Abstract. The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and s...

Abstract: This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems ...

We show how to optimize the shape of the transfer function of a linear time invariant (LTI) single-input-single-output (SISO) system. Since any transfer function is rational, this can be formulated as an optimization problem for the coefficients of polynomials. After characterizing the cone of polynomials which are nonnegative on intervals, we formulate this problem using semidefinite programmi...

In this paper, we give a necessary condition for an infinite word defined by a nondegenerate interval exchange on three intervals (3iet word) to be invariant by a substitution: a natural parameter associated to this word must be a Sturm number. We deduce some algebraic consequences from this condition concerning the incidence matrix of the associated substitution. As a by-product of our proof, ...

Basing on our recent results on the 1/n-expansion in unitary invariant random matrix ensembles , known as matrix models, we prove that the local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the Density of States, is independent of the form of the potential, determining the matrix model. Our proof is applicable to the case of real analytic potentials and...

We consider the higher-order nonlinear difference equation xn 1 α xn / A Bxn xn−k , n 0, 1, . . ., where parameters are positive real numbers and initial conditions x−k, . . . , x0 are nonnegative real numbers, k ≥ 2. We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the uniq...

We consider the higher-order nonlinear difference equation xn 1 p qxn−k / 1 xn rxn−k , n 0, 1, . . . with the parameters, and the initial conditions x−k, . . . , x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open probl...

In this paper we solve the problem about optimal interval quadrature formula for the class WrF of differentiable periodic functions with rearrangement invariant set F of their derivatives of order r. We prove that the formula with equal coefficients and n node intervals having equidistant midpoints is optimal for considering classes. To this end a sharp inequality for antiderivatives of rearran...

An approach for understanding the behaviour of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and the scale-invariant power-law behaviour of normalized factorial moments. The model can be used to describe multiparticle processes in terms of a decomposition...

A working memory model is describ<~d that is capable of storing and recalling arbitrary temporal sequences of events, including repeated items. These memories encode the invariant temporal order of sequential events that may be present<~d at widely differing speeds, durations, and interstimulus intervals. This temporal order code is designed to enable all possible groupings of sequential events...