We solve the special case of the Euclidean Traveling Salesman Problem where II m cities lie on the boundary of the convex hull of all n cities, and the other m cities lie on a line segment inside this convex hull by an algorithm which needs O(mn) time and O(n) space.

We prove that (1) for any complete lattice $L$, the set $\mathcal {D}(L)$ of all non-empty saturated compact subsets Scott space $L$ is a Heyting algebra (with reverse inclusion order); and (2) if latti

Suppose that A is a C∗-algebra acting on a Hilbert space H, and φ, ψ are mappings from A into B(H) which are not assumed to be necessarily linear or continuous. By a (φ, ψ)derivation we mean a linear mapping d : A → B(H) such that d(ab) = φ(a)d(b) + d(a)ψ(b) (a, b ∈ A). In this paper, we prove that if φ is a multiplicative(not necessary linear) ∗-mapping, then every ∗-(φ,φ)-derivation is automa...

It is well known that the absolute value map on the self-adjoint operators on an infinite dimensional Hilbert spaces is not Lipschitz continuous, although Lipschitz continuity holds on certain subsets of operators. In this note, we provide an elementary proof that the absolute value map is Lipschitz continuous on the set of all operators which are bounded below in norm by any fixed positive con...

We extend to its spin 3/2 supersymmetric partner the very recent demonstration that the massless limit of massive spin 2 exchange amplitudes can be made continuous in background AdS spaces, in contrast to the known flat space discontinuities for both systems. In an AdS background, unlike spin 2 where the limit m → 0 is the massless one, spin 3/2 “masslessness” requires m → √ −Λ/3 , the supergra...

Convex hull is widely used in computer graphic, image processing, CAD/CAM and pattern recognition. In this work, we derive some new convex hull properties and then propose a fast algorithm based on these new properties to extract convex hull of the object in binary image. It is achieved by computing the extreme points, dividing the binary image into several regions, scanning the regions existin...

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

In this paper we investigate the role of domain representability and Scott-domain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α (= the non-empty player) in the strong Ch...