Noninvasive Measurement of Perfusion in Rabbit VX2 Tumors Using Flow sensitive Alternting Inversing Recovery with an Extra Radiofrequency Pulse

Introduction:MR arterial spin-labeling technique is useful to measure tissue perfusion. The purpose of this study was to evaluate the feasibility of using a novel arterial spin-labeling technique to characterize regions of hyper and hypovascularity in experimental tumors in rabbits.     

How Important are Models to Operational Research?

This paper starts from the assumption that the use of modelsis central to the methodology of operational research (OR).The concept is clarified by reference to its formal use in mathematicallogic. A justification for the use of models in decision makingis given. This is contrasted with the reasons why traditionalOR models are frequently not used by practising OR workers (letalone managers). An attempt is made to resolve this contrastbetween the practice of OR by academics with those closer tocommercial decision making. The proper relationship betweenthe two activities is suggested.     

Integer programming and pricing revisited

Three applications of duality are mentioned: mathematical, computational,and economic. One of the earliest attempts toproduce a dualof an integer programme with economic interpretations was byGomory & Baumol in 1960. This is describedtogether withits economic properties and some refinements and corrections.A more recent integer programming dual due to Chvátal,whose main use to date has been computational, is then described.It is shown that this can be given an economic interpretationas a generalization of Gomory & Baumol‘s dual whichrectifies some of the deficiencies of the latter. The computationalproblems of calculating Chvátal’s dual are remarkedon.     

Best Chebyshev approximation from families of ordinary differential equations

Within the framework of the Meinardus and Schwedt theory ofnonlinear Chebyshev approximation we consider the approximationof functions and data by approximants generated from the solutionof parameter dependent initial value problems in ordinary differentialequations. New results are obtained for the uniqueness and characterizationof best approximations in terms of properties of the differentialequation. Some examples of new approximating families are givenalong with computed best approximations.     

Reflection at a Discontinuity in a Transmission Line

An exact expression is obtained for the reflection coefficientwhen a TEM wave, propagating along a co-axial line in a regionwhere both conductors are perfectly conducting, is incidenton a region where the inner conductor consists of dielectriccoated with a resistive film whilst the outer conductor remainsperfectly conducting.     

Note on a Singular Integral Equation

A simple direct relationship is.established between solutionsof a singular integral equation encountered in wave-guide theoryand in the theory of dislocations and the solutions of the singularCarleman integral equation.