We study the asymptotic behaviour of the powers T of a composition operator T on an arbitrary Banach space X of holomorphic functions on the open unit disc D of C. We show that for composition operators, one has the following dichotomy: either the powers converge uniformly or they do not converge even strongly. We also show that uniform convergence of the powers of an operator T ∈ L(X) is very ...

Various notions of coverage provided by wireless sensor networks have attracted considerable attention over the past few years. In general, coverage can be expressed geometrically, by relating the positions, and associated coverage regions, of individual sensors to some underlying surveillance domain. The most natural notion is area coverage, where the goal is to achieve coverage for all points...

We present a procedure for computing the convolution of exponential signals without the need of solving integrals or summations. The procedure requires the resolution of a system of linear equations involving Vandermonde matrices. We apply the method to solve ordinary differential/difference equations with constant coefficients. 1 Notation and Definitions Below we introduce the definitions and ...

This supplement contains our reworking of Neyman's calculations. It is important to note that, although our proofs may not be technically elegant, they are designed to reveal explicitly the errors of Neyman (1935). A.1 Randomized Complete Block Designs Consider N blocks and T treatments, with each block having T experimental units, and treatments randomized to experimental units independently a...

The molecular structures of the two lowest melting oddand even-numbered α,β-unsaturated carboxylic acids—(E)-hept-2-enoic acid (C7) and (E)-oct-2-enoic acid (C8)—are herein reported. The title compounds were crystallized by slow evaporation of ethanolic solutions at ́30 ̋C. C7 crystallizes in the triclinic space group P1 with two molecules in the unit cell and C8 in the monoclinic space group C2...

A new method of reliability analysis of complex systems and software supporting is suggested. It is based on modelling of their evolution by means of semi–Markov processes. The results are obtained under general assumptions concerning the distributions of failure and repair times of the system’s unit. We will consider a complex system S with repairable units. It consists from N, (N ≥ 1) units a...

Given a compact connected set E in the unit disk B2, we give new upper bound for conformal capacity of condenser (B2,E) terms hyperbolic diameter t E. Moreover, t>0, construct and apply novel numerical methods to show that it has larger than with same diameter. The is called Reuleaux triangle geometry constant width equal t.

Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$‎. ‎We investigate some operator theoretic properties of‎ ‎bilateral composition operator $C_{ph‎, ‎T}‎: ‎f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq‎ ‎+infty$.‎ ‎Compactness and weak compactness of $C_{ph‎, ‎T}$ on $H^p(X)$‎ ‎are characterized an...

A nonrelational theory of cross-modal matching, including magnitude estimation, is proposed for the general class of 1-dimensional measurement structures that have real-unit (ratio and interval scale) representations. A key feature of these structures is that each point of the structure can be mapped into each other point by a translation, which is the structural analogue of ratio scale transfo...

Every collection of n (arbitrary-oriented) unit squares can be packed translatively into any equilateral triangle of side length 2.3755 ̈ ? n. Let the coordinate system in the Euclidean plane be given. For 0 ≤ αi ă π{2, denote by Spαiq a square in the plane with sides of unit length and with an angle between the x-axis and a side of Spαiq equal to αi. Furthermore, let T psq be an equilateral tr...