In mathematics , the Segreembedding is used in projective geometry to consider the cartesian product of two or more projective space s as a projective variety . It is named after Corrado Segre . Definition The Segre map may be defined as the map math sigma P n times P m to P n 1 m 1 1 math taking a pair of points math X , Y in P n times P m math to their product math sigma X 0 X 1 cdots X n , Y 0 Y 1 cdots Y m mapsto X 0Y 0 X 0Y 1 cdots X iY j cdots X nY m math the X sub i sub Y sub j sub are taken ... is the Segreembedding . Counting dimensions, it shows how the product of projective spaces of dimensions ... mechanics and quantum information theory . More precisely, the Segre map describes how to take products of projective Hilbert space s. In algebraic statistics , Segre varieties correspond to independence models. The Segreembedding of P sup 2 sup × P sup 2 sup in P sup 8 sup is the only ... coordinates on the space. The image of the map is a variety, called a Segre variety . It is sometimes ... . Properties The Segre variety is an example of a determinantal variety it is the zero locus of the 2× 2 minors of the matrix math Z i,j math . That is, the Segre variety is the common zero locus ... to be the natural coordinate on the image of the Segre map. The fibers of the product are linear ... Quadric For example with m n 1 we get an embedding of the product of the projective line with itself ... 2&Z 3 end matrix right Z 0Z 3 Z 1Z 2. math Segre threefold The map math sigma P 2 times P 1 to P 5 math is known as the Segre threefold . It is an example of a rational normal scroll. The intersection of the Segre threefold and a three plane math P 3 math is a twisted cubic curve . Veronese variety The image of the diagonal math Delta subset P n times P n math under the Segre map is the Veronese variety of degree two math nu 2 P n to P n 2 2n . math Applications Because the Segre map is to the categorical ... Category Projective geometry fr Plongement de Segre ... more details
Segre may be Beniamino Segre 1903 1977 , Italian geometer Corrado Segre 1863 1924 , Italian geometer distantly related to Beniamino Emilio Segr 1905 1989 , Italian American physicist Segre River , a river in Catalonia See also Segre classification Segreembedding Segr disambig Category Surnames it Segre sl Segre ... more details
of the comprehensiveness of the man. See also Segre classification Segre cubic SegreembeddingSegre surface Zeuthen Segre invariant References Maurizio Avellone, Aldo Brigaglia & Carmela Zappulla ...distinguish Beniamino Segre Infobox scientist name Corrado Segre box width image Corrado Segre.jpg image ... known for notable students prizes Corrado Segre 20 August 1863 18 May 1924 was an Italians ... geometry . Segre developed his entire career at the University of Turin , first as a student ... 1885 to 88. Then for 36 years he had the chair in higher geometry following D Ovidio. Segre and Giuseppe ... young researchers, Segre and Peano, both of them only just past twenty and both working at the University ... studies on such issues. The Erlangen program of Felix Klein appealed early on to Segre, and he ... conics. About Segre, Hawkins writes ...shortly after he assumed the chair of projective geometry .... ... Segre convinced one of the students at Turin, Gino Fano , to make a translation which was published ... provided Segre with another project. He encouraged Mario Pieri to make a translation, Geometria di Posizione 1889 , while Segre composed a biographical sketch of von Staudt that was included in the publication. Segre also expanded algebraic geometry by consideration of multicomplex number s, in particular the bicomplex number s. Segre s 1892 contribution to Mathematische Annalen shows him extending the work of William Rowan Hamilton and William Kingdon Clifford on biquaternion s. But Segre was unaware ... known work of Segre is an inspirational essay meant for Italian students, translated by J.W. Young ... have made it a favorite. In a 1926 memorial article, H.F. Baker called Segre the father of the Italian ... Baker title Corrado Segre journal Journal of the London Mathematical Society volume 1 issue 4 pages ... title Corrado Segre journal Bulletin of the American Mathematical Society volume 33 issue 3 pages .... A mathematical controversy with C. Segre Archive for the History of Exact Sciences 40 3 247 74 ... more details
