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Planewaves, Pseudopotentials and the LAPW Method

David J. Singh Lars Nordström

Second Edition.

Resumen/Descripción – provisto por la editorial

No disponible.

Palabras clave – provistas por la editorial

Characterization and Evaluation of Materials; Optical and Electronic Materials; Solid State Physics; Spectroscopy and Microscopy; Metallic Materials

Disponibilidad
Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2006 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-28780-5

ISBN electrónico

978-0-387-29684-5

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2006

Tabla de contenidos

Introduction

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 1-3

Density Functional Theory and Methods

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 5-21

Planewave Pseudopotential Methods

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 23-41

Introduction to the LAPW Method

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 43-52

Nitty-Gritties

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 53-106

Car-Parrinello and the LAPW Method

David J. Singh; Lars Nordström

In Chapters 7 and 8we invested a good deal of time and energy in developing the many results we need from differential geometry. The time has now come to begin to reap the benefits of our investment, while at the same time developing some themes a little further for later exploitation. This chapter focuses on the celebrated volume-of-tubes formula of Wey1 [73, 168], which expresses the Lebesgue volume of a tube of radius ρ around a set embedded in ℝ or S(ℝ{sl}) in terms of the radius of the tube1 and the Lipschitz–Killing curvatures of (see Theorem 10.5.6). It is an interesting fact, particularly in view of the fact that this is a book about probability that is claimed to have applications to statistics, and despite the fact thatWeyl’s formula is today the basis of a large literature in geometry, that the origins of the volume-of-tubes formulas were inspired by a statistical problem. This problem, along with its solution due to Hotelling [79], were related to regression analysis and involved the one-dimensional volume-of-tubes problem on a sphere, not unrelated to the computation we shall do in a moment.

Pp. 107-122