In this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m) × so(m). We show that the restriction of these systems onto some subvarieties of the orbits written in new matrix variables admits a new r × r matrix Lax representation in a generalized...

In this paper, using the Steklov function, we introduce the generalized continuity modulus and denethe class of functions Wr;kp;' in the space Lp. For this class, we prove an analog of the estimates in [1]in the space Lp.

We show that an embedded minimal annulus Σ ⊂ B which intersects ∂B orthogonally and is invariant under reflection through the coordinate planes is the critical catenoid. The proof uses nodal domain arguments and a characterization, due to Fraser and Schoen, of the critical catenoid as the unique free boundary minimal annulus in Bn with lowest Steklov eigenvalue equal to 1. We also give more gen...

We construct an exact analytic solution to the Friedmann equations with a stringy inspired scalar matter and show explicitly an absence of the “Big Rip” singularity. The notable feature of this model is a wrong sign of the kinetic term and a special polynomial form of the effective tachyon potential. The method developed in the fivedimensional brane-world scenario is used. We show that the solu...

A generic Lagrangian, in arbitrary spacetime dimension, describing the interaction of a graviton, a dilaton and two antisymmetric tensors is considered. An isotropic p-brane solution consisting of three blocks and depending on four parameters in the Lagrangian and two arbitrary harmonic functions is obtained. For speci c values of parameters in the Lagrangian the solution may be identi ed with ...

We construct an exact analytic solution to the Friedman equations with a stringy inspired scalar matter and show explicitly an absence of the “Big Rip” singularity. The notable feature of this model is a wrong sign of the kinetic term and a special polynomial form of the effective tachyon potential. The method developed in the fivedimensional brane-world scenario is used. We show that the solut...

We construct an exact analytic solution to the Friedman equations with a stringy inspired scalar matter and show explicitly an absence of the “Big Rip” singularity. The notable feature of this model is a wrong sign of the kinetic term and a special polynomial form of the effective tachyon potential. The method developed in the fivedimensional brane-world scenario is used. We show that the solut...

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue problem by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an Steklov eigenvalue problem on the coarsest finite element space. This co...

In 1999, A. Connes and D. Kreimer have discovered the Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann — Hilbert problem. In this work a generalization of their scheme to the case of quantum electrodynamics is proposed. The action of the gauge group on the Hopf algebra of diagrams are de...