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Topic: Solomon Golomb

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	Solomon W. Golomb - Wikipedia, the free encyclopedia
		Golomb rulers, used in astronomy and in data encryption, are also named for him.
		Golomb received a B.A. from Johns Hopkins University and an M.A. and a Ph.D. degree in mathematics from Harvard University in 1957 with a dissertation on "Problems in the Distribution of the Prime Numbers".
		Golomb pioneered the identification of the characteristics and merits of maximum length shift register sequences, also known as pseudorandom or pseudonoise sequences, which have extensive military, industrial and consumer applications.
	en.wikipedia.org /wiki/Solomon_W._Golomb (412 words)

	Golomb ruler - Wikipedia, the free encyclopedia
		In mathematics, a Golomb ruler, named after Solomon W. Golomb, is a set of marks at integer positions along an imaginary ruler such that no two pairs of marks are the same distance apart.
		Translation and reflection of a Golomb ruler are considered trivial, so the smallest mark is customarily put at 0 and the next mark at the smaller of its two possible values.
		One practical use of Golomb rulers is in the design of phased array radio antennae such as radio telescopes.
	en.wikipedia.org /wiki/Golomb_ruler (609 words)

	Golomb Rulers - The Search For 20 and 21!
		Golomb rulers refer to a spacing technique that is used in a variety of areas such as astronomy (placement of antennas), xray sensing devices (placement of sensors), and myriad other fields such as data encryption.
		Golomb rulers are named after Dr. Solomon W. Golomb, a professor of Mathematics with a special interest in combinatorial analysis, number theory, coding theory and communications.
		Golomb rulers can play a significant role in combinatorics, coding theory and communications, and Dr. Golomb was one of the first to analyze them for use in these areas.
	members.aol.com /golomb20/intro.htm (1581 words)

	USC Viterbi School of Engineering : Sol Golomb Elected to NAS
		Golomb is holder of the Andrew and Erna Viterbi Chair in Communications in the USC School of Engineering.
		The election of Golomb brings to 11 the number of USC faculty who are members of the NAS; nine are in the college, while Golomb's colleague Robert E. Hellwarth now shares with Golomb the rare distinction of membership in both the NAS and the NAE.
		At USC, Golomb was president of the Faculty Senate from 1976 to 1977 and vice provost for research from 1986 to 1989.
	viterbi.usc.edu /news/news/2003/2003_04_30_golomb.htm (1156 words)

	Co to linijka Golomba? (Site not responding. Last check: 2007-11-03)
		Golomb, a professor of Mathematics with a special interest in combinatorial analysis, number theory, coding theory and communications.
		Golomb rulers can also play a significant role in combinatorics, coding theory and communications, and Dr. Golomb was one of the first to analyze them for use in these areas.
		Golomb rulers are usually characterized by their differences, rather than absolute distances as in the above diagram.
	republika.pl /zimniak/golomb.html (483 words)

	Graceful Graphs
		Graceful graphs are the creation of Solomon W. Golomb, professor of electrical engineering and mathematics at the University of Southern California.
		Golomb rulers with more than 4 divisions (not perfect Golomb rulers) are those which measure unique lengths.
		To locate a distant radio source, it is essential to determine the angle between the antenna baseline and the direction of the wave fronts arriving from the source.
	kevingong.com /Math/GracefulGraphs.html (2204 words)

	Modular and Regular Golomb Rulers
		Golomb rulers of the same length are used to generate self-orthogonal codes, codes that do not share common differences.
		For a Golomb ruler with n marks to be perfect it must be of length n choose 2, because if it were shorter then some distance would be measured twice since there are less distances than measurements.
		Modular Golomb Rulers, sometimes called Circular Golomb Rulers, are a particular case of Golomb Rulers that have a near optimal construction.
	cgm.cs.mcgill.ca /~athens/cs507/Projects/2003/JustinColannino (1902 words)

