We study the eeects of the use of near-degenerate elements in nite and boundary element methods, and their analogues with mul-tiresolution methods. The main results include: an improved bound for the embedding constant in the Bramble{Hilbert lemma; characterization of the best N-term approximation of solutions of nonlinear operator equations ; best N-term approximation by near-degenerate normal...

This paper establishes that a class of $ N $-player stochastic games with singular controls, either bounded velocity or finite variation, can both be approximated by mean field (MFGs) controls velocity. More specifically, it shows (i) the optimal control to an MFG \theta is shown \epsilon_N $-NE game velocity, = O(\frac{1}{\sqrt{N}}) $, and (ii) this (\epsilon_N + \epsilon_{\theta}) where \epsi...

We study various approximation classes associated with m-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respective...

We investigate the Besov regularity for solutions of elliptic PDEs. This is based on regularity results in Babuska-Kondratiev spaces. Following the argument of Dahlke and DeVore, we first prove an embedding of these spaces into the scale B τ,τ (D) of Besov spaces with 1 τ = r d + 1 p . This scale is known to be closely related to n-term approximation w.r.to wavelet systems, and also adaptive Fi...

Investigation is made of the ion optical properties of inhomogeneous magnetic sector fields. In first order approximation the field is assumed to vary proportional to c * (0 n <C 1 ) ; the term in the magnetic field expansion which determines the second order aberrations is chosen independent of n , which makes the elimination possible of e. g. the second order angular aberration. From the EULE...