Lattice parameter and luminescence properties of europium activated yttrium oxide

Samples of yttrium oxide doped with trivalent europium have been prepared by ceramic techniques, under different synthesis conditions; barium chloride (BaCl₂) and sodium tetraborate (Na₂B₄O₇) were tested as flux. The improvement of luminescence properties in dependence on substitution of Eu³⁺ for Y³⁺ in the host lattice, under electron and UV excitations is demonstrated. The lattice parameter as a quantitative assessment of activator incorporation degree is proposed. The obtained results are discussed with respect to the employed processing method.     

An Average-Stretch Full-Network Model for Rubber Elasticity

Two constitutive models that are based on the classical non-Gaussian, Kuhn-Grün probability distribution function are reviewed. It is shown that all chains of a network cell structure comprised of a finite number of identical chains in an affine deformation referred to principal axes may have the same invariant stretch, if and only if the chains are oriented initially along any of eight directions forming the diagonals of a unit cube. The 4-chain tetrahedral and the 8-chain cubic cell structures are familiar admissible models having this property. An easy derivation of the constitutive equation for the Wu and van der Giessen full-network model of initially identical chains arbitrarily oriented in the undeformed state is presented. The constitutive equations for the neo-Hookean model, the 3 -chain model, and the equivalent 4- and 8-chain models are then derived from the Wu and van der Giessen equation. The squared chain stretch of an arbitrarily directed chain averaged over a unit sphere surrounding all chains radiating from a cross-link junction as its center is determined. An average-stretch, full-network constitutive equation is then derived by approximation of the Wu and van der Giessen equation. This result, though more general in that no special chain cell morphology is introduced, is the same as the constitutive equation for the 4- and 8-chain models. Some concluding remarks on extensions to amended models are presented.     

On separation of gradient Young measures

Let be a linear subspace of real matrices without rank-one matrices and let be a finite set. Suppose is a bounded arcwise connected Lipschitz domain and is a sequence of bounded vector-valued mappings in such that in as , where is the closed -neighbourhood and the distance function to . We give estimates for such that up to a subsequence, in for some fixed . In other words, we give estimates on such that separates gradient Young measure. The two point set with is a special case of such sets up to a translation. Received: 20 July 2001 / Accepted: 23 January 2002 / Published online: 5 September 2002     

Design and Fabrication of Composite Smart Structures with High Electric and Mechanical Performances for Future Mobile Communication

In this paper, we have developed a load-bearing outer skin for antennas, which is termed a composite smart structure (CSS). The CSS is a multilayer composite sandwich structure in which antenna layers are inserted. A direct-feed stacked patch antenna is considered. A design procedure including the structure design, material selection, and design of antenna elements in order to obtain high electric and mechanical performances is presented. An optimized honeycomb thickness is selected for efficient radiation and impedance characteristics. High gain conditions can be obtained by placing the outer facesheet in the resonance position, which is at about a half wavelength distance from the ground plane. The measured electrical performances show that the CSS has a great bandwidth (over 10%) and a higher gain than an antenna without a facesheet and has excellent mechanical performances, owing to the composite laminates and honeycomb cores. The CSS concept can be extended to give a useful guide for manufacturers of structural body panels and for antenna designers.     

A Higher-Dimensional Version of the Brody Reparametrization Lemma

We prove a generalization of the Brody reparametrization lemma.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1369 – 1377, October, 2004.     

A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U     

Uniqueness for Cesàro summable double Walsh series

We prove a Tauberian theorem for Walsh series of two variables, and use it to obtain several results about uniqueness of Cesàro summable double Walsh series. Namely, we show that up to sets of measure zero, Cesàro summability of double Walsh series is the same as convergence of the square dyadic partial sums and, under a suitable growth condition, that uniqueness holds for Cesàro summable double Walsh series.     

Operational research in the UK Ministry of Defence: an overview

The paper presents a survey of operational research (OR) as it is currently used in the UK Ministry of Defence (MoD). After a short historical introduction summarising developments since 1945, it identifies the impact which the end of the Cold War has had on defence operational analysis (OA), as the discipline is generally called within MoD, in terms of the problems studied, the technical challenges presented and the techniques employed. The factors, both external and internal, that have led to the MoD maintaining and indeed expanding its OA activity against a background of falling defence budgets are discussed in the context of previously reported research on the survival and success of OR groups.     

Maximizing revenue in the airline industry under one-way pricing

The paper describes a methodology that has been implemented in a major British airline to find the optimal price to charge for airline tickets under one-way pricing. An analytical model has been developed to describe the buying behaviour of customers for flights over the selling period. Using this model and a standard analytical method for constrained optimization, we can find an expression for the optimal price structure for a flight. The expected number of bookings made on each day of the selling period and in each fare class given these prices can then be easily calculated. A simulation model is used to find the confidence ranges on the numbers of bookings and these ranges can be used to regulate the sale of tickets. A procedure to update the price structure based on the remaining capacity has also been developed.