Hauptman, Herbert A. (Herbert Aaron) 19172011
Overview
Works:  28 works in 111 publications in 2 languages and 2,027 library holdings 

Genres:  Conference papers and proceedings Abstracts 
Roles:  Author, Author of introduction, Editor 
Classifications:  QA241, 512.72 
Publication Timeline
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Most widely held works about
Herbert A Hauptman
 On the beauty of science : a Nobel laureate reflects on the universe, God, and the nature of discovery by Herbert A Hauptman( Book )
 Herbert Hauptman : portrait of a laureate( Visual )
 Hauptman, Herbert Aaron : xray crystallography( )
Most widely held works by
Herbert A Hauptman
101 great ideas for introducing key concepts in mathematics : a resource for secondary school teachers by
Alfred S Posamentier(
Book
)
6 editions published between 2000 and 2001 in English and held by 344 WorldCat member libraries worldwide
Offers teachers tools and ideas for introducing concepts and topics common to all secondary mathematic subjects including algebra, geometry, and trigonometry
6 editions published between 2000 and 2001 in English and held by 344 WorldCat member libraries worldwide
Offers teachers tools and ideas for introducing concepts and topics common to all secondary mathematic subjects including algebra, geometry, and trigonometry
Crystal structure determination; the role of the cosine seminvariants by
Herbert A Hauptman(
Book
)
14 editions published in 1972 in English and Undetermined and held by 263 WorldCat member libraries worldwide
The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the socalled structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the Emap (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role
14 editions published in 1972 in English and Undetermined and held by 263 WorldCat member libraries worldwide
The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the socalled structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the Emap (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role
101+ great ideas for introducing key concepts in mathematics : a resource for secondary school teachers by
Alfred S Posamentier(
Book
)
5 editions published in 2006 in English and held by 256 WorldCat member libraries worldwide
Contains a compilation of 116 ideas and suggestions for secondary school teachers to introduce key mathematics concepts to students. Ideas are organized by subject area, and identify the "objective," "materials," and "procedure" for each technique
5 editions published in 2006 in English and held by 256 WorldCat member libraries worldwide
Contains a compilation of 116 ideas and suggestions for secondary school teachers to introduce key mathematics concepts to students. Ideas are organized by subject area, and identify the "objective," "materials," and "procedure" for each technique
Table of all primitive roots for primes less than 5000 by
Herbert A Hauptman(
Book
)
12 editions published between 1970 and 1971 in English and held by 134 WorldCat member libraries worldwide
Although primitive roots have played an important role in the development of the classical theory of numbers, knowledge of their distribution is still limited. The Naval Research Laboratory has produced and publishes herein a table of all the primitive roots of the primes less than 5000, the most extensive tabulation of its kind now available. Also presented are a description of its construction and a brief historical account of a number of conjectures and several recent results. (Author)
12 editions published between 1970 and 1971 in English and held by 134 WorldCat member libraries worldwide
Although primitive roots have played an important role in the development of the classical theory of numbers, knowledge of their distribution is still limited. The Naval Research Laboratory has produced and publishes herein a table of all the primitive roots of the primes less than 5000, the most extensive tabulation of its kind now available. Also presented are a description of its construction and a brief historical account of a number of conjectures and several recent results. (Author)
Solution of the phase problem. 1. The centrosymmetric crystal, by Herbert Hauptman and Jerome Karle by
Herbert A Hauptman(
Book
)
24 editions published in 1953 in English and held by 126 WorldCat member libraries worldwide
24 editions published in 1953 in English and held by 126 WorldCat member libraries worldwide
Combinatorial image analysis : 12th international workshop, IWCIA 2008, Buffalo, NY, USA, April 79, 2008 : proceedings by
Valentin E Brimkov(
Book
)
10 editions published in 2008 in English and Undetermined and held by 75 WorldCat member libraries worldwide
