Professor Leonid Ushkalov’s Skovorodiana

Leonid Dust Trail Theories

At the end of the 19th century, Irish astronomers Johnstone Stoney and A.M.W. Downing showed in principle how to predict meteor storms. Their work and later developments applying similar ideas are reviewed here. The theories essentially involve determining the dynamical behavior of dust trails, which are narrow, dense structures within a broader stream. The formation of dust trails and the main...

Editorial - Leonid Pavlovich Shilnikov

This special issue presents a selection of papers from the conference “Dynamics, Bifurcations and Strange Attractors” dedicated to the memory of Leonid Pavlovich Shilnikov (1934–2011) to commemorate his contributions to the theory of dynamical systems and bifurcations. The conference was held at the Lobachevsky State University of Nizhny Novgorod, Russia, on 1–5 July 2013. The conference was at...

Leonid Pavlovich Shil ’ nikov ( obituary )

A remarkable mathematician, one of the most prominent specialists in the theory of dynamical systems and bifurcation theory, a laureate of the Lyapunov Prize of the Russian Academy of Sciences and of the Lavrent’ev Prize of the National Academy of Sciences of Ukraine, a Humboldt Professor, Head of the Department of Differential Equations of the Research Institute of Applied Mathematics and Cybe...

Jaakko Astola and Leonid Yaroslavsky

On Leonid Gurvits's Proof for Permanents

We give a concise exposition of the elegant proof given recently by Leonid Gurvits for several lower bounds on permanents. 1. PERMANENTS. The permanent of a square matrix A = (ai, j ) i, j=1 is defined by perA = ∑ π∈Sn n ∏ i=1 ai,π(i), (1) where Sn denotes the set of all permutations of {1, . . . , n}. (The name “permanent” has its root in Cauchy’s fonctions symétriques permanentes [2], as a co...