A long standing conjecture of Richter and Thomassen states that the total number of intersection points between any n simple closed Jordan curves in the plane, so that any pair of them intersect and no three curves pass through the same point, is at least (1− o(1))n. We confirm the above conjecture in several important cases, including the case (1) when all curves are convex, and (2) when the f...

Berry's category of dI-domains with stable functions is a relatively intricate , yet elegant framework for semantics of programming languages. Despite over fteen years of work in the area, the exact reasons for dis-tributivity (Axiom d) and nitariness (Axiom I) have not been fully ex-plicated. This paper shows that Axiom d and Axiom I are important when one works within the realm of Scott-domai...

The notion of completeness in metric spaces and that of completing a metric space are traditionally discussed in terms of Cauchy sequences. The main reason being that this concept deals precisely with the issue of convergence of sequences in the sense that every convergent sequence is a Cauchy sequence. The paper deals with completion in a setting that avoids explicit reference to Cauchy sequen...

A topological group G is h-complete if every continuous homomorphic image of G is (Ra˘ ıkov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-complete. In this paper, we establish open-map properties of hereditarily h-complete groups with respect to large classes of groups, and prove a theorem on the (total) minimality of sub-directly represented groups. Num...

Stable bistructures are a generalisation of event structures to represent spaces of functions at higher types; the partial order of causal dependency is replaced by two orders, one associated with input and the other output in the behaviour of functions. They represent Berry’s bidomains. The representation can proceed in two stages. Bistructures form a categorical model of Girard’s linear logic...

A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. Norms ‖T n‖ converge to zero arbitrarily fast. Let H be a complex separable Hilbert space and let B(H) denote the algebra of all continuous linear operator on H. If T ∈ B(H) then {T}′ = {A ∈ B(H) : AT = TA} is called the commutant of T . By a subspace we always mean a closed linear subspace. If A ⊂ B(H...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

We study the calculation of quasi-bound states in nMOS inversion channels and their impact on direct tunneling currents through the dielectric layer. For typical device parameters, the gate leakage in inversion is dominated by this tunneling component. However, a strong inaccuracy arises, if the eigenvalues of the closed system are used for the quasi-bound state tunneling current. We propose si...

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pseudo Uryshon) - fs bicsp's introduced both their induced bitopological spaces. It shown that hereditary property satisfied for with respect to but other mentioned types separations satisfies clos...