Distinguish mile Borel Infobox scientist name ArmandBorel image Armand Borel.jpg image size caption ArmandBorel in Bonn, 1967. birth date Birth date 1923 5 21 df y birth place La Chaux de Fonds , Switzerland ... awards religion signature filename only footnotes ArmandBorel 21 May 1923 &ndash 11 August 2003 was a Switzerland ... Citation last1 Borel first1 Armand author1 link ArmandBorel title Seminar on transformation ..., No. 46 year 1960 mr 0116341 Citation last1 Borel first1 Armand author1 link ArmandBorel title Cohomologie ... BFb0097851 year 1964 volume 2 mr 0174045 Citation last1 Borel first1 Armand author1 link Armand ... doi 10.1007 BFb0096867 year 1967 volume 36 mr 0221507 Citation last1 Borel first1 Armand author1 link ArmandBorel title Introduction aux groupes arithm tiques publisher Hermann location Paris language ... Scientifiques et Industrielles, No. 1341 year 1969 mr 0244260 Citation last1 Borel first1 Armand author1 link ArmandBorel title Repr sentations de groupes localement compacts publisher Springer ... 1972 volume 276 mr 0414779 Citation last1 Borel first1 Armand author1 link ArmandBorel title Linear ... Borel first1 Armand author1 link ArmandBorel title Intersection cohomology origyear 1984 url http ... Birkh user Classics isbn 978 0 8176 4764 3 year 2008 mr 0788171 Citation last1 Borel first1 Armand author1 link ArmandBorel last2 Grivel first2 P. P. last3 Kaup first3 B. last4 Haefliger first4 Andr ... isbn 978 0 12 117740 9 year 1987 volume 2 mr 882000 Citation last1 Borel first1 Armand author1 link ArmandBorel title Automorphic forms on SL sub 2 sub R publisher Cambridge University Press series ... last1 Borel first1 Armand author1 link ArmandBorel title Semisimple groups and Riemannian symmetric ... 16 mr 1661166 Citation last1 Borel first1 Armand author1 link ArmandBorel last2 Wallach first2 N. title ... 2000 volume 67 mr 1721403 Citation last1 Borel first1 Armand author1 link ArmandBorel title Essays ..., R.I. isbn 978 0 8218 0288 5 year 2001 mr 1847105 Citation last1 Borel first1 Armand author1 ... more details
Borel may refer to ArmandBorel 1923 2003 , Swiss mathematician Calvin Borel , American jockey Cleopatra Borel Brown Daniel Borel mile Borel 1871 1956 , French mathematician Eric Borel Ernest Borel Eugene Borel , member of Swiss Federal Council Felice Borel Gabriel Borel , French aircraft designer George Frederik Willem Borel , Dutch military figure Henri Borel , Dutch writer, son of George Frederik Willem Borel Jacques Borel , French novelist Pascal Borel Pascale Borel Pierre Borel Raymond BorelBorel, California , former community in Kern County Borel algebra , operating on Borel sets, named after mile Borel, also Borel measure , the measure on a Borel algebra Borel subgroup , in the theory of algebraic groups, named after ArmandBorelBorel crater , a lunar crater Etablissements Borel , an aircraft manufacturing company founded by Gabriel Borel disambig surname cs Borel de Borel fr Borel it Borel nl Borel ja ru sr ... more details
Armand is a French male name and a surname, the French form of Herman . ref http www.behindthename.com name armand Behind the Name Armand ref Armand may refer to People Armand photographer 1901 63 , Armenian photographer Armand de Bourbon, prince de Conti 1629 66 , French noble Armand de Gontaut, baron de Biron 1524 92 , French soldier Armand de Gramont, comte de Guiche 1637 73 , French noble Armand de La Richardie 1686 1758 , French Roman Catholic missionary Armand de Pontmartin 1811 90 , French literary critic and essayist Armand, duc d Aiguillon 1750 1800 , French noble Armand Hammer 1898 1990 , American Industrialist Armand Mouyal 1925 88 , French world champion p e fencer Armand of Kersaint 1742 93 , French sailor and politician Abraham Armand , Roman Catholic priest David Armand , English actor mile Armand 1872 1962 , French anarchist Fr ydis Armand born 1949 , Norwegian actress Gesner Armand born 1936 , Haitian painter Gisken Armand born 1962 , Norwegian actress Inessa Armand 1874 1920 , French communist Jean Armand de Lestocq 1692 1767 , French adventurer Joseph Fran ois Armand 1820 1903 , Canadian politician Louis Armand 1905 71 , French Resistance member Martin Armand , Iranian graphic designer and body painter Sylvain Armand born 1980 , French footballer Fictional characters Armand The Vampire Chronicles , character from the The Vampire Chronicles novels Count Armand , character from the movie The Legend of Zorro Armand St. Just , character from the Scarlet Pimpernel novels Armand Duval, character from the romantic novel La Dame aux Camelias Other Armand Commission , first commission of the European Atomic Energy Community Armand de Brignac , champagne brand produced by Champagne Cattier Armand s Legion , Continental Army military unit Places Saint Armand, Quebec St. Armand, New York St. Armand s Key in Florida References references Disambig Category French masculine given names Category surnames de Armand es Armand fr Armand ja pt Armand ... more details