	USC College : News : NAS Greets Golomb With Open Arms
		Golomb came to USC in 1963 and has served in numerous academic capacities.
		Golomb also has the rare distinction of membership in both the NAS and the National Academy of Engineering.
		Golomb earned his bachelor’s degree from Johns Hopkins University, and his master’s and doctoral degrees from Harvard University, all in mathematics.
	www.usc.edu /schools/college/news/golomb.html (454 words)

	USC Trojan Family Magazine - Winter 1999: In Support: Great Communicators
		Solomon W. Golomb, an expert in digital and space communications, will be the first holder of the Andrew and Erna Viterbi Chair in Communications, according to an announcement by dean of engineering Leonard Silverman.
		Golomb and Viterbi have been friendsand colleagues since Viterbi was a member of Golomb’s research section at Caltech’s Jet Propulsion Laboratory in the 1950s.
		Golomb’s worldwide fame in communications theory rests on the continuing significance of work he began more than 40 years ago – and has been at the forefront of developing ever since.
	www.usc.edu /dept/pubrel/trojan_family/winter99/insupport/Viterbi.html (601 words)

	MATHEWS: Golomb Rulers
		A Golomb ruler is defined as a ruler which has marks at integer locations such that the distance between any two marks of the ruler is unique.
		Note that the mirror image of a optimum Golomb ruler is also optimum and only one of the two mirror rulers is mentioned in the table.
		Golomb rectangles are introduced by J. Robinson as two-dimensional arrays N X M of ones and zeros such that the difference between the positions of every pair of ones in the array, considered as vectors, are distinct.
	www.wschnei.de /number-theory/golomb-rulers.html (651 words)

	MegaMath Challenge #2 Find a HexaTriNet
		A Golomb Ruler is a set of integers such that no two pairs of numbers from the set have the same difference.
		Solomon W. Golomb, a professor of Mathematics with interests in number theory, coding theory, and communications.
		A Golomb ruler is a way to place marks along a line so that each pair of marks measures a unique distance.
	home1.gte.net /res0quh7/hexa.html (462 words)

	Graceful Graphs: Connections to Golomb Rulers and Other Studies (Site not responding. Last check: 2007-11-03)
		The Golomb ruler can be described as a problem in radio astronomy: Using as few telescopes as possible (telescopes are expensive), construct a line of telescopes such that for every distance between 1 and N (for some N), there is a pair of telescopes that far apart from each other.
		Such a labelling is what Golomb called a graceful labelling of the graph, which is then said to be graceful.
		However, Golomb was not the first to study graceful labellings; Alexander Rosa studied them under the notion of alpha- and beta-valuations.
	www.qbrundage.com /michaelb/pubs/graceful/golomb.html (294 words)

	Math Games: Rulers, Arrays, and Gracefulness
		Solomon Golomb became interested in this intermodulation-avoidance array, and changed the problem to a ruler with minimal markings.
		This property is similar to Golomb rulers, except the differences are allowed to be negative or positive, and uniqueness is only enforced within a given row.
		Solomon W. Golomb, Herbert Taylor, "Construction and Properties of Costas Arrays", Proceedings of the IEEE, Vol.
	www.maa.org /editorial/mathgames/mathgames_11_15_04.html (1796 words)

	Solomon W. Golomb, Ph.D. (Site not responding. Last check: 2007-11-03)
		Dr. Golomb, while completing his Ph.D., spent a year in Norway as a Fulbright Fellow.
		Golomb, who joined USC as a Professor in 1963, is a member of the National Academy of Engineering and a Fellow of both the IEEE and AAAS.
		He received the USC Presidential Medallion in 1985, was awarded the title of University Professor in 1993, and won the Shannon Award of the Information Theory Society of the IEEE in 1985 and the Hamming Medal of the IEEE in 2000.
	ee.usc.edu /faculty_staff/bios/golomb.html (204 words)

