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Topic: W V D Hodge

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	W. V. D. Hodge - Wikipedia, the free encyclopedia
		He was born in Edinburgh, and was the Lowndean Professor of Astronomy and Geometry at Cambridge from 1936 to 1970.
		The Hodge index theorem was a result on the intersection number theory for curves on an algebraic surface: it determines the signature of the corresponding quadratic form.
		Hodge also wrote (with Daniel Pedoe) a three-volume work on algebraic geometry with much concrete content - but illustrating what Elie Cartan called 'the debauch of indices', in its component notation.
	en.wikipedia.org /wiki/W._V._D._Hodge (476 words)

	Encyclopedia: W.-V.-D.-Hodge
		Hodge is the name of one of Samuel Johnsons cats, immortalized in a characteristically whimsical passage in James Boswells Life of Johnson: 1 The latter paragraph is used as the epigraph to Vladimir Nabokovs acclaimed poem/novel Pale Fire.
		In mathematics, Hodge theory is the study of the consequences for the algebraic topology of a smooth manifold M of the partial differential equation theory of generalised Laplacian operators associated to a Riemannian metric on M. It was developed by W. Hodge in the 1930s as an extension...
		In mathematics, the Hodge index theorem for an algebraic surface V determines the signature of the intersection pairing on the algebraic curves C on V. It says, roughly speaking, that the space spanned by such curves (up to linear equivalence) has a one-dimensional subspace on which it is positive...
	www.nationmaster.com /encyclopedia/W._V._D._Hodge (1345 words)

	Hodge theory - Wikipedia, the free encyclopedia
		In mathematics, Hodge theory is one aspect of the study of the algebraic topology of a smooth manifold M.
		The original formulation of Hodge theory, due to W. Hodge, was for the de Rham complex.
		In the case of singularities, the Hodge structure has to be modified to a mixed Hodge structure, where what survives is a filtration rather than a direct sum decomposition.
	en.wikipedia.org /wiki/Hodge_theory (673 words)

	Ca991402
		Hodge said that at one time he did ask his brother if his girlfriend might be interested in buying his half of the property but that the discussion did not lead to anything.
		Hodge also testified that appellant agreed to sell his share to appellee for $12,000; that the parties said appellee had already taken care of the $2,000 down payment; that appellant would carry the note for the $10,000 balance, payable over thirty-six months at eight percent interest; and that the monthly note would be $313.
		Hodge also testified that prior to the fire, appellee had sent him some of the monthly payments and that he in turn had sent some of those payments to appellant and applied the rest to expenses on the Rabb Apartments.
	courts.state.ar.us /opinions/2001a/20010214/ca991402.html (4449 words)

	Station Information - Hodge conjecture
		Hodge, who between 1930 and 1940 enriched the description of De Rham cohomology to include extra structure which is present in the case of algebraic varieties (though not restricted to that case).
		Suppose V is a non-singular algebraic variety of dimension n over the complex numbers.
		It is also the case that when H* is large in dimension, the example chosen as V can be regarded as somewhat special: so the conjecture discusses what you could call the interesting cases and is harder to prove, the further away we are from a generic case.
	www.stationinformation.com /encyclopedia/h/ho/hodge_conjecture.html (597 words)

	Station Information - W. V. D. Hodge
		He was born in Edinburgh, and was a professor at Cambridge from 1936 to 1970.
		In broad terms, Hodge theory contributes both to the discrete and the continous classification of algebraic varieties.
		Hodge also wrote (with Pedoe) a three-volume work on algebraic geometry with much concrete content - but illustrating what Elie Cartan called 'the debauch of indices', in its component notation.
	www.stationinformation.com /encyclopedia/w/w_/w__v__d__hodge.html (413 words)

	Hodge conjecture -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		The Hodge conjecture is a major unsolved problem of (Click link for more info and facts about algebraic geometry) algebraic geometry.
		Hodge, who between 1930 and 1940 enriched the description of (Click link for more info and facts about De Rham cohomology) De Rham cohomology to include extra structure which is present in the case of algebraic varieties (though not restricted to that case).
		Suppose V is a non-singular algebraic variety of dimension n over the (A number of the form a+bi where a and b are real numbers and i is the square root of -1) complex numbers.
	www.absoluteastronomy.com /encyclopedia/H/Ho/Hodge_conjecture.htm (608 words)