This volume constitutes the refereed proceedings of the 12th International Workshop on Combinatorial Image Analysis, IWCIA 2008, held in Buffalo, NY, USA, in April 2008. The 28 revised full papers and 10 revised poster papers presented were carefully reviewed and selected from 117 initial submissions. The papers are organized in topical sections on digital geometry and topology, curves and surfaces, combinatorics in digital spaces: lattice polygons, polytopes, tilings, and patterns, image representation, segmentation, grouping, and reconstruction, applications of computational geometry, integer and linear programming to image analysis, fuzzy and stochastic image analysis, parallel architectures and algorithms, grammars and models for image or scene analysis, as well as discrete tomography, medical imaging, and biometrics
10 editions published in 2008 in English and Undetermined and held by 75 WorldCat member libraries worldwide
This volume constitutes the refereed proceedings of the 12th International Workshop on Combinatorial Image Analysis, IWCIA 2008, held in Buffalo, NY, USA, in April 2008. The 28 revised full papers and 10 revised poster papers presented were carefully reviewed and selected from 117 initial submissions. The papers are organized in topical sections on digital geometry and topology, curves and surfaces, combinatorics in digital spaces: lattice polygons, polytopes, tilings, and patterns, image representation, segmentation, grouping, and reconstruction, applications of computational geometry, integer and linear programming to image analysis, fuzzy and stochastic image analysis, parallel architectures and algorithms, grammars and models for image or scene analysis, as well as discrete tomography, medical imaging, and biometrics
Computational Modeling of Objects Represented in Images Second International Symposium, CompIMAGE 2010, Buffalo, NY, USA,
May 57, 2010. Proceedings by
Reneta P Barneva(
)
7 editions published in 2010 in English and held by 38 WorldCat member libraries worldwide
7 editions published in 2010 in English and held by 38 WorldCat member libraries worldwide
Solution of the phase problem. I. The centrosystemmetric crystal by
Herbert A Hauptman(
Book
)
2 editions published in 1953 in English and held by 27 WorldCat member libraries worldwide
2 editions published in 1953 in English and held by 27 WorldCat member libraries worldwide
Direct methods in crystallography : proceedings of the Intercongress Symposium ; sponsored by the International Union of Crystallography
and the Medical Foundation of Buffalo, Inc. Research Laboratories and held in Buffalo, New York, August 36, 1976 by Intercongress Symposium(
Book
)
3 editions published in 1978 in English and held by 26 WorldCat member libraries worldwide
3 editions published in 1978 in English and held by 26 WorldCat member libraries worldwide
Some labeling theorems for planar linear graphs : a contribution to the fourcolor problem by Horace Maynard Trent(
Book
)
2 editions published in 1969 in English and held by 9 WorldCat member libraries worldwide
According to Courant and Robbins, the fourcolor problem was probably proposed by Mobius in 1840. It was proposed again by De Morgan in 1850 and by Cayley in 1878. The problem may be stated as follows: Given any linear graph which will map on a plane (or sphere), it is possible to assign one of four colors to each face of the map so that no two faces colored alike have a common edge on their boundaries. In 1879 Kempe published a proof of the conjecture. However, in 1890, Heawood showed that Kempe's proof was defective, by use of a counterexample that disproved one of Kempe's assertions. The portion of this manuscript from Comment 18 through Lemma 24 is designed to take care of the analog to Heawood's counterexample. In the same paper, Heawood showed that five colors were sufficient to color a planar map. The problem has received much attention in the intervening years. Although a number of interesting results have been obtained since 1890, no one has been able to exhibit a planar graph that required more than four colors, nor has anyone been able to prove that four colors were sufficient in all cases. The situation up to now is summed up rather well by Courant and Robbins, 'Despite the efforts of many famous mathematicians, the matter essentially rests with this more modest result: It has been proved that five colors suffice for all maps and it is conjectured that four will likewise suffice.' This manuscript presents a new approach to and a partial proof of the conjecture. (Author)
2 editions published in 1969 in English and held by 9 WorldCat member libraries worldwide