	Solomon Golomb (Site not responding. Last check: 2007-11-03)
		For Solomon Golomb, mathematician and inventor of pentaminoes.
		If two squares side by side is a "domino", then n squares joined side by side to make a shape is a "polyomino", an idea invented by mathematician Solomon Golomb of USC.
		There are twelve pentaminoes and six letters in "Golomb", which leads to the nice challenge of spelling "Golomb" using just two letters to make each letter shape.
	www.scottkim.com /inversions/gallery/golomb.html (307 words)

	Golomb coding - TheBestLinks.com - Computer, Geometric distribution, Entropy coding, Unary coding, ...
		Golomb coding is a form of entropy coding invented by Solomon W. Golomb that is optimal for alphabets following geometric distributions, that is, when small values are vastly more common than large values.
		It is equivalent to Golomb coding where the tunable parameter is a power of two.
		This makes it extremely efficient for use on computers, since the division operation becomes a bitshift operation and the remainder operation becomes a bitmask operation.
	www.thebestlinks.com /Golomb_coding.html (214 words)

	Gerard's Pentomino Page
		These names were first proposed by Solomon W. Golomb in his excellent book "Polyominoes".
		Solomon Golomb can be considered the "inventor" or rather the "discoverer" of the concept of polyomoes, back in 1953.
		When Golomb's book was first published in 1965, the number of solutions of the four possible rectangular puzzles had all been determined by a computer program.
	www.xs4all.nl /~gp/pentomino.html (799 words)

	Norton Starr Checkerboard Tromino Puzzle (Site not responding. Last check: 2007-11-03)
		Golomb in a 1953 lecture and then in his 1954 article, "Checkerboards and polyominoes" [6].
		Golomb showed that a large number of deficient squares can be filled by trominoes.
		Golomb's classic book on this subject, Polyominoes, appeared in 1965 and then in a second edition, in 1994 [7].
	www.amherst.edu /~nstarr/puzzle.html (1424 words)

	USC Viterbi School of Engineering : Mars Pictures Coded by USC
		To accomplish this, the images and other information acquired by the vehicles is processed in onboard computers using coding techniques that enable the messages sent home to be far smaller -- contain far fewer symbols -- than the original raw data.
		The mathematical heart of LOCO-I are what are known as Golomb codes, building on research published in 1966 by Golomb, who had then been at USC three years.
		Golomb's name occurs more than 34 times in the original 2000 paper describing the LOCO-1.
	viterbi.usc.edu /news/news/2004/2004_01_30_mars.htm (408 words)

	Golomb's inductive proof of a tromino theorem
		Polyominos were invented by Solomon Golomb, then a 22 year-old student at Harvard, in 1954.
		You can test your understanding of Golomb's theorem by trying to tile the board manually.
		Golomb, Two Right Tromino Theorems, in The Changing Shape of Geometry, edited by C. Pritchard, Cambridge University Press, 2003
	www.cut-the-knot.org /Curriculum/Geometry/Tromino.shtml (374 words)

	American Scientist Online - Why Who Did What When (Site not responding. Last check: 2007-11-03)
		Three JPL scientists responded to the challenge: Solomon W. Golomb, a young mathematician and communication engineer; mathematician Basil Gordon, specialist in combinatorial analysis; and mathematician and electrical engineer Lloyd R. Welch, who two years later joined the Institute for Defense Analysis [sic].
		In the summer of 1957 they tackled the challenge of providing a mathematical generalization of the coding problem: What was the maximum size of a comma-free dictionary.
		Solomon W. Golomb spent several years at the Jet Propulsion Laboratory in Pasadena, California, before joining the faculty at University of Southern California in 1963, where he is currently Andrew and Erna Viterbi Professor of Communications.
	www.americanscientist.org /bookshelf/Leads01/whowrote.html (1489 words)

