A domain representation of a topological space X is a function, usually a quotient map, from a subset of a domain onto X . Several di erent classes of domain representations are introduced and studied. It is investigated when it is possible to build domain representations from existing ones. It is, for example, discussed whether there exists a natural way to build a domain representation of a p...

Pure type systems make use of domain-full-abstractions x : D : M. We present a variant of pure type systems, which we call domain-free pure type systems, with domain-free-abstractions x : M. Domain-free pure type systems have a number of advantages over both pure type systems and so-called type assignment systems (they also have some disadvantages) and have been used in theoretical developments...

In this paper we consider admissible domain representations of topological spaces. A domain representation D of a space X is λ-admissible if, in principle, all other λ-based domain representations E of X can be reduced to D via a continuous function from E to D. We present a characterisation theorem of when a topological space has a λ-admissible and κ-based domain representation. We also prove ...

Inhomogeneous phase separation and domain wall dynamics in the orthorhombically distorted La 0.87 MnO x Abstract. We observe the interesting magnetization and resistivity results in the orthorhombically distorted self doped manganite, La 0.87 MnO x. A significant irreversibility between zero-field-cooled and field-cooled resistivities as well as magnetization data is clearly observed up to a te...

environment assigning intervals to program variables. Writing X = {x1 ← �1� � � � � x� ← ��} for the function X mapping x� to �� such that X (x�) = ��, � = 1� � � � � �, the interval invariance equations would be 4 One of the 64 bits is used for garbage collection. 12 P. C�����   X1 = {x ← [min_int� max_int]} X2 = {x ← [1� 1] � L X3(x) = ∅ ? ∅ : let [�� �] = X3(x) in [min(� + 1� ma...

We consider the elliptic problem −Δu+ u= b(x)|u|p−2u+ h(x) in Ω, u∈H1 0 (Ω), where 2 < p < (2N/(N − 2)) (N ≥ 3), 2 < p <∞ (N = 2), Ω is a smooth unbounded domain in RN , b(x) ∈ C(Ω), and h(x) ∈ H−1(Ω). We use the shape of domain Ω to prove that the above elliptic problem has a ground-state solution if the coefficient b(x) satisfies b(x)→ b∞ > 0 as |x| →∞ and b(x)≥ c for some suitable constants ...

We introduce the property generalized subcompact and prove that subcompact implies generalized subcompact and that generalized subcompact implies domain representable. We develop a simplified characterization of domain representable. We also present an extension X of Debs’ space and prove that X is generalized subcompact but α does not have a stationary winning strategy in the Banach-Mazur game...

This paper presents a new numerical abstract domain for static analysis by abstract interpretation. This domain allows us to represent invariants of the form (x − y ≤ c) and (±x ≤ c), where x and y are variables values and c is an integer or real constant. Abstract elements are represented by Difference-Bound Matrices, widely used by model-checkers, but we had to design new operators to meet th...

We define the notion of a power stable ideal in a polynomial ring R[X] over an integral domain R. It is proved that a maximal ideal χ M in R[X] is power stable if and only if P t is P primary for all t ≥ 1 for the prime ideal P = M ∩ R. Using this we prove that for a Hilbert domain R any radical ideal in R[X] which is a finite intersection G-ideals is power stable. Further, we prove that if R i...