	W. V. D. Hodge (Site not responding. Last check: 2007-11-06)
		His discovery of topological relations between algebraic geometry and differentialgeometry - now called Hodge theory and pertaining more generally to Kähler manifolds - was a major influence on subsequent work.
		The Hodge indextheorem was a result on the intersection number theoryfor curves on an algebraic surface : it determines the signature of the corresponding quadratic form.
		Infact a story of Hodge's lecturing style concerned his favouring not only of subscripts and superscripts, but of the lettersr and s - which he wrote on a flboard so as to be indistinguishable.
	www.therfcc.org /w.-v.-d.-hodge-210505.html (404 words)

	Neville Hodge of Joppatowne
		Hodge constantly challenges himself and his athletes to excel both on the track and in the classroom.
		Hodge inspires to build the Morgan State track and field program to a prominent force in the Mid-Eastern Athletic Conference and beyond.
		Hodge is now the world record holder for the 100 meters for 45 year old men.
	www.virginislandspace.com /nhodge.html (388 words)

	John Hodge
		Hodge worked in Coatbridge and Motherwell and it was not until he was nearly thirty that he became involved in trade union activities.
		Hodge was a useful acquisition as he was now arguing that any industrial action in wartime was equal to treason.
		Although Hodge was also elected in the 1922 General Election his attendance in the House of Commons after the First World War was poor and he rarely spoke in debates.
	www.spartacus.schoolnet.co.uk /TUhodge.htm (723 words)

	Hodge
		Hodge was appointed to an assistant lectureship at the University of Bristol in 1926 and spent five years there.
		In 1936 Hodge had been appointed as Lowndean Professor of Astronomy and Geometry, succeeding Baker, and he held this chair at Cambridge until 1970.
		Hodge was one of the originators of the British Mathematical Colloquium, an annual conference which visits different British universities.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Hodge.html (672 words)

	Hodge conjecture (Site not responding. Last check: 2007-11-06)
		It is a conjectural description of the link between the algebraic topology of a non-singular complex algebraic variety, andits geometry as captured by polynomial equations that define sub-varieties.
		Hodge, who between 1930 and 1940 enriched the description of De Rham cohomology to include extra structure which is present in thecase of algebraic varieties (though not restricted to that case).
		It is also the case that when H* is large in dimension, the example chosen as V can be regarded as somewhatspecial: so the conjecture discusses what you could call the interesting cases and is harder to prove, the further away we arefrom a generic case.
	www.therfcc.org /hodge-conjecture-213890.html (583 words)

	Hodge conjecture: Definition and Links by Encyclopedian.com - All about Hodge conjecture (Site not responding. Last check: 2007-11-06)
		It arose as a result of the work of W.V.D. Hodge, who between 1930 and 1940 enriched the description of De Rham cohomology to include extra structure which is present in the case of algebraic varieties (though not restricted to that case).
		For example in codimension 1, which is the most accessible case geometrically using hyperplane sections, the corresponding class is in the second cohomology group and can be computed by means of the first Chern class[?].
		From what has been said, this means that the stated conditions necessary to be a combination of algebraic cycles, are also sufficient.
	www.encyclopedian.com /ho/Hodge-conjecture.html (616 words)

	Algebraic geometry - Wikipedia, the free encyclopedia
		Just as continuous functions are the natural maps on topological spaces and smooth functions are the natural maps on differentiable manifolds, there is a natural class of functions on an algebraic set, called regular functions.
		It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal topological space, where the Tietze extension theorem guarantees that a continuous function on a closed subset always extends to the ambient topological space.
		Hodge, W., and Pedoe, Daniel, Methods of Algebraic Geometry: Volume 1, Cambridge University Press, 1994, ISBN 0521469007
	en.wikipedia.org /wiki/Algebraic_geometry (1802 words)

	Edwin Hodge @ Filmbug
		At age 9, Hodge attended a cattle call for what he thought was an audition for a commercial.
		On the big screen, Hodge was most recently seen in the Dennis Quaid film, The Alamo.
		Hodge portrayed one of the battle's seven survivors who lived to tell the story.
	www.filmbug.com /db/344457 (335 words)

