Let R be a real closed field (e.g. the field of real numbers) and S ⊂ R be a semi-algebraic set defined as the set of points in R satisfying a system of s equalities and inequalities of multivariate polynomials in n variables, of degree at most D, with coefficients in an ordered ring Z contained in R. We consider the problem of computing the real dimension, d, of S . The real dimension is the f...

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

We consider the problem of simultaneous nite gain L p-stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback. We show that bounded input nite-gain L p-stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open loop system are, and the locations of these poles play a...

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

Hausfater and colleagues stated that in febrile adult patients presenting to the emergency department (ED) a procalcitonin (PCT) ≥0.2 mcg/l can help physicians to identify bacterial/parasitic infections [1]. We disagree and want to illustrate that by calculating likelihood ratios (LR). A LR is a semi-quantitative measure of the performance of a diagnostic test, expressing the magnitude by which...

in this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. some results about existence of maximal m-open setsare given. moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.our results are supported by examples and counterexamples.

In this paper, we always assume that H is an N-dimensional complex Hilbert space. Let L(H) be the set of all linear operators from H to H . A state ρ of some quantum system, described by H , is a positive semi-definite operator of trace one, in particular, for each unit vector |ψ〉 ∈ H , the operator ρ = |ψ〉〈ψ| is said to be a pure state. The set of all states onH is denoted by D(H). If X,Y ∈ L(...

We study sets and groups definable in tame expansions of ominimal structures. Let M̃ = ⟨M, P ⟩ be an expansion of an o-minimal Lstructure M by a dense set P . We impose three tameness conditions on M̃ and prove a cone decomposition theorem for definable sets and functions in the realm of the o-minimal semi-bounded structures. The proof involves induction on the notion of ‘large dimension’ for def...