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...

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...

We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding these stochastic processes can be efficiently solved classically in the space-bounded case. The following corollaries are implied by our main result for any spac...

We consider a 2n × 2n system of conservation laws with stiff relaxation terms. The system arises from the modelling of multicomponent chromatography, and the zero relaxation limit is a n×n system of conservation laws of Temple class. For initial data which are small in BV, we establish an a priori bound on the total variation of the solution of the relaxation system. Moreover, we show that this...

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...