We show that if the set of all bounded strongly continuous cosine families on a Banach space X is treated as a metric space under the metric of the uniform convergence associated with the operator norm on the space L (X) of all bounded linear operators on X, then the isolated points of this set are precisely the scalar cosine families. By definition, a scalar cosine family is a cosine family wh...

In this paper, we apply the general method we have presented elsewhere and prove the convergence of a class of explicit and high-order accurate finite difference schemes for scalar nonlinear hyperbolic conservation laws in several space dimensions. We consider schemes constructed—from an £-scheme— by the corrected antidiffusive flux approach. We derive "sharp" entropy inequalities satisfied by ...

We propose an abstract two-level algorithm with convergence independent of the coarse-space size. The abstract algorithm is applied to problems of solids discretized on unstructured meshes. With no regularity assumptions we prove uniform convergence with respect to coarse-space size, domain, essential boundary conditions and jumps in Young modulus. Numerical experiments connrm the theory and sh...

Let X be a locally connected, b-compact metric space and E a closed subset of X. Let G be the space of all continuous real-valued functions defined on some closed subsets of E. We prove the equivalence of the τ aw and τ K topologies on G, where τ aw is the so called Attouch-Wets topology, defined in terms of uniform convergence of distance functionals, and τ K is the topology of Kuratowski conv...

Convergence and continuity analyses as well as exact evaluation of non-uniform subdivision surfaces at arbitrary parameter values have been very difficult because the subdivision matrix varies at each iteration step, unlike uniform subdivision surfaces. Using eigenanalysis and convergence properties of non-uniform subdivision surfaces that have been given by authors recently, a parameterization...

in a Banach space E with a strongly positive operator A and with an arbitrary positive parameter ε. We establish the well-posedness in difference analogue of Hölder space of the high order uniform difference scheme for (0.1). Moreover, in applications, the convergence estimates for the solutions of uniform difference schemes of the multidimensional parabolic differential equations with an arbit...

Let \(\Phi \) be a nuclear space, and let '\) denote its strong dual. In this paper, we introduce sufficient conditions for the almost sure uniform convergence on bounded intervals of time sequence '\)-valued processes having continuous (respectively, càdlàg) paths. The main result is formulated first in general setting cylindrical but later specialized to other situations interest. particular,...

Using fuzzy filters in the sense of P. Eklund and W. Gähler [2], it turns out that fuzzy preuniform convergence spaces introduced in [11] form a strong topological universe in which fuzzy topological spaces as well as fuzzy (quasi) uniform spaces can be studied. Thus, better tools such as the existence of natural function spaces, the existence of one-point extensions (and consequently, the here...

we develop a theory of stratified $lm$-filters which generalizes the theory of stratified $l$-filters. our stratification condition explicitly depends on a suitable mapping between the lattices $l$ and $m$. if $l$ and $m$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $l$-filters. based on the stratified $lm$-filters, a general theory of lattice-v...