Refimprove date October 2008 Infobox River river name Segre image name Lleida Riu de Lleida.jpg caption The Segre in Lleida origin Pyrenees br coord 42 24 8 N 2 6 31 E name source Segre display inline mouth Ebro br coord 41 21 42 N 0 18 15 E name Ebro Segre display inline,title basin countries Spain , France , Andorra length elevation 2400 m discharge watershed The Segre IPA ca se , IPA ca se e local lang fr S gre is a river tributary to the Ebro Ebre in Catalan language Catalan with a basin comprising territories across three states France , Andorra and Spain . The river Segre, known to Ancient Rome Roman s and Ancient Greece Greek s as Sicoris , and to the Arab people Arab s of Al Andalus as Nahr az Zayt n River of Olives ref name al Idrisi http ar.wikisource.org wiki D9 86 D8 B2 D9 87 D8 A9 D8 A7 D9 84 D9 85 D8 B4 D8 AA D8 A7 D9 82 D9 81 D9 8A D8 A7 D8 AE D8 AA D8 B1 D8 A7 D9 82 D8 A7 D9 84 D8 A2 D9 81 D8 A7 D9 82 D8 A7 D9 84 D8 A5 D9 82 D9 84 D9 8A D9 85 D8 A7 D9 84 D8 AE D8 A7 D9 85 D8 B3 D8 A7 D9 84 D8 AC D8 B2 D8 A1 D8 A7 D9 84 D8 A3 D9 88 D9 84.ar Nuzhatul Mushtaq Arabic ref has its Source river or stream source s on the north face of the Pic del Segre or Puigmal de SegreSegre s Peak in the French department Pyr n es Orientales historically the comarca of Alta ... River Spain Cinca . In Lleida The river Segre is an essential feature of the Lleida s geography ... park, Els Camps Elisis , is located immediately next to the Segre. ref http www.turismedelleida.com ... List of rivers of Spain References reflist External links commons Segre http www.habitat.aq.upm.es bpes onu98 bp445.en.html Environmental Action for River Segre La Mitjana , Lleida Spain Category Ebro ... Category Rivers of Spain Category Lleida catalonia geo stub an R o Segre be x old br Segre ca Segre cs Segre de Segre es R o Segre eu Segre ibaia fr S gre gl R o Segre it Segre fiume lt Segr nl Segre nn Segre oc Segre pl Segre pt Rio Segre ro R ul Segre ru sl Segre reka uk ... more details
Expand Spanish Batalla del Segre date July 2011 Campaignbox Spanish Civil War The Battle of Segre is the collective name of a series of battles that took place along the Segre River between 4 April 1938 and the 3 January 1939, during the Spanish Civil War after the Nationalist Faction had broken the lines of the Spanish Republican Army in the Aragon Offensive . See also Balaguer Offensive References Reflist coord missing Spain Category Battles of the Spanish Civil War Category 1938 in Spain Category Conflicts in 1938 Spain stub ca Batalla del Segre es Batalla del Segre fr Bataille du S gre ... more details
Notability Astro date February 2012 Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Segre symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered May 14, 1999 designations yes mp name 29910 alt names 1999 JV8 named after Corrado Segre mp category orbit ref epoch May 14, 2008 aphelion 3.4100027 perihelion 2.7261605 semimajor eccentricity 0.1114446 period 1962.9027733 avg speed inclination 10.68636 asc node 89.84107 mean anomaly 90.25733 arg peri 299.71980 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 13.4 29910 Segre 1999 JV8 is a Asteroid belt main belt asteroid discovered on May 14, 1999 by P. G. Comba at Prescott Observatory Prescott . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 29910 Segre JPL Small Body Database Browser on 29910 Segre DEFAULTSORT Segre Category Main Belt asteroids Category Astronomical objects discovered in 1999 beltasteroid stub fa it 29910 Segre hu 29910 Segre pl 29910 Segre pt 29910 Segre uk 29910 vi 29910 Segre yo 29910 Segre ... more details
distinguish Corrado Segre Infobox scientist name Beniamino Segre box width image Beniamino Segre.jpg image size 200px caption birth date Birth date df yes 1903 2 16 death date Death date and age df yes 1977 10 2 1903 2 16 birth place Turin , Italy death place Frascati , Italy nationality Italian field Mathematics known for notable students prizes Beniamino Segre 16 February 1903 2 October 1977 was an Italians Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry . Life and career He was born and studied in Turin . Among his main contributions to algebraic geometry are studies of birational invariants of algebraic ... known paper harv Segre 1955 he proved the following theorem In a Desarguesian plane of odd order ... ref http www history.mcs.st and.ac.uk Biographies Segre Beniamino.html Beniamino Segre . www history.mcs.st ... journal last1 Segre first1 Beniamino title Ovals in a finite projective plane mr 0071034 year 1955 ... pages 414 416 ref harv postscript None doi 10.4153 CJM 1955 045 x See also Segre class Corrado Segre ... Beniamino Segre work Acta Arithmetica url http matwbn.icm.edu.pl ksiazki aa aa45 aa4511.pdf accessdate July 9, 2009 http matwbn.icm.edu.pl ksiazki aa aa45 aa4512.pdf Publications of Beniamino Segre ... Segre and Italian Geometry work Rendiconti di Matematica url http www.mat.uniroma1.it rendicon ..., 2006 MacTutor Biography id Segre Beniamino http www.mat.uniroma3.it users sernesi BIBLIOGRAFIA segre beniamino.htm Edoardo Sernesi Beniamino Segre Torino 1903 Frascati 1977 incl. extensive bibliography External links MathGenealogy id 79643 Persondata Metadata see Wikipedia Persondata . NAME Segre ... , Italy DATE OF DEATH 2 October 1977 PLACE OF DEATH Frascati , Italy DEFAULTSORT Segre, Beniamino Category ... Kingdom Italy mathematician stub de Beniamino Segre it Beniamino Segre ht Beniamino Segre pms Beniamino Segre pt Beniamino Segre ... more details
