We present a generalization of V. Temlyakov’s weak greedy algorithm, and give a sufficient condition for norm convergence of the algorithm for an arbitrary dictionary in a Hilbert space. We provide two counter-examples to show that the condition cannot be relaxed for general dictionaries. For a class of dictionaries with more structure, we give a more relaxed necessary and sufficient condition ...

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L (G), and the Fourier algebra, A(G), of a locally compact group, G. Barry Johnson introduced the important concept of amenability for Banach algebras in [20], where he proved, among many other things, that a group algebra L1(G) is amenable precisely when the locally ...

We establish the weak continuity of the Gauss-Coddazi-Ricci system for isometric embedding with respect to the uniform L-bounded solution sequence for p > 2, which implies that the weak limit of the isometric embeddings of the manifold is still an isometric embedding. More generally, we establish a compensated compactness framework for the Gauss-Codazzi-Ricci system in differential geometry. Th...

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0 < t 6 T in some bounded three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and tha...

The existence of stationary solutions to the Povzner equation is established for a class of problems in bounded domains with smooth boundaries. The result holds for general type collision kernels under assumptions of angular cutoo. The boundary conditions with xed in-data and with a linear operator of diiuse reeection type are considered. The method is based on constructing approximate solution...