	W. V. D. Hodge -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		William Vallance Douglas Hodge (17 June 1903 - 7 July 1975) was a Scottish (A person skilled in mathematics) mathematician, specifically a (A mathematician specializing in geometry) geometer.
		He was born in (The capital of Scotland; located in the Lothian Region on the south side of the Firth of Forth) Edinburgh, and was a professor at (A city in eastern England on the River Cam; site of Cambridge University) Cambridge from 1936 to 1970.
		In (Click link for more info and facts about de Rham cohomology) de Rham cohomology terms, a cohomology class of degree k is represented by a k-form α on V(C).
	www.absoluteastronomy.com /encyclopedia/w/w/w._v._d._hodge.htm (490 words)

	[No title]
		A new extraction procedure which does not suffer from this disadvantage has now been introduced, and the early work is being repeated* (3) Work on the fractionation of lipids will be continued until the results for a fair number of different tobaccos are available.
		The effect of increasing puff volume is more 3120 (D. Wood) (R. Thornton) (R. Hook) (D. Miolyneux) (S. Evclyn) complex; the yield of methane always decreases, whereas the yield of carbon monoxide though decreasing for increased puff volume at one puff per minute increases when the smoking cycle is two or four puffs per minute.
		Hodge Australia BATCo document for Province of BritiSh Columbia I I November 1999 -32- Dr.
	www.library.ucsf.edu /tobacco/batco/OCR/9800/9886.txt (5339 words)

	Winston-Salem Journal \| Struggle: It was another disappointing night for Hodge (Site not responding. Last check: 2007-11-06)
		Hodge wore a stiff upper lip, determined that the Wolfpack's fourth consecutive loss signals the beginning of the turnaround rather than the beginning of the NCAA end.
		Hodge wore the vacant eyes of an All-America candidate who might not have found his name in all-county lights based on this performance.
		Hodge sought escape, grasping the ball firmly and swinging it in front of Ewing.
	www.journalnow.com /servlet/Satellite?pagename=WSJ/MGArticle/WSJ_ColumnistArticle&c=MGArticle&cid=1031780247605&path=!sports&s=1037645509200 (860 words)

	Male athlete of the year: Julius Hodge (Site not responding. Last check: 2007-11-06)
		Then came the win over Connecticut, revenge for Hodge after a controversial foul call his freshman year cost State a chance to beat the Huskies for a trip to the Sweet 16.
		This time there would be no controversy, with Hodge making the game winner, then brushing something off his shoulder on national television.
		Hodge's final resume puts him in elite company at State.
	www.technicianonline.com /story.php?id=011781 (372 words)

	Wasem v. Laskowski, 274 N.W.2d 219 (N.D. 1979)
		The term is also used to mean that the proponent has produced sufficient evidence to go to the trier of fact on the issue.
		Having found no error in the instructions given, we find no basis for a conclusion that there was an abuse of discretion in denying the motion for new trial.
		Mann's, 99 N.W.2d 849 (N.D. 1959) to the facts of that case--that the instruction given by the trial court with respect to res ipsa loquitur was an erroneous and prejudicial statement of the law.
	www.court.state.nd.us /court/opinions/9460.htm (3552 words)

	Danny Hodge: The giant Jr. Heavyweight
		As a nineteen-year-old straight out of high school, Hodge was at the time the youngest wrestler ever to represent the U.S., placing fifth at the 1952 Olympics in Helsinki in the freestyle competition.
		Hodge often wrestled outside of his weight class, taking on some of the biggest stars of the era.
		Hodge found life on the road taxing and came to hate the travel associated with pro wrestling.
	www.canoe.ca /SlamWrestlingBiosH/hodge_danny.html (1615 words)

	W. V. D. Hodge -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		For the companion of Samuel Johnson, see (Click link for more info and facts about Hodge (cat)) Hodge (cat).
		Further developments by others led in particular to an idea of mixed Hodge structure on singular varieties, and to deep analogies with (Click link for more info and facts about étale cohomology) étale cohomology.
		Hodge also wrote (with Pedoe) a three-volume work on algebraic geometry with much concrete content - but illustrating what (Click link for more info and facts about Elie Cartan) Elie Cartan called 'the debauch of indices', in its component notation.
	www.absoluteastronomy.com /encyclopedia/W/W/W._V._D._Hodge.htm (490 words)