aar surgery borel.pdf The birth of the Borel conjecture , Extract from letter from ArmandBorelBorel to Jean Pierre Serre Serre , 2nd May, 1953 Category Geometric topology Category Homeomorphisms ...In mathematics , specifically geometric topology , the Borel conjecture asserts that an Aspherical space aspherical closed manifold is determined by its fundamental group , up to homeomorphism . It is a Rigidity mathematics rigidity conjecture, demanding that a weak, algebraic notion of equivalence namely, a homotopy homotopy equivalence imply a stronger, topological notion namely, a homeomorphism . Precise formulation of the conjecture Let math M math and math N math be closed manifold closed and Aspherical space aspherical topological manifold s, and let math f M to N math be a homotopy homotopy equivalence . The Borel conjecture states that the map math f math is homotopic to a homeomorphism . Since aspherical manifolds with isomorphic fundamental groups are homotopy equivalent, the Borel conjecture implies that aspherical closed manifolds are determined, up to homeomorphism, by their fundamental groups. This conjecture is false if topological manifold s and homeomorphisms are replaced by smooth manifold s and diffeomorphism s counterexamples can be constructed by taking a connected sum with an exotic sphere . The origin of the conjecture In a May 1953 letter to Jean Pierre Serre Serre web reference below , ArmandBorel asked the question whether two aspherical manifolds with isomorphic ... manifold s is homotopic to an isometry in particular, to a homeomorphism. The Borel conjecture is a topological .... Relationship to other conjectures The Borel conjecture implies the Novikov conjecture for the special ... to math S 3 math . This is not a special case of the Borel conjecture, because math S 3 math is not aspherical. Nevertheless, the Borel conjecture for the Torus 3 torus math T 3 S 1 times S 1 times S 1 math implies the Poincar conjecture for math S 3 math . References F.T. Farrell, The Borel ... more details
the group B is a Borel subgroup and N is the normalizer of a maximal torus contained in B . The notion was introduced by ArmandBorel , who played a leading role in the development of the theory of algebraic ...In the theory of algebraic groups , a Borel subgroup of an algebraic group G is a maximal Zariski topology Zariski closed and connected solvable group solvable algebraic subgroup . For example, in the group GL sub n sub n x n invertible matrices , the subgroup of invertible upper triangular matrix upper triangular matrices is a Borel subgroup. For groups realized over algebraically closed field s, there is a single conjugacy class of Borel subgroups. Subgroups between a Borel subgroup B and the ambient group G are called parabolic subgroups . Parabolic subgroups P are also characterized, among algebraic subgroups, by the condition that G P is a complete variety . Working over algebraically closed fields, the Borel subgroups turn out to be the minimal parabolic subgroups in this sense. Thus B is a Borel subgroup when the homogeneous space G B is a complete variety which is as large as possible . For a simple algebraic group G , the set of conjugacy class es of parabolic subgroups is in bijection with the set of all subsets of nodes of the corresponding Dynkin diagram the Borel subgroup corresponds to the empty set and G itself corresponding to the set of all nodes. In general each node of the Dynkin diagram determines a simple negative root and thus a one dimensional root group of G ... root groups. Moreover any parabolic subgroup is conjugate to such a parabolic subgroup. Borel subgroups ... subalgebra math mathfrak h math , given an order theory ordering of math mathfrak h math , the Borel ... with positive weight. A Lie subalgebra of math mathfrak g math containing a Borel subalgebra is called ... New York publisher Springer year 1972 isbn 0 387 90108 6 cite book author A. Borel title Essays in the History ... of Mathematics http eom.springer.de B b017160.htm Borel subgroup in Springer Encyclopaedia ... more details
