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...

We prove existence of weak solutions to an eigenvalue Steklov problem defined in a bounded domain with a Lipschitz continuous boundary.

This paper studies a family of Hilbert spaces of real harmonic functions on bounded regions in Rn and will show that, for a range of values of s, they are reproducing kernel Hilbert spaces. The spaces are characterized by their boundary traces and the inner products are defined via their expansions in the harmonic Steklov eigenfunctions of the region. The reproducing kernels will then be descri...

In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology hollow sphere and equipped with warped product metric. Precisely, aim at studying continuous dependence warping function defining respect to spectrum. We first show that knowledge spectrum up exponential decreasing error is enough determine uniquely neighbourhood boundary. Second, when f...

We study approximation properties of linear sampling operators in the spaces Lp for 1≤p<∞. By means Steklov averages, we introduce a new measure smoothness that simultaneously contains information on function and discrete behaviour at points. The enables us to improve extend several classical results theory case operators. In particular, obtain matching direct inverse inequalities Lp, find exac...

We construct periodic families of Poincaré spaces. This gives a partial solution to a question posed by Hodgson in the proceedings of the 1982 Northwestern homotopy theory conference. In producing these families, we formulate a recognition principle for Poincaré duality in the case of finite complexes having one top cell that splits of after a single suspension. We also explain how a Z-equivari...