Unconditionally converging polynomials on Banach spaces

We prove that weakly unconditionally Cauchy (w.u.C.) series and unconditionally converging (u.c.) series are preserved under the action of polynomials or holomorphic functions on Banach spaces, with natural restrictions in the latter case. Thus it is natural to introduce the unconditionally converging polynomials, defined as polynomials taking w.u.C. series into u.c.\ series, and analogously, the unconditionally converging holomorphic functions. We show that most of the classes of polynomials which have been considered in the literature consist of unconditionally converging polynomials. Then we study several ``polynomial properties'' of Banach spaces, defined in terms of relations of inclusion between classes of polynomials, and also some ``holomorphic properties''. We find remarkable differences with the corresponding ``linear properties''. For example, we show that a Banach space $E$ has the polynomial property (V) if and only if the spaces of homogeneous scalar polynomials ${\cal P}(^k\!E)$, $k\in{\bf N}$, or the space of scalar holomorphic mappings of bounded type ${\cal H}_b(E),$ are reflexive. In this case the dual space $E^*$, like the dual of Tsirelson's space, is reflexive and contains no copies of $\ell_p$

Benchmark example problems for beams at elevated temperatures

The paper presents development of a series of solutions for beams at elevated temperatures which are supposed to serve as benchmark problems for applications of computational models in fire structural engineering. Three cases of loading i.e. pure bending, central force, and uniformly distributed loading, are considered for a simply supported, and fixed on both ends beams at uniformly distributed elevated temperature varying in time. The results are provided in terms of the midspan deflection for specified loading levels and temperatures. The results mainly obtained using finite element (FE) models and two commercial codes, are verified through comparison with analytical solutions for simplified cases and through parametric study aimed to examine the effect of modelling parameters. The numerical results are subjected to mesh density study using the grid convergence index (GCI) concept

An analysis of the Total Quality Management practices of the contractors supporting the Apache Helicopter Program

This thesis study explores the Total Quality Management (TQM) practices of the prime contractors and subtier contractors supporting the Apache Helicopter Program. The Apache Helicopter Product Manager is searching for ways to lower costs and improve the quality and reliability of his product over the long-term. The Apache Helicopter, with the Longbow upgrade, is projected to remain in service to the year 2045. The defense contractors and subcontractors supporting the Apache Helicopter Program must adopt a business operating philosophy that fosters continuous process and quality improvement Total Quality Management has become the management philosophy of choice. The subtier suppliers and vendors play an important role in the quality improvement capability of the prime contractors. The subtier contractors must also have the ability to continuously improve their process capabilities. This study intends to discover what can be done, if anything, to get the subtier contractors to adopt the management philosophy of TQM.http://archive.org/details/annalysisoftotal1094535069NANAU.S. Army (USA) autho

On (V*) sets and Pelczynski's property (V*).

The concept of (V*) set was introduced, as a dual companion of that of (V)-set, by Pelczynski in his important paper [14]. In the same paper, the so called properties (V) and (V*) are defined by the coincidence of the (V) or (V*) sets with the weakly relatively compact sets. Many important Banach space properties are (or can be) defined in the same way; that is, by the coincidence of two classes of bounded sets. In this paper, we are concerned with the study of the class of (V*) sets in a Banach space, and its relationship with other related classes. To this general study is devoted Section I. A (as far as we know) new Banach space property (we called it property weak (V*)) is defined, by imposing the coincidence of (V*) sets and weakly conditionally compact sets. In this way, property (V*) is decomposed into the conjunction of the weak (V*) property and the weak sequential completeness. In Section II, we specialize to the study of (V*) sets in Banach lattices. The main result in the section is that every order continuous Banach lattice has property weak (V*), which extends previous results of E. and P. Saab ([16]). Finally, Section III is devoted to the study of (V*) sets in spaces of Bochner integrable functions. We characterize a broad class of (V*) sets in L1(μ, E), obtaining similar results to those of Andrews [1], Bourgain [6] and Diestel [7] for other classes of subsets. Applications to the study of properties (V*) and weak (V*) are obtained. Extension of these results to vector valued Orlicz function spaces are also given

Multirectangular invariants for power Köthe spaces

Using some new linear topological invariants, isomorphisms and quasidiagonal isomorphisms are investigated on the class of first type power Köthe spaces [Proceedings of 7th Winter School in Drogobych, 1976, pp. 101–126; Turkish J. Math. 20 (1996) 237–289; Linear Topol. Spaces Complex Anal. 2 (1995) 35–44]. This is the smallest class of Köthe spaces containing all Cartesian and projective tensor products of power series spaces and closed with respect to taking of basic subspaces (closed linear hulls of subsets of the canonical basis). As an application, it is shown that isomorphic spaces from this class have, up to quasidiagonal isomorphisms, the same basic subspaces of finite (infinite) type

Criteria for existence of Riesz bases consisting of root functions of Hill and 1D Dirac operators

We study the system of root functions (SRF) of Hill operator $Ly = -y^{\prime \prime} +vy$ with a singular potential $v \in H^{-1}_{per}$ and SRF of 1D Dirac operator Ly = i {pmatrix} 1 & 0 0 & -1 {pmatrix} \frac{dy}{dx} + vy with matrix $L^2$-potential v={pmatrix} 0 & P Q & 0 {pmatrix}, subject to periodic or anti-periodic boundary conditions. Series of necessary and sufficient conditions (in terms of Fourier coefficients of the potentials and related spectral gaps and deviations) for SRF to contain a Riesz basis are proven. Equiconvergence theorems are used to explain basis property of SRF in $L^p$-spaces and other rearrangement invariant function spaces