Electromagnetic forces in high field magnet coils

There has been considerable study in recent years of the mechanical effects of the electromagnetic forces in large high field magnet coils. The problem of supporting the electromagnetic forces acting on the windings has become a limiting factor in the design of such magnets. Caldwell has already obtained a mathematical model representing the stress distribution in magnet windings but a number of simplifying assumptions were made in deriving the equations. This paper checks the accuracy of this method by comparing it with homogeneous thick cylinder theory which involves the calculation of stresses by solving the Timoshenko stress equations. Thus values of the circumferential stress are compared for two different coil configurations and reasonable agreement is obtained.     

Electromagnetic field in a neighborhood of a focus

The hf wave field near a focus in an inhomogeneous medium is described by a recurrent system of equations the solutions of which are matched with various incoming and corresponding outgoing waves. In particular, a homocentric diaphragm ray solution is considered.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 126–136, 1976.     

Contact singularities

 A contact singularity is a normal singularity (V,0) together with a holomorphic contact form η on V\ Sing V in a neighbourhood of 0, i.e. η∧ (dη) ^r has no zero, where dim V=2r+1. The main result of this paper is that there are no isolated contact singularities. Received: 15 February 2001 / Revised version: 29 April 2002     

Electromagnetic field theory solution of the infinite tapered-plane transmission line

Zusammenfassung Für den eingeschwungenen Zustand dertapered-plane transmission line wird eine neue Lösungsmethode beschrieben und gezeigt, dass die Impedanztransformation direkt vom Verhältnis der Abstände zwischen Anfang und Ende der leitenden Ebenen bestimmt wird. Die Phasendifferenz der Spannungen zwischen den Leitungsenden ist dem Öffnungswinkel der beiden Ebenen proportional. Kriterien für den Entwurf solcher Leitungen lassen sich angeben.

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This work was submitted byNoach Amitay in partial fulfillment of the Degree Doctor of Philosophy.     

Weakly-exceptional quotient singularities

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D _n , E ₆, E ₇, E ₈. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.     

Log terminal singularities

The aim of this work is to simplify the definitions related to the study of singularities of normal varieties initiated in [3 de Fernex, T., Hacon, C. (2009). Singularities on normal varieties. Singularities on normal varieties 145, Fasc. 2:393–414. [Google Scholar]] and [8 Urbinati, S. (2012). Discrepancies of non-?-Gorenstein varieties. Michigan Math. J. 61(2):265–277.[Crossref], [Web of Science ®] , [Google Scholar]]. We introduce a notion of discrepancy for normal varieties, and we define log terminal⁺ singularities. We use finite generation to relate these new singularities with log terminal singularities (in the sense of [3 de Fernex, T., Hacon, C. (2009). Singularities on normal varieties. Singularities on normal varieties 145, Fasc. 2:393–414. [Google Scholar]]).