In the present paper, we introduce some Stancu type generalization of Szász-Mirakyan-Baskakov type operators. We estimate the moments for these operators using the hypergeometric series, which can be related to Laguerre polynomials. We estimate point wise convergence, asymptotic expansion and error estimate in terms of higher order modulus of continuity of function in simultaneous approximation...

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...

Cosmological consequences of adding the Cold Dark Matter (CDM) to the exactly solvable stringy Dark Energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the String Field Theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial ...

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 consider the exterior Neumann problem of the Laplacian with boundary condition on a prolate spheroid. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet-to-Neumann map. Our approach is particularly suitable for handling of scattered data, e.g. satellite data. We also propose a preconditioning technique based on doma...

Cosmological consequences of adding the Cold Dark Matter (CDM) to the exactly solvable stringy Dark Energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the String Field Theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial ...

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...