Steklov Mathematical Institute

About: Steklov Mathematical Institute is a facility organization based out in Moscow, Russia. It is known for research contribution in the topics: Boundary value problem & Integrable system. The organization has 2153 authors who have published 5027 publications receiving 124773 citations.

Rivaroxaban versus Warfarin in Nonvalvular Atrial Fibrillation

Abstract: Methods In a double-blind trial, we randomly assigned 14,264 patients with nonvalvular atrial fibrillation who were at increased risk for stroke to receive either rivaroxaban (at a daily dose of 20 mg) or dose-adjusted warfarin. The per-protocol, as-treated primary analysis was designed to determine whether rivaroxaban was noninferior to warfarin for the primary end point of stroke or systemic embolism. Results In the primary analysis, the primary end point occurred in 188 patients in the rivaroxaban group (1.7% per year) and in 241 in the warfarin group (2.2% per year) (hazard ratio in the rivaroxaban group, 0.79; 95% confidence interval [CI], 0.66 to 0.96; P<0.001 for noninferiority). In the intention-to-treat analysis, the primary end point occurred in 269 patients in the rivaroxaban group (2.1% per year) and in 306 patients in the warfarin group (2.4% per year) (hazard ratio, 0.88; 95% CI, 0.74 to 1.03; P<0.001 for noninferiority; P = 0.12 for superiority). Major and nonmajor clinically relevant bleeding occurred in 1475 patients in the rivaroxaban group (14.9% per year) and in 1449 in the warfarin group (14.5% per year) (hazard ratio, 1.03; 95% CI, 0.96 to 1.11; P = 0.44), with significant reductions in intracranial hemorrhage (0.5% vs. 0.7%, P = 0.02) and fatal bleeding (0.2% vs. 0.5%, P = 0.003) in the rivaroxaban group. Conclusions In patients with atrial fibrillation, rivaroxaban was noninferior to warfarin for the prevention of stroke or systemic embolism. There was no significant between-group difference in the risk of major bleeding, although intracranial and fatal bleeding occurred less frequently in the rivaroxaban group. (Funded by Johnson & Johnson and Bayer; ROCKET AF ClinicalTrials.gov number, NCT00403767.)

Linear and Quasi-linear Equations of Parabolic Type

Abstract: Introductory material Auxiliary propositions Linear equations with discontinuous coefficients Linear equations with smooth coefficients Quasi-linear equations with principal part in divergence form Quasi-linear equations of general form Systems of linear and quasi-linear equations Bibliography.

A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number

Abstract: The hypotheses concerning the local structure of turbulence at high Reynolds number, developed in the years 1939-41 by myself and Oboukhov (Kolmogorov 1941 a,b,c; Oboukhov 1941 a,b) were based physically on Richardson's idea of the existence in the turbulent flow of vortices on all possible scales l < r < L between the ‘external scales’ L and the ‘internal scale’ l and of a certain uniform mechanism of energy transfer from the coarser-scaled vortices to the finer.

A Course in Metric Geometry

Abstract: Metric Spaces Length Spaces Constructions Spaces of Bounded Curvature Smooth Length Structures Curvature of Riemannian Metrics Space of Metric Spaces Large-scale Geometry Spaces of Curvature Bounded Above Spaces of Curvature Bounded Below Bibliography Index.

Quantization of Lie Groups and Lie Algebras

Abstract: Publisher Summary This chapter focuses on the quantization of lie groups and lie algebras. The Algebraic Bethe Ansatz—the quantum inverse scattering method—emerges as a natural development of the various directions in mathematical physics: the inverse scattering method for solving nonlinear equations of evolution, the quantum theory of magnets, the method of commuting transfer-matrices in classical statistical mechanics, and factorizable scattering theory. The chapter discusses quantum formal groups, a finite-dimensional example, an infinite-dimensional example, and reviews the deformation theory and quantum groups.