The Segre classification is an algebraic classification of rank two symmetric tensor s. The resulting types are then known as Segre types . It is most commonly applied to the energy momentum tensor or the Ricci tensor and primarily finds application in the classification of exact solutions in general relativity . See also Corrado Segre Jordan normal form Petrov classification References cite book author Stephani, Hans Kramer, Dietrich MacCallum, Malcolm Hoenselaers, Cornelius and Herlt, Eduard title Exact Solutions of Einstein s Field Equations location Cambridge publisher Cambridge University Press year 2003 isbn 0 521 46136 7 See section 5.1 for the Segre classification. cite journal author Segre, C. title Sulla teoria e sulla classificazione delle omografie in uno spazio lineare ad uno numero qualunque di dimensioni journal Memorie della R. Accademia dei Lincei year 1884 volume 3a pages 127 Category Linear algebra Category Tensors Category Tensors in general relativity algebra stub relativity stub ... more details
Refimprove date December 2009 Luigi Gigi Segre 1919 1963 was an Italian automotive designer and engineer, leading the Carrozzeria Ghia from 1953, when Mario Boano left, until his death in 1963, from complications during surgery. Segre was widely known for styling the Karmann Ghia 1953 , and he also consulted on the styling of the Renault Dauphine . Overall, Dauphine styling was a scaled down version of the Renault Fr gate ref name independ cite news title Renault Dauphine publisher The Independent, 3 March 2008 url http www.independent.co.uk life style motoring features renault dauphine 394436.html location London date 3 March 2008 ref and in June 1953, Pierre Lefaucheux , Renault s chairman, requested Segre s and Carrozzeria Ghia assistance, especially with integrating the Dauphine s engine s air intake at the rear doors. ref name dauphinomaniac2 cite web title D une n c ssit aux prototypes 109 ... publisher Dauphinomaniac in French url http www.dauphinomaniac.org ref Segre also established the Officine Stampaggi Industriali OSI coachbuilding company with Arrigo Olivetti in 1960. References Reflist Persondata name Segre, Luigi alternative names short description date of birth 1919 place of birth date of death 1963 place of death Use dmy dates date March 2011 DEFAULTSORT Segre, Luigi Category Italian automobile designers Category 1919 births Category 1963 deaths Italy bio stub Automobile bio stub ... more details
In algebraic geometry , a Segre surface , studied by harvs txt authorlink Corrado Segre first Corrado last Segre year 1884 and harvs txt authorlink Beniamino Segre first Beniamino last Segre year 1951 , is an intersection of two quadric surface quadrics in 4 dimensional projective space . They are rational surface s isomorphic to a projective plane blowing up blown up in 5 points with no 3 on a line, and are del Pezzo surface s of degree 4, and have 16 rational lines. The term Segre surface is also occasionally used for various other surfaces, such as a quadric in 3 dimensional projective space, or the hypersurface math x 1 x 2 x 3 x 2 x 3 x 4 x 3 x 4 x 5 x 4 x 5 x 1 x 5 x 1 x 2 0. , math References Citation last1 Segre first1 Corrado title Etude des diff rentes surfaces du 4 sup e sup ordre conique double ou cuspidale g n rale ou d compos e consid r es comme des projections de l intersection de deux vari t s quadratiques de l espace quatre dimensions url http dx.doi.org 10.1007 BF01443412 publisher Springer Berlin Heidelberg year 1884 journal Mathematische Annalen issn 0025 5831 volume 24 pages 313 444 Citation doi 10.1093 qmath 2.1.216 last1 Segre first1 Beniamino title On the inflexional curve of an algebraic surface in S sub 4 sub id MathSciNet id 0044861 year 1951 journal The Quarterly Journal of Mathematics. Oxford. Second Series issn 0033 5606 volume 2 issue 1 pages 216 220 Category Algebraic surfaces Category Complex surfaces ... more details
In mathematics , the Segre class is a characteristic class used in the study of singular vector bundle s. The total Segre class is inverse to the total Chern class , and thus provides equivalent information the advantage of the Segre class is that it generalizes to singular vector bundles, while the Chern class does not. The Segre class is named after Beniamino Segre . Definition For a holomorphic vector bundle math E math over a complex manifold math M math a total Segre class math s E math is the inverse to the total Chern class math c E math , see e.g. ref Fulton W. 1998 . Intersection theory , p.50. Springer, 1998. ref . Explicitly, for a total Chern class math c E 1 c 1 E c 2 E cdots , math one gets the total Segre class math s E 1 s 1 E s 2 E cdots , math where math c 1 E s 1 E , quad c 2 E s 1 E 2 s 2 E , quad dots, quad c n E s 1 E c n 1 E s 2 E c n 2 E cdots s n E math Let math x 1, dots, x k math be Chern roots, i.e. formal eigenvalues of math frac i Omega 2 pi math where math Omega math is a curvature of a connection on math E math . While the Chern class s E is written as math c E prod i 1 k 1 x i c 0 c 1 cdots c k , math where math c i math is an elementary symmetric polynomial of degree math i math in variables math x 1, dots, x k math the Segre for the dual bundle math E vee math which has Chern roots math x 1, dots, x k math is written as math s E prod i 1 k frac 1 1 x i s 0 s 1 cdots math Expanding the above expression in powers of math x 1, dots x k math one can see that math s i E vee math is represented by a complete homogeneous symmetric polynomial of math x 1, dots x k math References reflist Category Characteristic classes ... more details
