In this paper, we provide uniform estimates for V-cycle algorithms with one smoothing on each level. This theory is based on some elliptic regularity but does not require a smoother interaction hypothesis (sometimes referred to as a strengthened Cauchy Schwarz inequality) assumed in other theories. Thus, it is a natural extension of the full regularity V-cycle estimates provided by Braess and H...

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points...

A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a Glivenko–Cantelli-type convergence result. The results use conditions based on the metric entropy of the index class. In contrast to related earlier work, no Gaussian assumption i...

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in R. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α-order fractional derivatives of the velocity for some α > 0 in the space variables in L, which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the Lequicontinu...

The lattice Boltzmann method (LBM) has recently become an alternative and promising computational fluid dynamics approach for simulating complex fluid flows. Despite its enormous success in many practical applications, the standard LBM is restricted to the lattice uniformity in the physical space. This is the main drawback of the standard LBM for flow problems with complex geometry. Several app...

We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L∞-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γp-convergence. If the dimension of the space N satisfies N − 1 < p ≤ N and if the number of the conne...

We consider the particle filter approximation of the optimal filter in non-compact state space models. A time-uniform convergence result is built on top of a filter stability argument developed by Douc, Moulines, and Ritov (2009), under the assumption of a heavy-tailed state process and an informative observation model. We show that an existing set of sufficient conditions for filter stability ...

In this paper, we introduce generalized difference sequence spaces via ideal convergence, lacunary of χ sequence spaces over p−metric spaces defined by Musielak function, and examine the Musielak-Orlicz function which satisfies uniform ∆2 condition, and we also discuss some topological properties of the resulting spaces of χ with respect to ideal structures which is solid and monotone. Hence, g...