Basic topological constructions of manifold stratified spaces and stratified approximate fibrations are studied. These include products of manifold stratified spaces, products and compositions of stratified approximate fibrations and Euclidean stabilization of stratified approximate fibrations. The main result shows that the adjunction of two manifold stratified spaces via a manifold stratified...

This paper studies Tikhonov regularization for finitely smoothing operators in Banach spaces when the penalizationenforces too much smoothness sense that penalty term is not finite at truesolution. In a Hilbert space setting, Natterer [Applicable Anal., 18 (1984), pp. 29-37] showed with help of spectral theory optimal rates can be achieved this situation. ("Oversmoothing does harm.") For oversm...

This paper addresses the problem of reconstructing partially observed stochastic processes. The L convergence of the filtering and smoothing densities in state space models is studied, when the transition and emission densities are estimated using non parametric kernel estimates. An application to real data is proposed, in which a wave time series is forecasted given a wind time series.

Human's exploration of space has changed over time, depending on the expansion limits his knowledge. Space is infinite, but it limited by possibility human The original man knew very little about in which he lived - its shape, size, content, etc. Over began to take shapes that describe it. Those forms are dimensions, increased as knowledge in-creased. Knowledge spread more and more, from Earth'...

The convergence of the discontinuous Galerkin method for the nonlinear (cubic) Schrödinger equation is analyzed in this paper. We show the existence of the resulting approximations and prove optimal order error estimates in L∞(L2). These estimates are valid under weak restrictions on the space-time mesh.

The paper improves the classical uniqueness result for the Euler system in the n dimensional case assuming that ∇u E ∈ L 1 (0, T ; BM O(Ω)), only. Moreover the rate of the convergence for the inviscid limit of solutions to the Navier-Stokes equations is obtained, provided the same regularity of the limit Eulerian flow. A key element of the proof is a logarithmic inequality between the Hardy and...

Space-time multigrid refers to the use of methods solve discretized partial differential equations considering at once multiple time steps. A new theoretical analysis is developed for case where one uses coarsening in space only. It proves bounds on 2-norm iteration matrix that connect it norm when using same method corresponding stationary problem. When properly defined wavefront type smoother...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.