Optimal Control of Applications for Hybrid Cloud Services

Development of cloud computing enables to move Big Data in the hybrid cloud services. This requires research of all processing systems and data structures for provide QoS. Due to the fact that there are many bottlenecks requires monitoring and control system when performing a query. The models and optimization criteria for the design of systems in a hybrid cloud infrastructures are created. In this article suggested approaches and the results of this build.Comment: 4 pages, Proc. conf. (not published). arXiv admin note: text overlap with arXiv:1402.146

Multiplicity estimate for solutions of extended Ramanujan's system

We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011)

Nonexistence of steady waves with negative vorticity

We prove that no two-dimensional Stokes and solitary waves exist when the vorticity function is negative and the Bernoulli constant is greater than a certain critical value given explicitly. In particular, we obtain an upper bound $F \lesssim \sqrt{2}$ for the Froude number of solitary waves with a negative constant vorticity, sufficiently large in absolute value