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     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

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.     

Electrical properties and memory effect in the field effect transistor based on organic ferroelectric insulator and pentacene

We have fabricated a field effect transistor (FET) based on an organic ferroelectric insulator and molecular conductor, and investigated the electrical properties and memory effects on the PEN-FET. We have observed a drastic change in the drain current at around the coercive electric fieldE _c of the organic ferroelectric insulator in not only a FET (PEN-FET) based on a pentacene (PEN) film but also a FET (IPEN-FET) based on an iodine doped PEN film. The magnitude of the change of the drain current for the IPEN-FET is 200 times larger than that for the PEN-FET. It is expected from these results that the PEN-FET (especially the IPEN-FET) is an improvement in such devices, since it operates at a low gate electric field accompanied by the appearance of the spontaneous polarization in the organic ferroelectric insulator. In addition, we have found that the drain current for the PEN-FET does not return to the initial drain current ofE _G =0 V/cm for more than one week, even if the gate electric field is changed to 0 V/cm from 500 V/cm(>E _c ). From these results, it is suggested that the PEN-FET becomes a memory device.     

CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENTIABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary decimal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.     

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

Divisible Effect Algebras

Divisible effect algebras and their relations to convex effect algebras and MV-algebras are studied. A categorical equivalence between divisible effect algebras and rational vector spaces is proved. Infinitesimal, sharp and extremal elements in divisible effect algebras are studied and their relations to properties of the state space are shown.