Brian J. McCartin

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Lamé's formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition. They are shown to form a complete orthonormal system. Various properties of the spectrum and modal functions are explored. 1. Introduction. The eigenstructure(More)
A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon theMoore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrixtheoretic(More)
Imaging technologies such as cine-radiography, cine-MRI, and X-ray stereo photogrammetry have become popular diagnostic tools in biomechanical studies of musculoskeletal systems. However, their widespread use for research purposes has been restricted due to their high cost and somewhat limited availability. In an attempt to develop a reliable low cost(More)
Hikari Ltd is a publisher of international scientific journals and books. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the publisher Hikari Ltd. for all of the sacrifices that they made for their children. Preface v PREFACE In Lord Rayleigh's(More)
Previous theoretical (McCartin 1989a) and computational (McCartin 1989b) results on exponential splines are herein applied to provide approximate solutions of high order accuracy to nonlinear hyperbolic conservation laws. The automatic selection of certain "tension" parameters associated with the exponential spline allows the sharp resolution of shocks and(More)