we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

State of the art set expansion algorithms produce varying quality expansions for different entity types. Even for the highest quality expansions, errors still occur and manual refinements are necessary for most practical uses. In this paper, we propose algorithms to aide this refinement process, greatly reducing the amount of manual labor required. The methods rely on the fact that most expansi...

A δ-uniform BSS machine is a standard BSS machine which does not rely on exact equality tests. We prove that, for any real closed archimedean field R, a set is δ-uniformly semi-decidable iff it is open and semi-decidable by a BSS machine which is locally time bounded; we also prove that the local time bound condition is nontrivial. This entails a number of results about BSS machines, in particu...

Recall that a subset of R is called semi-algebraic if it can be represented as a (finite) boolean combination of sets of the form {~ α ∈ R : p(~ α) = 0}, {~ α ∈ R : q(~ α) > 0} where p(~x), q(~x) are n-variable polynomials with real coefficients. A map from R to R is called semi-algebraic if its graph, considered as a subset of R, is so. The geometry of such sets and maps (“semi-algebraic geome...

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g x, t I t 1 − R μe−μx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discus...

formalized in terms of a hypergraph G = (V,E) whose edges arrive one-by-one and the goal is to construct an edge cover F ⊆ E with the objective of minimizing the cardinality (or cost in the weighted case) of F . We further consider a parameterized relaxation of this problem, where given some 0 ≤ < 1, the goal is to construct an edge (1− )-cover, namely, a subset of edges incident to all but an ...