Infobox Writer for more information see Template Infobox Writer doc name Cesare Segre image imagesize caption pseudonym birthdate Birth date 1928 4 4 birthplace Verzuolo , Italy deathdate deathplace occupation Philologist nationality flagicon Italy Italy Italian period Medieval , 1990, 2000 genre History historical , Philology philological , semiotics movement spouse Maria Luisa Meneghetti partner children relatives influences influenced Benvenuto Terracini, Santorre Debenedetti signature website http www.iusspavia.it eng centri.php?id 16&sez 1 IUSS Pavia Cesare Segre born April 4, 1928 in Verzuolo , Province of Cuneo is an Italy Italian philologist , semiotics semiotician and literary critic of Jewish descent, currently the Director of the Texts and Textual Traditions Research Centre of the Institute for Advanced Studies of Pavia IUSS . He lived and studied in Turin , where he was awarded his degree in 1950, a pupil of Benvenuto Terracini and famous uncle Santorre Debenedetti . A professor of Romance Philology since 1954, he taught at the universities of Trieste and Pavia , where in the 1960s he became Chair of this discipline. Segre was also a Visiting Professor at the University of Manchester , Federal University of Rio de Janeiro University of Rio de Janeiro , Harvard University , Princeton University , Berkeley University . He collaborated with numerous academic magazines and journals, among which Studi di filologia italiana , Cultura neolatina , L Approdo letterario he has ... Ossola an anthology of Italian poetry published by Giulio Einaudi Editore Einaudi . Segre ... Studies . With his important research, Segre has contributed to the introduction of formalist and structural ... Traditions Research Centre, Pavia Persondata Metadata see Wikipedia Persondata . NAME Segre, Cesare ... DATE OF DEATH PLACE OF DEATH DEFAULTSORT Segre, Cesare Category 1928 births Category Living people Category ..., Berkeley faculty et Cesare Segre fr Cesare Segre it Cesare Segre ... more details
In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 or sometimes 5 dimensional projective space, studied by harvs txt first Corrado last Segre authorlink Corrado Segre year 1887 . The Segre cubic is the set of points x sub 0 sub x sub 1 sub x sub 2 sub x sub 3 sub x sub 4 sub x sub 5 sub of P sup 5 sub satisfying the equations math displaystyle x 0 x 1 x 2 x 3 x 4 x 5 0 math math displaystyle x 0 3 x 1 3 x 2 3 x 3 3 x 4 3 x 5 3 0. math Its intersection with any hyperplane x sub i sub 0 is the Clebsch cubic surface . Its intersection with any hyperplane x sub i sub x sub j sub is Cayley s nodal cubic surface . Its dual is the Igusa quartic 3 fold in P sup 4 sup . Its Hessian is the Barth Nieto quintic . A cubic hypersurface in P sup 4 sub has at most 10 nodes, and up to isomorphism the Segre cubic is the unique one with 10 nodes. Its nodes are the points conjugate to 1 1 1 &minus 1 &minus 1 &minus 1 under permutations of coordinates. References Citation last1 Hunt first1 Bruce title The geometry of some special arithmetic quotients publisher Springer Verlag location Berlin, New York series Lecture Notes in Mathematics isbn 978 3 540 61795 2 doi 10.1007 BFb0094399 id MathSciNet id 1438547 year 1996 volume 1637 Citation last1 Hunt first1 Bruce title Nice modular varieties url http projecteuclid.org getRecord?id euclid.em 1045759526 id MR R1806296 year 2000 journal Experimental Mathematics issn 1058 6458 volume 9 issue 4 pages 613 622 Citation last1 Segre first1 Corrado title Sulla variet cubica con dieci punti doppii dello spazio a quattro dimensioni. url http books.google.com books?id 9lSAAAAYAAJ&pg PA791 language Italian id JFM 19.0673.01 year 1887 journal Atti della Reale Accademia delle scienze di Torino volume XXII pages 791 801 Category Threefolds ... more details
In linguistics , center embedding refers to the process of embedding a phrase in the middle of another phrase of the same type. This often leads to difficulty with parsing which would be difficult to explain on grammatical grounds alone. The most frequently used example involves embedding a relative clause inside another one as in A man that a woman loves math Rightarrow math A man that a woman that a child knows loves math Rightarrow math A man that a woman that a child that a bird saw knows loves math Rightarrow math A man that a woman that a child that a bird that I heard saw knows loves In theories of natural language parsing , the difficulty with multiple center embedding is thought to arise from limitations of the human short term memory . In order to process multiple center embeddings, we have to store many subject linguistics subject s in order to connect them to their Predicate grammar predicate s. An interesting theoretical point is that sentences with multiple center embedding are Grammaticality grammatical , but unacceptable. Such examples are behind Noam Chomsky s comment that, Languages are not designed for parsability ... we may say that languages, as such, are not usable. Chomsky, 1991 Some researchers such as Peter Reich came up with theories that though single center embedding is acceptable as in the man that boy kicked is a friend of mine , double center embedding ... center embedding of clauses is exactly 3 in written language. He provided thirteen genuine examples ... for an obscure aspect of grammar , center embedding is the focus of a science fiction novel, Ian Watson author Ian Watson s The Embedding , and plays a part in Ted Chiang s Story of Your Life . References ... King, Michael Rosner, Geoffrey Sampson, and Nino Varile. 1982 . A Myth about Centre Embedding. Lingua 58 327 340. Karlsson, Fred. 2007 . Constraints on multiple center embedding of clauses. Journal of Linguistics ... embedding. The general gist is quite understandable, but the details of the relationships are hard to manage ... more details