According to Courant and Robbins, the fourcolor problem was probably proposed by Mobius in 1840. It was proposed again by De Morgan in 1850 and by Cayley in 1878. The problem may be stated as follows: Given any linear graph which will map on a plane (or sphere), it is possible to assign one of four colors to each face of the map so that no two faces colored alike have a common edge on their boundaries. In 1879 Kempe published a proof of the conjecture. However, in 1890, Heawood showed that Kempe's proof was defective, by use of a counterexample that disproved one of Kempe's assertions. The portion of this manuscript from Comment 18 through Lemma 24 is designed to take care of the analog to Heawood's counterexample. In the same paper, Heawood showed that five colors were sufficient to color a planar map. The problem has received much attention in the intervening years. Although a number of interesting results have been obtained since 1890, no one has been able to exhibit a planar graph that required more than four colors, nor has anyone been able to prove that four colors were sufficient in all cases. The situation up to now is summed up rather well by Courant and Robbins, 'Despite the efforts of many famous mathematicians, the matter essentially rests with this more modest result: It has been proved that five colors suffice for all maps and it is conjectured that four will likewise suffice.' This manuscript presents a new approach to and a partial proof of the conjecture. (Author)
101 (+13) great ideas for introducing key concepts in mathematics : a resource for secondary school educators by
Alfred S Posamentier(
Book
)
1 edition published in 2006 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 7 WorldCat member libraries worldwide
Direct methods in crystallography : proceedings of the intercongress symposium(
Book
)
2 editions published in 1976 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1976 in English and held by 6 WorldCat member libraries worldwide
The fabulous Fibonacci numbers by
Alfred S Posamentier(
Book
)
3 editions published between 2007 and 2014 in English and Polish and held by 4 WorldCat member libraries worldwide
Explores the complexity and wideranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers
3 editions published between 2007 and 2014 in English and Polish and held by 4 WorldCat member libraries worldwide
Explores the complexity and wideranging applications of the Fibonacci sequence, which appears in nature, art, economics, and the "golden ratio," which is derived from this simple pattern of numbers
The centrosymmetric crystal by
Herbert A Hauptman(
Book
)
2 editions published in 1953 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1953 in English and held by 3 WorldCat member libraries worldwide
Galois theory of equations by
Herbert A Hauptman(
)
2 editions published in 1939 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1939 in English and held by 2 WorldCat member libraries worldwide
Computer Program for the LeastSquares Determination of the Phases of the Crystal Structure Factors by J. H Hancock(
Book
)
2 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
An effective technique, employing the Principle of Least Squares, which leads from the values of the crystal structure invariants to the values of individual phases, has recently been obtained. In the present report the details of the computer program which implements this technique are described. An auxiliary program to identify the required structure invariants has also been written and is contained herein. (Author)
2 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
An effective technique, employing the Principle of Least Squares, which leads from the values of the crystal structure invariants to the values of individual phases, has recently been obtained. In the present report the details of the computer program which implements this technique are described. An auxiliary program to identify the required structure invariants has also been written and is contained herein. (Author)
Problemsolving strategies for efficient and elegant solutions : a resource for the mathematics teacher by
Alfred S Posamentier(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
The text demonstrates ten of the most common problemsolving strategies, and stresses that teachers should present them as useful tools for everyday life
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
The text demonstrates ten of the most common problemsolving strategies, and stresses that teachers should present them as useful tools for everyday life
Computer Program for the Calculation of the Crystal Structure Invariants Based on Certain Conditonal Distributions by Janet E Fisher(
Book
)
