We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent of the Gibbs measure, are given by a variational principle, which generalizes Li and Ma’s result and Bowen’s result.

In this paper, for a given sequentially Yoneda-complete T1 quasi-metric space (X, d), the domain theoretic models of the hyperspace K0(X) of nonempty compact subsets of (X, d) are studied. To this end, the ω-Plotkin domain of the space of formal balls BX, denoted by CBX is considered. This domain is given as the chain completion of the set of all finite subsets of BX with respect to the Egli-Mi...

In this paper, by means of operations (is called in [1, 2, 3] φ,ψ) we shall define φψ-continuity between two L-fuzzy quasi-uniform spaces. We shall prove that φψ-continuity between two L-fuzzy quasi-uniformity induces φψ-continuity between L-fuzzy topology generated by them. We shall investigate some Theorems on L-fuzzy uniform spaces. 2000 Mathematics Subject Classification:54A40, 03E72

di(x,A) = inf{di(x,A) : a ∈ A}, i ∈ I Hi(A,B) = max{sup di(a,B), sup di(A, b)} = sup{|di(x,A) − di(x,B)|} where a ∈ A, b ∈ B and x ∈ X It is well known that on 2 , Hi is a pseudometric, called the induced Hausdorff pseudometric induced by di, i ∈ I. Let (X,U) be a unifrom space with an augumented associated family p∗. p∗ also induces a uniformity U∗ on 2 defined by the base β∗ = {V ∗(i, ε) : i ...

We continue to study a simple integro-differential equation: the Quasi-Steady equation (QS) of flame front dynamics. This second order quasi-linear parabolic equation with a non-local term is dynamically similar to the Kuramoto-Sivashinsky (KS) equation. In [FGS03], where it was introduced, its well-posedness and proximity for finite time intervals to the KS equation in Sobolev spaces of period...

Quasi-stationarity is ubiquitous in complex dynamical systems. In brain dynamics, there is ample evidence that event-related potentials (ERPs) reflect such quasi-stationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study, we elaborate a recent approach for detecting quasi-stationary states as recurrence domains by means of recu...

In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: T3 subcompact spaces, strongly α-favorable spaces with a Gδ-diagonal or with a base of countable order, and complete quasi-developable T3-spaces. It follows th...

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as δ-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the δ-quasi-self-similar sets satisfying the open set condition we obtain the same resu...

In this paper we consider how the∇–, ∆– and global dimensions of a quasi-hereditary algebra are interrelated. We first consider quasi-hereditary algebras with simple preserving duality and such that if μ < λ then ∇. f.d.(L(μ)) < ∇. f.d.(L(λ)) where μ, λ are in the poset and L(μ), L(λ) are the corresponding simples. We show that in this case the global dimension of the algebra is twice its ∇–fil...