Approximated Leont’ev coefficients

Direct approximation theorems for Dirichlet series in the norm of uniform convergence

We consider functions f ∈ AC(D) on a convex polygon D ⊂ C and their regularity in terms of Tamrazov’s moduli of smoothness. Using the relation between Fourier and Leont’ev coefficients given in (CMFT 1(1) (2001) 193) we prove direct approximation theorems of Jackson type for the Dirichlet expansion f (z) ∼ ∑ ∈ f ( ) e z L′( ) , where L(z)=∑Nk=1dkeakz is a quasipolynomial with respect to the ver...

A qMC-spectral method for elliptic PDEs with random coefficients on the unit sphere

We present a quasi-Monte Carlo spectral method for a class of elliptic partial differential equations (PDEs) with random coefficients defined on the unit sphere. The random coefficients are parametrised by the Karhunen-Loève expansion, while the exact solution is approximated by the spherical harmonics. The expectation of the solution is approximated by a quasi-Monte Carlo integration rule. A m...

On Weak Approximation of Stochastic Differential Equations with Discontinuous Drift Coefficient1

In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered. Here as the approximated process, the Euler-Maruyama approximation of SDEs with approximated drift coefficients is used, and we provide a rate of weak convergence of them. Finally we present a rate of weak convergence of the Euler-Maruyama approximation...

What Can Be Approximated by Polynomials with Integer Coefficients

Bootstrap Current Coefficients in Stellarators

A method to derive analytical expressions for bootstrap current coefficients is studied. The drift kinetic equation is divided into two parts corresponding to the effects of local and global structures of magnetic fields. The divided transport coefficients can be approximated by connecting the results of only three types of asymptotic expansions of the divided equations. The current coefficient...