In Galois theory , a branch of mathematics , the embedding problem is a generalization of the inverse Galois problem . Roughly speaking, it asks whether a given Galois extension can be embedded into a Galois extension in such a way that the restriction map between the corresponding Galois group s is given. Definition Given a field mathematics field K and a finite Group mathematics group H , one may pose the following question the so called inverse Galois problem . Is there a Galois extension F K with Galois group isomorphic to H . The embedding problem is a generalization of this problem Let L K be a Galois extension with Galois group G and let f H &rarr G be an epimorphism. Is there a Galois extension F K with Galois group H and an embedding L &rarr F fixing K under which the restriction map from the Galois group of F K to the Galois group of L K coincides with f ? Analogously, an embedding problem for a profinite group F consists of the following data Two profinite groups H and G and two continuous epimorphisms F &rarr G and f H &rarr G . The embedding problem is said to be finite if the group H is. A solution sometimes also called weak solution of such an embedding problem is a continuous homomorphism F &rarr H such that f . If the solution is surjective, it is called a proper solution . Properties Finite embedding problems characterize profinite groups ... generated profinite group. Then F is projective if and only if any finite embedding problem for F is solvable. F is free of countable rank if and only if any finite embedding problem for F is properly ..., B. B. Lur e, D. K. Faddeev, The embedding problem in Galois theory Translations of Mathematical ... Verlag, Heidelberg, 2005. A. Ledet, Brauer type embedding problems Fields Institute Monographs, no. 21, 2005 . Vahid Shirbisheh, Galois embedding problems with abelian kernels of exponent p VDM ... more details
In mathematics , the Kuratowski embedding allows one to view any metric space as a subset of some Banach space . It is named after Kazimierz Kuratowski . Specifically, if X , d is a metric space, x sub 0 sub is a point in X , and C sub b sub X denotes the Banach space of all bounded continuous function continuous real valued functions on X with the uniform norm supremum norm , then the map math Phi X rarr C b X math defined by math Phi x y d x,y d x 0,y quad mbox for all quad x,y in X math is an isometry . ref citation title Geometric embeddings of metric spaces url http www.math.jyu.fi research reports rep90.ps author Juha Heinonen date January 2003 accessdate 6 January 2009 ref Note that this embedding depends on the chosen point x sub 0 sub and is therefore not entirely canonical. The Kuratowski Wojdys awski theorem states that every bounded metric space X is isometric to a closed set closed subset of a Convex set convex subset of some Banach space. ref citation author Karol Borsuk title Theory of retracts year 1967 place Warsaw . Theorem III.8.1 ref N.B. the image of this embedding is closed in the convex subset, not necessarily in the Banach space. Here we use the isometry math Psi X rarr C b X math defined by math Psi x y d x,y quad mbox for all quad x,y in X math The convex set mentioned above is the convex hull of X . In both of these embedding theorems, we may replace ... norm, since C sub b sub X is a closed linear subspace of sup sup X . These embedding ... enlarging the codomain to a Banach space containing X . History Formally speaking, this embedding ... variation of this embedding appears already in the paper of Fr chet ref Fr chet M. Sur quelques points ... he first introduces the notion of metric space. See also Tight span , an embedding of any metric space into an injective metric space defined similarly to the Kuratowski embedding References reflist DEFAULTSORT Kuratowski Embedding Category Functional analysis Category Metric geometry ru ... more details
Font embedding is inclusion of font files inside an electronic document. This has been possible with Portable Document Format PDF , Microsoft Word for Windows and some other applications for many years. It is controversial because it allows copyright ed fonts to be freely distributed. In word processors Microsoft Word for Windows has permitted font embedding in some document formats since Word 97 such as .doc or .rtf . But this feature does not work correctly in some Word versions. ref cite web url http support.microsoft.com kb 275953 title Embedded fonts are not displayed as expected in the documents that are saved as Rich text format RTF in Word accessdate 2010 12 15 ref OpenOffice.org supports font embedding in the PDF export feature. ref cite web url http wiki.services.openoffice.org wiki API Tutorials PDF export title API Tutorials PDF export accessdate 2010 12 15 ref Font embedding in word processors is not widely supported. ref cite web url https list.unm.edu cgi bin wa?A2 ind0504d&L rtf l&T 0&F &S &P 60 title Embedding fonts in RTF file date 2005 04 23 accessdate 2010 03 17 ref ref cite web url http www.openoffice.org issues show bug.cgi?id 20370 title OpenOffice.org Issue MS Interoperability embedd fonts into the document accessdate 2010 03 17 ref For example, if an RTF file with embedded font is opened in other word processor than MS Word, it will usually remove embedded fonts. On the Web main Font embedding on the Web main Comparison of layout engines Web Typography Currently, Internet Explorer , Firefox , Safari web browser Safari , Opera web browser Opera and Google Chrome support automatic downloading of fonts used on a website using CSS2 or CSS3 . Controversy Font embedding is a controversial practice because it allows copyrighted fonts to be freely distributed. The controversy can be mitigated by only embedding the characters required to view the document ... digital rights management DRM protections. The Acid3 test requires font embedding with minimal DRM ... more details
In mathematics, the James embedding is an embedding of a real, complex, or hyperbolic projective space into a sphere, introduced by harvs txt last James authorlink Ioan James year1 1958 year2 1959 . References Citation last1 James first1 I. M. title Embeddings of real projective spaces doi 10.1017 S0305004100003108 id MR 0096228 year 1958 journal Proc. Cambridge Philos. Soc. volume 54 pages 555 557 Citation last1 James first1 I. M. title Some embeddings of projective spaces doi 10.1017 S0305004100034083 id MR 0109350 year 1959 journal Proc. Cambridge Philos. Soc. volume 55 pages 294 298 Category Algebraic topology ... more details
otheruses4 the general Pl cker embedding the classical case of 2 planes in 4 space Pl cker coordinates In mathematics, the Pl cker embedding describes a method to realize the Grassmannian of all r dimensional subspaces of a vector space V as a subvariety of the projective space of the r th exterior power of that vector space, P sup r sup V . The Pl cker embedding was first defined, in the case r 2, n 4, in Pl cker coordinates coordinates by Julius Pl cker as a way of describing the lines in three dimensional space which, as projective line s in real projective space , correspond to two dimensional subspaces of a four dimensional vector space . This was generalized by Hermann Grassmann to arbitrary r and n using a generalization of Pl cker s coordinates, sometimes called Grassmann coordinates . Definition The Pl cker embedding over the field K is the map defined by math begin align iota colon mathbf Gr r, K n & rightarrow mathbf P wedge r K n operatorname span v 1, ldots, v r & mapsto K v 1 wedge cdots wedge v r end align math where Gr r , K sup n sup is the Grassmannian , i.e., the space of all r dimensional subspaces of the n dimensional vector space , K sup n sup . This is an isomorphism from the Grassmannian to the image of , which is a projective variety. This variety can be completely characterized as an intersection of quadrics, each coming from a relation on the Pl cker or Grassmann coordinates that derives from linear algebra. References Citation last1 Griffiths first1 Phillip author1 link Phillip Griffiths last2 Harris first2 Joseph author2 link Joe Harris mathematician title Principles of algebraic geometry publisher John Wiley & Sons location New York series Wiley Classics Library isbn 978 0 471 05059 9 id MathSciNet id 1288523 year 1994 DEFAULTSORT Plucker embedding Category Algebraic geometry Category Differential geometry ... more details
In topological graph theory , an embedding also spelled imbedding of a graph mathematics graph math G ... space compact , connected space connected 2 manifold . Informally, an embedding of a graph into a surface .... Often, an embedding is regarded as an equivalence class under homeomorphisms of ... of graph embedding by omitting the non intersection condition for edges. In such contexts the stricter definition is described as non crossing graph embedding . ref citation contribution Enumerating ... definition of graph embedding. The weaker definition is discussed in the articles graph ... year 2001 isbn 0486417417 . ref A 2 cell embedding or map is an embedding in which every face is homeomorphic ... . ref A closed 2 cell embedding is an embedding in which the closure of every face is homeomorphic ... surface of non orientable genus n . ref name gt01 Combinatorial embedding main Rotation system An embedded ... embedding as opposed to the term topological embedding , which refers to the previous definition in terms of points and curves . Sometimes, the rotation system itself is called a combinatorial embedding ... constitutes the boundaries of the faces of the embedding. However handling these face based orders ... as well as to find the embedding. The first breakthrough in this respect happened in 1979, when algorithms ... last1 Mohar first1 Bojan authorlink Bojan Mohar title A linear time algorithm for embedding graphs ... distinct halfplane s having that line as their common boundary. An embedding like this in which the edges are drawn on halfplanes is called a book embedding of the graph. This metaphor comes from ... i , i sup 2 sup , i sup 3 sup of the moment curve . An embedding of a graph into three dimensional space in which no two of the cycles are topologically linked is called a linkless embedding . A graph has a linkless embedding if and only if it does not have one of the seven graphs of the Petersen family as a minor graph theory minor . See also Embedding , for other kinds of embeddings Book thickness ... more details
In order theory mathematical order theory , an order embedding is a special kind of monotone function , which provides a way to include one partially ordered set into another. Like Galois connection s, order embeddings constitute a notion which is strictly weaker than the concept of an order isomorphism . A way to understand the different nature of both of these weakenings by exploiting some category theory is discussed at the end of this article. Formal definition Formally, given two partially ordered sets S , &le and T , &le , a function f S &rarr T is an order embedding if f is both order preserving and order reflecting , i.e. for all x and y in S , one has math x leq y text if and only if f x leq f y . math Note that such a function is necessarily injective , since f x f y implies x &le y and y &le x . If an order embedding between two posets S and T exists, one says that S can be embedded into T . Properties An order isomorphism can be characterized as a surjective order embedding. As a consequence, any order embedding f restricts to an isomorphism between its domain mathematics domain S and its range mathematics range f S , which justifies the term embedding . On the other hand, it might well be that two necessarily infinite posets are mutually embeddable into each other without being isomorphic. An example is provided by the set of real number s and its interval mathematics interval &minus 1,1 . Ordering both sets in the natural way, one clearly finds that &minus 1,1 can be embedded into the reals. On the other hand, one can define a function e from the real numbers to &minus 1,1 as math e x frac 2 pi arctan x math This is in fact just the projection of the real number line to half of the circle with circumference 4 see trigonometric function s for details . Now it is easy to see that e embeds the reals into &minus 1,1 . Yet, the two posets are not isomorphic &minus 1,1 has both a least element least and a greatest element , which are not present in the case of the real ... more details
In combinatorics , a matroid embedding is a set system F , E , where F is a collection of feasible sets , that satisfies the following properties Accessibility Property Every non empty feasible set X contains an element x such that X x is feasible Extensibility Property For every feasible subset X of a basis i.e. , maximal feasible set B , some element in B but not in X belongs to the extension ext X of X , or the set of all elements e not in X such that X e is feasible Closure Congruence Property For every superset A of a feasible set X disjoint from ext X , A e is contained in some feasible set for either all or no e in ext X The collection of all subsets of feasible sets forms a matroid . Matroid embedding was introduced by Helman et al. in 1993 to characterize problems that can be optimized by a greedy algorithm . References cite journal author Helman, Paul Moret, Bernard M. E. Shapiro, Henry D. year 1993 title An exact characterization of greedy structures journal SIAM Journal on Discrete Mathematics volume 6 issue 2 pages 274&ndash 283 doi 10.1137 0406021 Category Matroid theory ... more details
In graph theory , book embedding is a generalization of planar graph planar embedding to nonplanar surfaces in the form of a book , a collection of pages half plane s joined together at the spine of the book the shared boundary of all the half planes . The vertices of the graph are embedded on the spine, and each edge must lie in one of the pages. Book embeddings and book thickness were first studied by L. Taylor Ollman in 1973, ref citation first L. Taylor last Ollmann contribution On the book thicknesses of various graphs editor1 first Frederick editor1 last Hoffman editor2 first Roy B. editor2 last Levow editor3 first Robert S. D. editor3 last Thomas title Proc. 4th Southeastern Conference on Combinatorics, Graph Theory and Computing volume VIII series Congressus Numerantium page 459 year 1973 . ref and have since been studied by many other researchers from the points of view of graph theory, VLSI , ref citation title Embedding graphs in books A layout problem with applications to VLSI design url http www.math.ucsd.edu fan mypaps fanpap