This document is an instruction manual for the complex analysis portion of the course on Mathematical Methods.
Harold V. McIntosh
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Harold V. McIntosh
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José Pedro Hernández Enríquez
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Harold V. McIntosh
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Harold V. McIntosh
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Detailed examination of the resonances in the Dirac harmonic oscillator, using results from the differential equation solver SERO.
Harold V. McIntosh
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As part of a collection of samples illustrating the use of the second order real differential equation solver SERO, some variants on the theme of periodic potentials are discussed. Constructing the stability chart for a periodic potential is one of the most important uses of the program, although details of specific solutions are also frequently called for.
Harold V. McIntosh
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REC-R is one of a series of specialized REC programs; in this case one which provides assistance in graphing the solutions of real, second order differential equations. It is therefore an adjunct to the program SERO which serves the same purpose.
Harold V. McIntosh
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In studying the symmetry groups of a crystal lattice in the presence of a magnetic field, the projective representations of these groups must be considered, because of the phase change in the wave functions which is due to the gauge transformations which accompany the geometric symmetries. These projective representations are ordinary representations of a group which is isomorphic to the generalized Dirac groups. The irreducible representations of the symmetry adapted functions of these groups can be obtained by means of techniques arising from the method of induced representations for those groups which can be exhibited as semi-direct products.
Para estudiar los grupos de simetría de una red cristalográfica en presencia de un campo magnético deben considerarse las representaciones proyectivas de dichos grupos, debido al cambio de fase que sufren las funciones de onda y que proviene de las transformaciones de norma que acompañan a las simetrías geométricas. Estas representaciones proyectivas son representaciones ordinarias de un grupo que es isomórfico a los grupos generalizados de Dirac. Las representaciones irreducibles y las funciones adaptadas a la simetría de dichos grupos se puede obtener mediante técnicas que resultan del método de representaciones inducidas para los grupos que se pueden exhibir como productos semi-directos.
Harold V. McIntosh
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Harold V. McIntosh
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Harold V. McIntosh
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Last version: May 31, 2000
Harold V. McIntosh
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A concordance for rule 110
The Typical places where various triangles can be found in Rule 110.
Harold V. McIntosh .
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The Ninth Reasearch Summer was held in Mexico during July and August, 1999. The participants in my portion of this enterprise prepared individual reports of their summer's work, which can be consulted elsewhere. So here we survey some of the background ideas, topics discussed, and mention a few of the results obtained.
Harold V. McIntosh
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Harold V. McIntosh
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Maps and cutouts for a variety of flexagons are presented, emphasizing those which can be cut out, mostly from single sheets of paper. Since TeX may not align front and back images, and in any event if cutting up the booklet is not desired, the .eps files can be printed directly to get sheets suitable for cutting. In the same spirit, only those sheets which are going to be used right away need be printed.
Harold V. McIntosh
This paper is available in Acrobat PDF (octagon.pdf) Size: 193 KB.
Maps and cutouts for a variety of flexagons are presented, emphasizing those which can be cut out, mostly from single sheets of paper. Since TeX may not align front and back images, and in any event if cutting up the booklet is not desired, the .eps files can be printed directly to get sheets suitable for cutting. In the same spirit, only those sheets which are going to be used right away need be printed.
Harold V. McIntosh
This paper is available in Acrobat PDF (heptagon.pdf) Size: 106 KB.
Maps and cutouts for a variety of flexagons are presented, emphasizing those which can be cut out, mostly from single sheets of paper. Since TeX may not align front and back images, and in any event if cutting up the booklet is not desired, the .eps files can be printed directly to get sheets suitable for cutting. In the same spirit, only those sheets which are going to be used right away need be printed.
Harold V. McIntosh
This paper is available in Acrobat PDF (hexagon.pdf) Size: 186 KB.
Maps and cutouts for a variety of flexagons are presented, emphasizing those which can be cut out, mostly from single sheets of paper. Since TeX may not align front and back images, and in any event if cutting up the booklet is not desired, the .eps files can be printed directly to get sheets suitable for cutting. In the same spirit, only those sheets which are going to be used right away need be printed.
Harold V. McIntosh
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