We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set E ⊂ R. We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset E of E where the minimum of g is attained, provided that E is non-empty and has at least one compact connected component.

recognition of relationship between the present day stress state and fractures is very important in fractured reservoirs. fractures that are parallel or oblique to maximum horizontal stress have more tendencies to tensile deformation and tensile deformed fractures will be more permeable. the dalan formation is one of the main gas reservoirs of iran witch most of the production from this formati...

Let X be a Banach space and E be a closed bounded subset of X. For x ∈ X we set D(x,E) = sup{‖x− e‖ : e ∈ E}. The set E is called remotal in X if for any x ∈ X, there exists e ∈ E such that D(x,E) = ‖x− e‖ . It is the object of this paper to give new results on remotal sets in L(I,X), and to simplify the proofs of some results in [5].

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...

In this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

in order to study the relationship between random boolean sets and some explanatory variables, this paper introduces a propagation model. this model can be applied when corresponding poisson process of the boolean model is related to explanatory variables and the random grains are not affected by these variables. an approximation for the likelihood is used to find pseudo-maximum likelihood esti...

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

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...

Besicovitch and Rado [1] and Kinney [5] proved the following result: There is a closed set E ⊂ R2 with measure zero which contains a circle of every radius. The construction of Besicovitch and Rado works in Rd: If d ≥ 3 there is a closed set E ⊂ Rd with measure zero which contains a sphere of every radius. We will give an exposition of this construction in Section 1 below. One can ask whether a...

Let M = (E,F) be a matroid on a set E, and B one of its bases. A closed set θ ⊆ E is saturated with respect to B when |θ ∩B| = r(θ), where r(θ) is the rank of θ. The collection of subsets I of E such that |I ∩ θ| ≤ r(θ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by MB . In this paper we prove that a grap...