We construct a complete lattice Z such that the binary supremum function sup : Z × Z → Z is discontinuous with respect to the product topology on Z × Z of the Scott topologies on each copy of Z. In addition, we show that bounded completeness of a complete lattice Z is in general not inherited by the dcpo C(X,Z) of continuous functions from X to Z where X may be any topological space and where o...

Schemata theory, Markov chains, and statistical mechanics have been used to explain how evolutionary algorithms (EAs) work. Incremental success has been achieved with all of these methods, but each has been stymied by limitations related to its less-thanglobal view. We show that moving the question into topological space helps in the understanding of why EAs work. Purpose. In this paper we use ...

Hull-form optimization is a complex engineering problem. Owing to the several numerical simulations and design-performance spaces, hull-form considered an inefficient process, which makes determining global optimum difficult. This study used rough set theory (RST) acquire knowledge reduce design space for optimization. Furthermore, we studied one of problems by practically applying RST appropri...

We revisit the read-only random-access model, in which the input array is read-only and a limited amount of workspace is allowed. Given a set of N two-dimensional points in a read-only input array and Θ(S) bits of extra workspace (where S ≥ lgN), we present an algorithm that runs in O(N/S + N lgS) time for constructing the convex hull formed by the given points. Following a lower bound for sort...

The hull kernel topology on the set of all prime α-ideals of an ADL is introduced. Many properties of this space are studied. Using the topological properties of the space of prime α-ideals various equivalent conditions for an ADL to be a -ADL are furnished. Mathematics Subject Classification: 06D99

In this paper we prove that Urysohn univeral space is hyperconvex. We also examine the Gromov hyperbolicity and hyperconvexity of metric spaces. Using fourpoint property, we give a proof of the fact that hyperconvex hull of a δ-Gromov hyperbolic space is also δ-Gromov hyperbolic.

The group generated by the kinematic dynamo operator in the space of continuous divergence-free sections of the tangent bundle of a smooth manifold is studied. As shown in previous work, if the underlying Eulerian flow is aperiodic, then the spectrum of this group is obtained from the spectrum of its generator by exponentiation, but this result does not hold for flows with an open set of period...

What is materiality? And is it of a different order from semiosis? In this commentary I reflect on the place of materiality—that quality of material phenomena—and materialization—the processes by which such qualities are actualized in social life—in Matthew Hull’s brilliant book, Government of paper (GoP). The analytic materiality is central to Hull’s ethnography, both theoretically (it informs...

In this paper we defined prime ideal and maximal ideal and proved several properties of these. We have discussed the space of prime ideals of a C-algebra A with respect to the hull-kernel topology, which is called the prime spectrum of A and denoted by Spec A. It is also proved that Spec A is a T0 space.

Suppose that (X,A) is a measurable space and Y is a metrizable, Souslin space. Let Au denote the universal completion of A. For x ∈ X, let f(x, ·) be the lower semicontinuous hull of f(x, ·). If f : X × Y → R is (Au ⊗ B(Y ),B(R))-measurable, then f is (Au ⊗ B(Y ),B(R))-measurable.