stable distributions and discover many connections with their classical counterparts. Our main result is an explicit formula for the Mellin transform, which leads to explicit series representations for the characteristic function and for the density of a free stable distribution. All of these formulas bear close… (More)