2 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Effective techniques leading from the values of the crystal structure invariants to the values of the individual phases have recently been obtained. In the present report a new formula expressing the structure invariants in terms of the observed crystal structure amplitudes is given, and a computer program is described which facilitates the computation of the invariants. (Author)
2 editions published in 1970 in English and held by 2 WorldCat member libraries worldwide
Effective techniques leading from the values of the crystal structure invariants to the values of the individual phases have recently been obtained. In the present report a new formula expressing the structure invariants in terms of the observed crystal structure amplitudes is given, and a computer program is described which facilitates the computation of the invariants. (Author)
The conditional probability distribution of crystal structure invariants(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
New methods for solving complex noncentrosymmetric crystal structures have been developed at NRL. A vital part of the method involves evaluating the structure invariants cos(phi(sub vector h(sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))), where vectors ((h sub 1) + (h sub 2) + (h sub 3)) = 0, directly from the normalized structure factor amplitudes. The theoretical conditional probability distribution of cos(phi(sub vector h (sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))) and the theoretical expected values of the structure invariants are essential to this computation. This report tabulates the conditional distribution and the expectations. (Author)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
New methods for solving complex noncentrosymmetric crystal structures have been developed at NRL. A vital part of the method involves evaluating the structure invariants cos(phi(sub vector h(sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))), where vectors ((h sub 1) + (h sub 2) + (h sub 3)) = 0, directly from the normalized structure factor amplitudes. The theoretical conditional probability distribution of cos(phi(sub vector h (sub 1)) + phi (sub vector h (sub 2)) + phi (sub vector h (sub 3))) and the theoretical expected values of the structure invariants are essential to this computation. This report tabulates the conditional distribution and the expectations. (Author)
Research notes, Nobel lecture and biographies by
Herbert A Hauptman(
)
in English and held by 1 WorldCat member library worldwide
Four sets of Dr. Hauptman's notes regarding his research into the molecular structures of crystallized materials, ca. 1985; a published copy of his Nobel lecture, "Direct Methods and Anamalous Dispersion," given 9 Dec. 1985; and biographical information, 19921995
in English and held by 1 WorldCat member library worldwide
Four sets of Dr. Hauptman's notes regarding his research into the molecular structures of crystallized materials, ca. 1985; a published copy of his Nobel lecture, "Direct Methods and Anamalous Dispersion," given 9 Dec. 1985; and biographical information, 19921995
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Canada Combinatorial analysis Computational complexity Computer algorithms Computer graphics Computer science Computer software Computer vision Crystallographers Crystallography Crystallography, Mathematical Crystals Electronic data processing Equations, Simultaneous Fibonacci numbers Fourcolor problem Graph theory Hauptman, Herbert A.(Herbert Aaron), Image analysis Image processing Image processingData processing Invariants Mathematicians MathematicsStudy and teaching (Secondary) New York (State)Buffalo Nobel Prize winners Optical pattern recognition Pattern perception Phase rule and equilibrium Physics Probabilities Problem solving Roots, Numerical Scientists United States Xray crystallography
Alternative Names
Hauptman, H.A.
Hauptman, Herbert 19172011
Hauptman, Herbert A.
Hauptman, Herbert Aaron.
Hauptman, Herbert Aaron 19172011
Herbert A. Hauptman Amerikaans wiskundige
Herbert A. Hauptman amerikansk matematikar
Herbert A. Hauptman amerikansk matematiker
Herbert A. Hauptman matemàtic estatunidenc
Herbert A. Hauptman matemático estadounidense
Herbert A. Hauptman USamerikanischer Mathematiker, Biophysiker und Nobelpreisträger für Chemie
Herbert Aaron Hauptman
Herbert Aaron Hauptman mathématicien américain
Herbert Hauptman amerikansk matematiker
Herbert Hauptman amerykański matematyk i chemik, noblista
Herbert Hauptman matematico e chimico statunitense
Герберт Аарон Гауптман
Хауптман, Херберт Аарон
Հերբերտ Արոն Հաուպտման
הרברט האופטמן
הרברט האופטמן מתמטיקאי אמריקאי
هربرت هاپتمن ریاضیدان آمریکایی
هيربرت هاوبتمان
هيربرت هاوبتمان رياضياتي أمريكي
ہربرٹ اے ہاوپٹمین
ہربرٹ ہاؤپٹمین
হার্বার্ট হপ্টম্যান
হার্বার্ট হপ্টম্যান মার্কিন গণিতবিদ
하우프트만, 헤르트 A
ハーバート・ハウプトマン
赫伯特·豪普特曼
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