Classification of finite groups generated by reflections and rotations

We survey the existing parts of a classification of finite groups generated by orthogonal transformations in a finite-dimensional Euclidean space whose fixed point subspace has codimension one or two and extend it to a complete classification. These groups naturally arise in the study of the quotient of a Euclidean space by a finite orthogonal group and hence in the theory of orbifolds.Comment: 38 pages, accepted by Transformation Group

One Relator Quotients of Graph Products

In this paper, we generalise Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups

Gaussian modeling and Schmidt modes of SPDS biphoton states

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long

Innovation capacity of Russia and the Baltics: a comparative approach

This article considers the possibility of Russian integration into a common research, technological, and innovative space of the Baltic region. The author presents the results of a comparative analysis of innovative development in Russia and the Baltic Sea countries based on the calculation of an integral research and technological potential index for the Russian Federation, the Northwestern Federal District of Russia, Sweden, Denmark, Finland, Norway, Germany, Poland, Estonia, Lithuania, and Latvia. The paper describes the level of research and technological development of Russia in 2008-2010 in terms of human resources, R&D, material and technical components, and the transformation capacity of innovative potential. The author identifies the key issues in the field of research and innovation that inhibit the growth of research and technological potential concentration, as well as innovative development of the Russian Federation. The article considers the prospects for the development of research and technological potential in Russia through the use of instruments of international research and technological cooperation in the Baltic Sea region