Showing papers in "Ima Journal of Applied Mathematics in 1969"
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TL;DR: In this article, a theory for the machining of an arbitrary distribution of irregularities on to an anode for the cases where the cathode profile is specified and the resultant anode shape must be found, and where a cathode curve must be designed to give a required anode curve.
Abstract: Further solutions to the potential equation with moving boundary conditions, applicable to the electrochemical machining process, are presented. A theory is proposed for the machining of an arbitrary distribution of irregularities on to an anode for the cases where the cathode profile is specified and the resultant anode shape must be found, and where a cathode profile must be designed to give a required anode shape. Limitations on the application of this theory are discussed. The effects of overpotential are also discussed; overpotential only at the cathode is shown to reduce the limiting amplitude which can be obtained on the anode, and to increase the machining time required to achieve it. Overpotential only at the anode has no effect on this limiting amplitude, but again increases the necessary machining time.
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TL;DR: In this paper, the authors considered a variational principle for Fredholm integral equations in which the range of integration is fixed but unknown, and they considered the inclusion and indentation problems in the theory of elasticity.
Abstract: : The paper considers a variational principle for Fredholm integral equations in which the range of integration is fixed but unknown. Equations of this type occur in the study of inclusion and indentation problems in the theory of elasticity. (Author)
TL;DR: In this article, the authors explain why the continued fraction of the real root of the cubic equation x3-8x-10 = 0 has a number of very large partial quotients, and then show how its consideration naturally leads one into some very deep branches of the theory of numbers before the reason for the phenomenon becomes clear.
Abstract: Brillhart discovered in 1965 that the continued fraction of the real root of the cubic equation x3—8x—10 = 0 has a number of very large partial quotients. In this paper we explain why this phenomenon is surprising and then show how its consideration naturally leads one into some very deep branches of the theory of numbers before the reason for the phenomenon becomes clear. In order to make the paper intelligible to non-specialists we give a brief account of the classical theories of continued fractions, quadratic forms and modular functions in the appropriate sections.