On perturbations of the isometric semigroup of shifts on the semiaxis

We study perturbations $(\tilde\tau_t)_{t\ge 0}$ of the semigroup of shifts $(\tau_t)_{t\ge 0}$ on $L^2(\R_+)$ with the property that $\tilde\tau_t - \tau_t$ belongs to a certain Schatten-von Neumann class \gS_p with $p\ge 1$. We show that, for the unitary component in the Wold-Kolmogorov decomposition of the cogenerator of the semigroup $(\tilde\tau_t)_{t\ge 0}$, {\it any singular} spectral type may be achieved by \gS_1 perturbations. We provide an explicit construction for a perturbation with a given spectral type based on the theory of model spaces of the Hardy space $H^2$. Also we show that we may obtain {\it any} prescribed spectral type for the unitary component of the perturbed semigroup by a perturbation from the class \gS_p with $p>1$

Использование золошлаковых материалов теплоэнергетики в строительных материалах

The possible trends to improve the building-technical properties of dry ashes characteristics formed as a result of solid fuel combustion at thermal power stations are presented. The results of different fly-ash conditioning technologies application to widen the trends and to increase the volumes of their use in the construction materials and products.Представлены возможные направления улучшения строительно-технических характеристик сухих зол, образующихся при сжигании твердого топлива на тепловых электростанциях. Приведены результаты применения различных технологий кондиционирования свойств золы для расширения направлений и увеличения объемов их использования при производстве строительных материалов и изделий

Nonperturbative Tests of Three-Dimensional Dualities

We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three-sphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal N = 2 gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of N = 8 super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit