manu/mldr-zoomed-100char-total-queries-documents

chunk_id stringlengths 3 9	chunk stringlengths 1 100
9846_43	for the Belgian government. The purpose of this program was to "catch up" with the advances made
9846_44	in the English-speaking world during the war. It resulted in the construction of the Machine
9846_45	mathématique IRSIA-FNRS. From 1952 Belevitch represented the electrical engineering aspect of this
9846_46	project. In 1955 Belevitch became director of the Belgian Computing Centre (Comité d'Étude et
9846_47	d'Exploitation des Calculateurs Électroniques) in Brussels which operated this computer for the
9846_48	government. Initially, only the 17-rack prototype was operational. One of the first tasks to
9846_49	which it was put was the calculation of Bessel functions. The full 34-rack machine was moved from
9846_50	Antwerp and put into service in 1957. Belevitch used this machine to investigate transcendental
9846_51	functions.
9846_52	In 1963 Belevitch became head of the newly formed Laboratoire de Recherche MBLE (later Philips
9846_53	Research Laboratories Belgium) under the Philips director of research Hendrik Casimir in Eindhoven.
9846_54	This facility specialised in applied mathematics for Philips and was heavily involved in computing
9846_55	research. Belevitch stayed in this post until his retirement in November 1984.
9846_56	Belevitch died on 26 December 1999. He is survived by a daughter, but not his wife.
9846_57	Works
9846_58	Belevitch is best known for his contributions to circuit theory, particularly the mathematical
9846_59	basis of filters, modulators, coupled lines, and non-linear circuits. He was on the editorial
9846_60	board of the International Journal of Circuit Theory from its foundation in 1973. He also made
9846_61	major contributions in information theory, electronic computers, mathematics and linguistics.
9846_62	Belevitch dominated international conferences and was prone to asking searching questions of the
9846_63	presenters of papers, often causing them some discomfort. The organiser of one conference at
9846_64	Birmingham University in 1959 made Belevitch the chairman of the session in which the organiser
9846_65	gave his own presentation. It seems he did this to restrain Belevitch from asking questions.
9846_66	Belevitch stopped attending conferences in the mid-1970s with the exception of the IEEE
9846_67	International Symposium on Circuits and Systems in Montreal in 1984 in order to receive the IEEE
9846_68	Centennial Medal.
9846_69	Circuit theory
9846_70	Scattering matrix
9846_71	It was in his 1945 dissertation that Belevitch first introduced the important idea of the
9846_72	scattering matrix (called repartition matrix by Belevitch). This work was reproduced in part in a
9846_73	later paper by Belevitch, Transmission Losses in 2n-terminal Networks. Belgium was occupied by
9846_74	Nazi Germany for most of World War II and this prevented Belevitch from any communication with
9846_75	American colleagues. It was only after the war that it was discovered that the same idea, under
9846_76	the scattering matrix name, had independently been used by American scientists developing military
9846_77	radars. The American work by Montgomery, Dicke and Purcell was published in 1948. Belevitch in
9846_78	his work had applied scattering matrices to lumped-element circuits and was certainly the first to
9846_79	do so, whereas the Americans were concerned with the distributed-element circuits used at microwave
9846_80	frequencies in radar.
9846_81	Belevitch produced a textbook, Classical Network Theory, first published in 1968 which
9846_82	comprehensively covered the field of passive one-port, and multiport circuits. In this work he
9846_83	made extensive use of the now-established S parameters from the scattering matrix concept, thus
9846_84	succeeding in welding the field into a coherent whole. The eponymous Belevitch's theorem,
9846_85	explained in this book, provides a method of determining whether or not it is possible to construct
9846_86	a passive, lossless circuit from discrete elements (that is, a circuit consisting only of inductors
9846_87	and capacitors) that represents a given scattering matrix.
9846_88	Telephone conferencing
9846_89	Belevitch introduced the mathematical concept of conference matrices in 1950, so called because
9846_90	they originally arose in connection with a problem Belevitch was working on concerning telephone
9846_91	conferencing. However, they have applications in a range of other fields as well as being of
9846_92	interest to pure mathematics. Belevitch was studying setting up telephone conferencing by
9846_93	connecting together ideal transformers. It turns out that a necessary condition for setting up a
9846_94	conference with n telephone ports and ideal signal loss is the existence of an n×n conference
9846_95	matrix. Ideal signal loss means the loss is only that due to splitting the signal between
9846_96	conference subscribers – there is no dissipation within the conference network.
9846_97	The existence of conference matrices is not a trivial question; they do not exist for all values of
9846_98	n. Values of n for which they exist are always of the form 4k+2 (k integer) but this is not, by
9846_99	itself, a sufficient condition. Conference matrices exist for n of 2, 6, 10, 14, 18, 26, 30, 38
9846_100	and 42. They do not exist for n of 22 or 34. Belevitch obtained complete solutions for all n up
9846_101	to 38 and also noted that n=66 had multiple solutions.
9846_102	Other work on circuits
9846_103	Belevitch wrote a comprehensive summary of the history of circuit theory. He also had an interest
9846_104	in transmission lines, and published several papers on the subject. They include papers on skin
9846_105	effects and coupling between lines ("crosstalk") due to asymmetry.
9846_106	Belevitch first introduced the great factorization theorem in which he gives a factorization of
9846_107	paraunitary matrices. Paraunitary matrices occur in the construction of filter banks used in
9846_108	multirate digital systems. Apparently, Belevitch's work is obscure and difficult to understand. A
9846_109	much more frequently cited version of this theorem was later published by P. P. Vaidyanathan.
9846_110	Linguistics
9846_111	Belevitch was educated in French but continued to speak Russian to his mother until she died. In
9846_112	fact, he was able to speak many languages, and could read even more. He studied Sanskrit and the
9846_113	etymology of Indo-European languages.
9846_114	Belevitch wrote a book on human and machine languages in which he explored the idea of applying the
9846_115	mathematics of information theory to obtain results regarding human languages. The book
9846_116	highlighted the difficulties for machine understanding of language for which there was some naive
9846_117	enthusiasm amongst cybernetics researchers in the 1950s.
9846_118	Belevitch also wrote a paper, On the Statistical Laws of Linguistic Distribution, which gives a
9846_119	derivation for the well-known empirical relationship, Zipf's law. This law, and the more complex
9846_120	Mandelbrot law, provide a relationship between the frequency of word occurrence in languages and
9846_121	the word's rank. In the simplest form of Zipf's law, frequency is inversely proportional to rank.
9846_122	Belevitch expressed a large class of statistical distributions (not only the normal distribution)
9846_123	in terms of rank and then expanded each expression into a Taylor series. In every case Belevitch
9846_124	obtained the remarkable result that a first order truncation of the series resulted in Zipf's law.
9846_125	Further, a second-order truncation of the Taylor series resulted in Mandelbrot's law. This gives
9846_126	some insight into the reason why Zipf's law has been found experimentally to hold in such a wide
9846_127	variety of languages.
9846_128	Control systems
9846_129	Belevitch played a part in developing a mathematical test for determining the controllability of
9846_130	linear control systems. A system is controllable if it can be moved from one state to another
9846_131	through the system state space in a finite time by application of control inputs. This test is
9846_132	known as the Popov-Belevitch-Hautus, or PBH, test. There is also a PBH test for determining the
9846_133	observability of a system – that is, the ability to determine the state of a system in finite time
9846_134	solely from the system's own outputs.
9846_135	The PBH test was originally discovered by Elmer G. Gilbert in 1963, but Gilbert's version only
9846_136	applied to systems that could be represented by a diagonalizable matrix. The test was subsequently
9846_137	generalised by Vasile M. Popov (in 1966), Belevitch (in Classical Network Theory, 1968) and Malo
9846_138	Hautus in 1969.
9846_139	IEEE and honours
9846_140	Belevitch was a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and was
9846_141	vice-chair of the Benelux section when it was formed in 1959. He was awarded the IEEE Centennial
9846_142	Medal, and in 1993, the Society Award (now called Mac Van Valkenburg Award) of the IEEE Circuits

9846_43

for the Belgian government. The purpose of this program was to "catch up" with the advances made

9846_44

in the English-speaking world during the war. It resulted in the construction of the Machine

9846_45

mathématique IRSIA-FNRS. From 1952 Belevitch represented the electrical engineering aspect of this

9846_46

project. In 1955 Belevitch became director of the Belgian Computing Centre (Comité d'Étude et

9846_47

d'Exploitation des Calculateurs Électroniques) in Brussels which operated this computer for the

9846_48

government. Initially, only the 17-rack prototype was operational. One of the first tasks to

9846_49

which it was put was the calculation of Bessel functions. The full 34-rack machine was moved from

9846_50

Antwerp and put into service in 1957. Belevitch used this machine to investigate transcendental

9846_51

functions.

9846_52

In 1963 Belevitch became head of the newly formed Laboratoire de Recherche MBLE (later Philips

9846_53

Research Laboratories Belgium) under the Philips director of research Hendrik Casimir in Eindhoven.

9846_54

This facility specialised in applied mathematics for Philips and was heavily involved in computing

9846_55

research. Belevitch stayed in this post until his retirement in November 1984.

9846_56

Belevitch died on 26 December 1999. He is survived by a daughter, but not his wife.

9846_57

Works

9846_58

Belevitch is best known for his contributions to circuit theory, particularly the mathematical

9846_59

basis of filters, modulators, coupled lines, and non-linear circuits. He was on the editorial

9846_60

board of the International Journal of Circuit Theory from its foundation in 1973. He also made

9846_61

major contributions in information theory, electronic computers, mathematics and linguistics.

9846_62

Belevitch dominated international conferences and was prone to asking searching questions of the

9846_63

presenters of papers, often causing them some discomfort. The organiser of one conference at

9846_64

Birmingham University in 1959 made Belevitch the chairman of the session in which the organiser

9846_65

gave his own presentation. It seems he did this to restrain Belevitch from asking questions.

9846_66

Belevitch stopped attending conferences in the mid-1970s with the exception of the IEEE

9846_67

International Symposium on Circuits and Systems in Montreal in 1984 in order to receive the IEEE

9846_68

Centennial Medal.

9846_69

Circuit theory

9846_70

Scattering matrix

9846_71

It was in his 1945 dissertation that Belevitch first introduced the important idea of the

9846_72

scattering matrix (called repartition matrix by Belevitch). This work was reproduced in part in a

9846_73

later paper by Belevitch, Transmission Losses in 2n-terminal Networks. Belgium was occupied by

9846_74

Nazi Germany for most of World War II and this prevented Belevitch from any communication with

9846_75

American colleagues. It was only after the war that it was discovered that the same idea, under

9846_76

the scattering matrix name, had independently been used by American scientists developing military

9846_77

radars. The American work by Montgomery, Dicke and Purcell was published in 1948. Belevitch in

9846_78

his work had applied scattering matrices to lumped-element circuits and was certainly the first to

9846_79

do so, whereas the Americans were concerned with the distributed-element circuits used at microwave

9846_80

frequencies in radar.

9846_81

Belevitch produced a textbook, Classical Network Theory, first published in 1968 which

9846_82

comprehensively covered the field of passive one-port, and multiport circuits. In this work he

9846_83

made extensive use of the now-established S parameters from the scattering matrix concept, thus

9846_84

succeeding in welding the field into a coherent whole. The eponymous Belevitch's theorem,

9846_85

explained in this book, provides a method of determining whether or not it is possible to construct

9846_86

a passive, lossless circuit from discrete elements (that is, a circuit consisting only of inductors

9846_87

and capacitors) that represents a given scattering matrix.

9846_88

Telephone conferencing

9846_89

Belevitch introduced the mathematical concept of conference matrices in 1950, so called because

9846_90

they originally arose in connection with a problem Belevitch was working on concerning telephone

9846_91

conferencing. However, they have applications in a range of other fields as well as being of

9846_92

interest to pure mathematics. Belevitch was studying setting up telephone conferencing by

9846_93

connecting together ideal transformers. It turns out that a necessary condition for setting up a

9846_94

conference with n telephone ports and ideal signal loss is the existence of an n×n conference

9846_95

matrix. Ideal signal loss means the loss is only that due to splitting the signal between

9846_96

conference subscribers – there is no dissipation within the conference network.

9846_97

The existence of conference matrices is not a trivial question; they do not exist for all values of

9846_98

n. Values of n for which they exist are always of the form 4k+2 (k integer) but this is not, by

9846_99

itself, a sufficient condition. Conference matrices exist for n of 2, 6, 10, 14, 18, 26, 30, 38

9846_100

and 42. They do not exist for n of 22 or 34. Belevitch obtained complete solutions for all n up

9846_101

to 38 and also noted that n=66 had multiple solutions.

9846_102

Other work on circuits

9846_103

Belevitch wrote a comprehensive summary of the history of circuit theory. He also had an interest

9846_104

in transmission lines, and published several papers on the subject. They include papers on skin

9846_105

effects and coupling between lines ("crosstalk") due to asymmetry.

9846_106

Belevitch first introduced the great factorization theorem in which he gives a factorization of

9846_107

paraunitary matrices. Paraunitary matrices occur in the construction of filter banks used in

9846_108

multirate digital systems. Apparently, Belevitch's work is obscure and difficult to understand. A

9846_109

much more frequently cited version of this theorem was later published by P. P. Vaidyanathan.

9846_110

Linguistics

9846_111

Belevitch was educated in French but continued to speak Russian to his mother until she died. In

9846_112

fact, he was able to speak many languages, and could read even more. He studied Sanskrit and the

9846_113

etymology of Indo-European languages.

9846_114

Belevitch wrote a book on human and machine languages in which he explored the idea of applying the

9846_115

mathematics of information theory to obtain results regarding human languages. The book

9846_116

highlighted the difficulties for machine understanding of language for which there was some naive

9846_117

enthusiasm amongst cybernetics researchers in the 1950s.

9846_118

Belevitch also wrote a paper, On the Statistical Laws of Linguistic Distribution, which gives a

9846_119

derivation for the well-known empirical relationship, Zipf's law. This law, and the more complex

9846_120

Mandelbrot law, provide a relationship between the frequency of word occurrence in languages and

9846_121

the word's rank. In the simplest form of Zipf's law, frequency is inversely proportional to rank.

9846_122

Belevitch expressed a large class of statistical distributions (not only the normal distribution)

9846_123

in terms of rank and then expanded each expression into a Taylor series. In every case Belevitch

9846_124

obtained the remarkable result that a first order truncation of the series resulted in Zipf's law.

9846_125

Further, a second-order truncation of the Taylor series resulted in Mandelbrot's law. This gives

9846_126

some insight into the reason why Zipf's law has been found experimentally to hold in such a wide

9846_127

variety of languages.

9846_128

Control systems

9846_129

Belevitch played a part in developing a mathematical test for determining the controllability of

9846_130

linear control systems. A system is controllable if it can be moved from one state to another

9846_131

through the system state space in a finite time by application of control inputs. This test is

9846_132

known as the Popov-Belevitch-Hautus, or PBH, test. There is also a PBH test for determining the

9846_133

observability of a system – that is, the ability to determine the state of a system in finite time

9846_134

solely from the system's own outputs.

9846_135

The PBH test was originally discovered by Elmer G. Gilbert in 1963, but Gilbert's version only

9846_136

applied to systems that could be represented by a diagonalizable matrix. The test was subsequently

9846_137

generalised by Vasile M. Popov (in 1966), Belevitch (in Classical Network Theory, 1968) and Malo

9846_138

Hautus in 1969.

9846_139

IEEE and honours

9846_140

Belevitch was a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and was

9846_141

vice-chair of the Benelux section when it was formed in 1959. He was awarded the IEEE Centennial

9846_142

Medal, and in 1993, the Society Award (now called Mac Van Valkenburg Award) of the IEEE Circuits