In this paper we discuss the notion of universality for classes candidate common Lyapunov functions linear switched systems. On one hand, prove that a family absolutely homogeneous is universal as soon it approximates arbitrarily well every convex function C0 topology unit sphere. other several obstructions class to be universal, showing, in particular, families piecewise-polynomial continuous ...

Purpose: Scoliosis is one of the most common spinal deformities that affect chest wall mechanics. Scoliosis results in ventilator disorders and respiratory muscle weakness. However, the mechanism of these disorders is still unknown. The main objective of this study was to identify the intensity of respiratory muscles activity in patients with idiopathic scoliosis compare with healthy indi...

For a polynomial f(x) in (Zp∩Q)[x] of degree d ≥ 3 let L(f⊗Fp;T ) be the L function of the exponential sum of f mod p. Let NP(f ⊗ Fp) denote the Newton polygon of L(f⊗Fp; T ). Let HP(f) denote the Hodge polygon of f , which is the lower convex hull in R2 of the points (n, n(n+1) 2d ) for 0 ≤ n ≤ d−1. We prove that there is a Zariski dense subset U defined over Q in the space A of degree-d monic...

In this paper, characterizations of the degree to which a mapping $mathcal{T} : L^{X}longrightarrow M$ is an $(L, M)$-fuzzy topology are studied in detail.What is more, the degree to which an $L$-subset is an $L$-open set with respect to $mathcal{T}$ is introduced.Based on that, the degrees to which a mapping $f: Xlongrightarrow Y$ is continuous,open, closed or a quotient mapping with respect t...

An algorithm is described for computing an interpolation spline of arbitrary but fixed degree which preserves the convexity of the given data set. Necessary and sufficient conditions for the solvability of the problem, some special cases and error estimations are given.

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

Let E be an elliptic curve over Q, and ρl : Gal(Q/Q)→GL2(Zl) its l-adic Galois representation. Serre observed that for l ≥ 5 there is no proper closed subgroup of SL2(Zl) that maps surjectively onto SL2(Z/lZ), and concluded that if ρl is surjective mod l then it is surjective onto GL2(Zl). We show that this no longer holds for l = 3 by describing a modular curve X9 of genus 0 parametrizing elli...