In this article we consider the existence, uniqueness and positivity of a first order non-linear periodic differential equation. The main tool employed is the Krasnosel’skĭı’s fixed point theorem for the sum of a completely continuous operator and a contraction.

The controllability problem for a class of impulsive fractional-order semilinear control system with nonlocal initial condition has been considered. Sufficient condition for the controllability is established by means of solution operator and application of Banach contraction theorem.

PREFACE 1. CONVERGENT. Does the set of cyclic operators have a non-empty interior?... 2. WEIGHTED. Is every part of a weighted shift similar to a weighted shift?. . . . 3. INVARIANT. If an intransitive operator has an inverse, is its inverse also intransitive? 4. TRIANGULAR. Is every normal operator the sum of a diagonal operator and a compact one? 5. DILATED. Is every subnormal Toeplitz operat...

We analyze entropy solutions for a class of Lévy mixed hyperbolicparabolic equations containing a non-local (or fractional) diffusion operator originating from a pure jump Lévy process. For these solutions we establish uniqueness (L1 contraction property) and continuous dependence results.

This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positive C0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the...

Abstract. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently...

Abstract. Let T and V be two Hilbert space contractions and let X be a linear bounded operator. It was proved by C. Foias and J.P. Williams that in certain cases the operator block matrix R(X ;T, V ) (equation (1.1) below) is similar to a contraction if and only if the commutator equation X = TZ−ZV has a bounded solution Z. We characterize here the similarity to contractions of some operator ma...

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...

The study purpose was to evaluate the use of computer-automated algorithms as a replacement for subjective, visual determination of muscle contraction onset using M-mode ultrasonography. Biceps and quadriceps contraction images were analyzed visually and with three different classes of algorithms: pixel standard deviation (SD), high-pass filter and Teager Kaiser energy operator transformation. ...

We consider the off-policy evaluation problem in Markov decision processes with function approximation. We propose a generalization of the recently introduced emphatic temporal differences (ETD) algorithm (Sutton, Mahmood, and White, 2015), which encompasses the original ETD(λ), as well as several other off-policy evaluation algorithms as special cases. We call this framework ETD(λ, β), where o...