	Atlas: On some groups of polyominoes with similar properties by Konstantin Delchev (Site not responding. Last check: 2007-11-03)
		Since polyominoes were introduced in mathematics by Solomon Golomb in 1951 the problem for their rectification is one of the most discussed problems in the field.
		Thus one of the ways to obtain general approach to the polyominoes is to group them in sets according to their tiling properties or shape.
		We generalize Golomb's set of boot polyominoes and give a mathematical proof for the non-rectifyability of one of the L-polyominoes studied by Dahlke with the help of computer.
	atlas-conferences.com /cgi-bin/abstract/camb-44 (272 words)

	Conjectures of Golomb and Dasgupta
		This document may be reproduced and distributed for educational and non-profit purposes.
		Anirban Dasgupta (Purdue University) attributes to Solomon W. Golomb the conjecture that for every integer k > 1, n/pi(n) = k for some integer n > 1.
		In the second table, the third and fourth columns display the smallest and largest values obtained for n, such that n/pi_2(n) = k, where k is given in the first column.
	www.trnicely.net /misc/dasgupta.html (285 words)

	Golomb, S.W.: Polyominoes: Puzzles, Patterns, Problems, and Packings.
		Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago.
		In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino.
		Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.
	pup.princeton.edu /titles/5415.html (237 words)

	Inleiding (Site not responding. Last check: 2007-11-03)
		Though the idea of such shapes has been around in Recreational Mathematics since the beginning of the 1900's, it was not until the latter half of the century that they became as popular as they are today.
		In 1953 Solomon W Golomb (an American professor) first introduced their names and outlined their possibilities to mathematicians, who seized on them with considerable interest.
		They were not brought to the notice of the world in general until 1957 when Martin Gardner (in his famous column in the Scientific American) wrote about them, and they have remained a rich source of spatial recreation ever since.
	www.ping.be /~demeod/inleidinge.html (276 words)

	Polypolygon Tilings (Site not responding. Last check: 2007-11-03)
		Mathematician Solomon W. Golomb coined the term "polyomino" in 1954 for figures made from squares; by analogy, "polyiamonds" are figures made from triangles and "polyhexes" are figures made from hexagons.
		Although all sorts of other figures are possible, only these three types seem to lend themselves to a wide variety of interesting tiling problems.
		Golomb registered the term "pentomino" as a trademark for puzzles involving this set of shapes.
	www.uwgb.edu /dutchs/symmetry/polypoly.htm (195 words)

	Terrence Sejnowski (Site not responding. Last check: 2007-11-03)
		The Golombs figured that a mathematical dance performance would be just right for Terry's scientifically minded friends.
		Terry is married to high-powered medical researcher Beatrice Golomb, who had just returned from a trip to Kuwait with high ranking governmental and military officials investigating Gulf War Syndrome.
		The surprise for me was discovering that the crossbar of the T could be rationalized as a rather snaky S, reminiscent of the top crossbar of the E in EGYPTIAN.
	www.scottkim.com /inversions/gallery/terrys.html (369 words)

	Ken's Pentominoes page
		They were re-popularized by Solomon Golomb in 1953 in a talk to the Harvard Math Club.
		In his book 'Polyominoes' (copyright 1965), though, Mr Golomb says that they were discussed heavily in the 1930s - 1940s in "Fairy Chess Review" (a British puzzle magazine), and that the underlying concept goes back to ancient times and the masters of Go.
		Solomon Golomb's book "Polyominoes" has quite a bit of information about pentominoes.
	hindskw.com /pentomno.html (2865 words)

	Kadon Enterprises, More About Polyforms
		The mathematical names for the various types have usually been introduced by their respective investigators.
		Solomon Golomb started the trend with "polyominoes." Shapes made of equilateral triangles became "polyiamonds," from diamond, made of two triangles.
		Shapes made of hexagons are simply "polyhexes," and shapes made of isosceles right triangles are "polytans," from their resemblance to tangrams.
	www.gamepuzzles.com /morepoly.htm (381 words)

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