	Introduction to Complex Manifolds (Site not responding. Last check: 2007-11-06)
		A basic question is then to find conditions for a complex manifold to admit imbedding in a complex projective space of sufficiently high dimension -- an answer to this question is provided by the Kodaira imbedding theorem.
		These are compact Kaehler manifolds which satisfy an arithmetical condition on the cohomology of the manifold (such manifolds are called Hodge manifolds).
		Hodge, The theory and applications of harmonic integrals.
	www.maths.lth.se /matematiklu/personal/jaak/Complex-Manifolds.html (218 words)

	American Mathematical Monthly, The: Vector calculus and the topology of domains in 3-space (Site not responding. Last check: 2007-11-06)
		The Hodge Decomposition Theorem provides the key by decomposing the space of vector fields on the domain into five mutually orthogonal subspaces that are topologically and analytically meaningful.
		Cantarella, D. DeTurck, H. Gluck, and M. Teytel, Influence of geometry and topology on helicity, in Magnetic Helicity in Space and Laboratory Plasmas, M. Brown, R. Canfield, and A. Pevtsov, eds, Geophysical Monograph 111, American Geophysical Union, Washington, DC, 1999, pp.
		Duff and D. Spencer, Harmonic tensors on Riemannian manifolds with boundary, Ann.
	www.findarticles.com /p/articles/mi_qa3742/is_200205/ai_n9034232 (1216 words)

	History for Hodge (Site not responding. Last check: 2007-11-06)
		Hodge currently has 1,505 points, 562 rebounds and 303 assists in his college career.
		Sophomore guard Engin Atsur said Hodge's work is also impacting the rest of the team positively.
		The freshmen on the team have been assisted by Hodge in their beginnings with the Pack.
	www.technicianonline.com /story.php?id=010644 (276 words)

	Jamaica Kincaid, Merle Hodge, George Lamming (Site not responding. Last check: 2007-11-06)
		The novels of Jamaica Kincaid, Merle Hodge and George Lamming plunge head on into this no-man's land, where the fl child is in a state of confusion, desperate to clutch his/her roots, roots that s/he has never developed.
		Hodge presents such a situation when the children are made to recite The Lord's Prayer, which is beyond both their comprehension and vocabulary, generating nothing but an incoherent gibberish.
		In these novels we find a gradual moving away of the protagonists to their 'promised land' by virtue of their educational excellence but 'quo vadis?' The roads are not laden with manna and what lies before them is nothing short of gross disappointment, they arrive in a strange land where they are denied acceptance.
	www.english-literature.org /essays/kincaid_hodge_lamming.html (3303 words)

	Hodge theory (Site not responding. Last check: 2007-11-06)
		In mathematics, Hodge theory is the study of theconsequences for the algebraic topology of a smooth manifold M of the partial differential equation theory ofgeneralised Laplacian operators associated to a Riemannian metric on M.
		This grading comes initially from the theory of harmonic forms, that are privileged representatives in a deRham cohomology class picked out by the Hodge Laplacian (generalising harmonic functions, which must be locallyconstant on compact manifolds by their maximum principle).
		In the case of singularities, the Hodge structure has to be modified to a mixed Hodge structure, where whatsurvives is a filtration rather thana direct sum decomposition.
	www.therfcc.org /hodge-theory-156615.html (314 words)

	Hodge The Cat (Site not responding. Last check: 2007-11-06)
		Hodge and Scherer took a Bob Cat and chain saws in order to help clear damage from the hurricane.
		Nor would it be just, under this head, to omit the fondness which he (Samuel Johnson) shewed for animals which he had taken under his protection.
		I never shall forget the indulgence with which he treated Hodge, his cat: for whom he himself used to go out and buy oysters, lest the servants having that trouble should take a dislike to the poor creature.
	www.wikiverse.org /hodge-the-cat (309 words)

	Algebraic geometry (Site not responding. Last check: 2007-11-06)
		The V stands for variety, which is a specific type of algebraic set we'll define later.
		In one of its forms, it says that S=I(V(S)) is the prime radical of the ideal generated by S. For various reasons we may not always want to work with the entire ideal corresponding to an algebraic set V. Hilbert's Basis Theorem implies that ideals in
		After a decade of rapid development the field stabilised in the 1970s, and applications were made, both to number theory and to more classical geometric questions on algebraic varieties, singularities and moduli.
	www.sciencedaily.com /encyclopedia/algebraic_geometry (1736 words)

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