Institute of Mathematics and Informatics

Семинар по Приложна математика
2025-03-27 14:00 - 15:30 (Europe/Sofia) | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
About m-ary Gray codes
Докладчик: д-р Мария Пашинска, ИМИ – БАН
Дата: 27.03.2025 г.
Час: 14:00 ч.
Място: зала 503
Резюме: We present several systemized implementations of the Gray code over an alphabet with m ≥ 2 elements. Gray codes are widely used in digital communications and effective generation of combinatorial objects. We consider two variants – reflected and modular m-ary Gray codes. We present algorithms for their generation and other important functions such as ranking and unranking and functions for generation of a maximal set of non-proportional vectors of length n over the given alphabet. Some applications of the m-ary Gray codes are also considered.
This talk is based on joined work with Stefka Bouyuklieva , Iliya Bouyukliev and Valentin Bakoev.

Семинар по Приложна математика
2025-06-03 15:00 - 16:30 | Zoom
Следващата сбирка на Семинара по приложна математика ще се проведе на 03.06.2025 г. от 15:00 в онлайн среда:
Join Zoom Meeting
https://us02web.zoom.us/j/87588684853?pwd=[REDACTED]
Meeting ID: 875 8868 4853
Passcode: [REDACTED]
A generalization of Meijer’s G function motivated by probability
Докладчик: Dmitrii Karp
Резюме: Meijer’s G function appeared in probability in 1930-ies even before Meijer’s work as the density of the product of independent beta variables and as the density of the likelihood ratio test for samples drawn from many classical probability distributions. It is defined by a contour integral of the appropriate ratio of gamma products (sometimes reducible to the inverse Mellin transform). Replacing the Euler gamma function by the Barnes double gamma function in this contour integral, we introduce a new family of special functions which we call Mellin-Barnes’ K function. It is a quite general family which contains Meijer’s G function (thus also all classical hypergeometric functions pFq), as well as several new functions that appeared recently in the study of random processes and the fractional fenomena. For example, the running supremum of an alpha-stable Levy process has density expressible by K function as well as does the exponential functionals of the hypergeometric process. In the talk, we will discuss the definition of the new function, its basic analytic and transformation properties and relations to the functions found in the literature. We further define a generalization of the Kilbas-Saigo function introduced earlier to solve in closed form certain classes of integral and differential equations of fractional order and observe that both the original and the generalized Kilbas-Saigo functions are special cases of our new function.
The talk is based on a joint work with Alexey Kuznetsov (York University, Toronto, Canada).