fc82embedding.pdf first1 Fan R. K. last1 Chung author1 link Fan Chung first2 Frank Thompson last2 Leighton author2 link F. Thomson Leighton first3 Arnold L. last3 Rosenberg author3 link Arnold L. Rosenberg journal SIAM. Journal on Algebraic and Discrete Methods volume 8 issue 1 pages 33 58 year 1987 doi 10.1137 0608002 . ref and graph drawing . Definitions A book B is a topological space consisting of a single line called the spine of B and a collection ... of G is mapped to the spine of B and every edge of G is mapped to a single page of B . A book embedding of G onto B is a graph embedding of G into B , i.e., the drawing of G on B without crossings. The book thickness or pagenumber of G is the minimum number of pages required for a book embedding of ... the embedded edges to cross the spine. Some authors call this notion topological book embedding ... title Topological book embedding of bipartite graphs journal IEICE Transactions on Fundamentals ... more details
In topological graph theory , a mathematical discipline, a linkless embedding of an undirected graph is an graph embeddingembedding of the graph into Euclidean space in such a way that no two cycles of the graph have nonzero linking number . A flat embedding is an embedding with the property that every ... of the graph. A linklessly embeddable graph is a graph that has a linkless or flat embedding these graphs ... s. ref name rst93a They may be recognized, and a flat embedding may be constructed for them, in linear ... for defining linkless embeddings of graphs is found by projecting the embedding onto the plane and counting the number of crossing number graph theory crossings of the projected embedding in which the first ..., such as the Whitehead link . An embedding of a graph into three dimensional space consists of a mapping ... formed in this way if all pairs of cycles have zero linking number, the embedding is said to be linkless ..., the cycle must be unlinked from all the other cycles disjoint from it in the graph. The embedding ... 1993a . A similar definition of a good embedding appears in harvtxt Motwani Raghunathan Saran 1988 see also harvtxt Saran 1989 and harvtxt B hme 1990 . ref A flat embedding is necessarily linkless ... disjoint cycles, and it is embedded to form the Whitehead link, then the embedding is linkless but not flat. A graph is said to be intrinsically linked if, no matter how it is embedded, the embedding ... tripartite graph K sub 3,3,1 sub . Every planar graph has a flat and linkless embedding simply embed ... to embed it linklessly into space every linkless embedding can be continuously deformed to lie on a flat ... line segments, the resulting embedding is flat. An apex graph , formed by adding a single vertex to a planar graph, also has a flat and linkless embedding embed the planar part of the graph on a plane ... through any other graph feature. ref name rst93a If a graph has a linkless or flat embedding ... If a graph G has a linkless or flat embedding, then every minor graph theory minor of G a graph ... more details
Semidefinite embedding SDE or maximum variance unfolding MVU is an algorithm in computer science that uses semidefinite programming to perform non linear dimensionality reduction of high dimensional coordinate vector vector ial input data. Non linear dimensionality reduction algorithms attempt to map high dimensional data onto a low dimensional Euclidean vector space . Maximum variance Unfolding is a member of the manifold learning family, which also include algorithms such as isomap and locally linear embedding . In manifold learning, the input data is assumed to be sampled from a low dimensional manifold that is embedded inside of a higher dimensional vector space. The main intuition behind MVU is to exploit the local linearity of manifolds and create a mapping that preserves local neighborhoods at every point of the underlying manifold. MVU creates a mapping from the high dimensional input vectors to some low dimensional Euclidean vector space in the following steps A neighborhood graph theory neighborhood graph is created. Each input is connected with its k nearest input vectors according to Euclidean distance metric and all k nearest neighbors are connected with each other. If the data ... graph while preserving the nearest neighbors distances. The low dimensional embedding is finally ... a low dimensional embedding into a Euclidean space were first proposed by Linial, London, and Rabinovich. Optimization Formulation Let math X , math be the original input and math Y , math be the embedding ... G ji K ii K jj K ij K ji , math In addition, we also want to constraint the embedding math Y , math ... embedding is much better in revealing the underlying dimension of the data compared to LLE and Laplacian eigenmaps. It also guarantees that the nearest neighbors in the embedding is the same ... hand, semidefinite embedding is much slower and harder to scale to large data. Semidefinite embedding ... linear embedding References http repository.upenn.edu cgi viewcontent.cgi 3farticle 1000 26context ... more details
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