In mathematics, Borel transform may refer to A transform used in Borel summation A generalization of this in Nachbin s theorem mathdab ... more details
In mathematics , specifically in Measure mathematics measure theory , a Borel measure is defined as follows let X be a locally compact Hausdorff space , and let math mathfrak B X math be the Sigma algebra Generated .CF.83 algebra smallest &sigma algebra that contains the open sets of X this is known as the algebra of Borel sets. Any measure defined on the algebra of Borel sets is called a Borel measure . Some authors require in addition that C for every compact set C . If a Borel measure is both inner regular and outer regular , it is called a regular Borel measure . If is both inner regular and Locally finite measure locally finite , it is called a Radon measure . Note that a locally finite Borel measure automatically satisfies C for every compact ... Hausdorff space, hence we can define a Borel measure on it. In this case, math mathfrak B textbf R math is the smallest algebra that contains the open intervals of R . While there are many Borel measures , the choice of Borel measure which assigns math mu a,b b a math for every interval math a,b math is sometimes called the Borel measure on R . In practice, even the Borel measure is not the most useful measure defined on the algebra of Borel sets indeed, the Lebesgue measure math lambda math is an extension of the Borel measure which possesses the crucial property that it is a complete measure unlike the Borel measure . To clarify, when one says that the Lebesgue measure math lambda math is an extension of the Borel measure math mu math , it means that every Borel measureable set E is also a Lebesgue measureable set, and the Borel measure and the Lebesgue measure coincide on the Borel sets i.e., math lambda E mu E math for every Borel measureable set . References cite book author ... 29715 X pages 158 184 DEFAULTSORT Borel Measure Category Measures measure theory de Borelma it Misura di Borel nl Borelmaat pl Miara borelowska pt Medida de Borel sv Borelm tt uk zh ... more details
Infobox scientist name mile Borel image Emile Borel 1932.jpg image size 200px caption mile Borel 1932 ... Lebesgue br Paul Montel br Georges Valiron known for awards F lix douard Justin mile Borel 7 January 1871 3 February 1956 ref DSB first Kenneth last May title Borel, mile volume 2 pages 302 305 ... 2.htm Emile Borel s biography Universit Lille Nord de France ref and politician . Borel was born in Saint ... of measure mathematics measure theory and its application to probability theory . The concept of a Borel ... a series of papers 1921 27 that first defined games of strategy. ref Emile Borel, Encyclop dia Britannica . http www.britannica.com EBchecked topic 74060 Emile Borel ref In 1913 and 1914 he bridged ... of the French Resistance . Borel died in Paris in 1956. Besides the Centre mile Borel at the Institut Henri Poincar in Paris and a Borel crater crater on the Moon , the following mathematical notions are named after him div style moz column count 2 column count 2 Borel algebra , Borel s lemma , Borel s law of large numbers , Borel measure , Borel Kolmogorov paradox , Borel Cantelli lemma , Borel Carath odory theorem , Heine Borel theorem , Borel summation . div Articles fr http amshistorica.cib.unibo.it ... reflist External links MacTutor Biography id Borel http www.genealogy.math.ndsu.nodak.edu html id.phtml?id 39071 mile Borel in the Mathematics Genealogy Project Universit Lille Nord de France Persondata Metadata see Wikipedia Persondata . NAME Borel, Emile ALTERNATIVE NAMES SHORT DESCRIPTION ... PLACE OF DEATH Paris , France DEFAULTSORT Borel, Emile Category 1871 births Category 1956 deaths Category ... French politicians ar bn ca mile Borel cs mile Borel de mile Borel es mile Borel fa fr mile Borel io mile Borel it mile Borel he kk , ht Emile Borel hu mile Borel nl mile Borel ja no mile Borel nn mile Borel pms mile Borel pl mile Borel pt mile Borel ro mile Borel ru , sk mile Borel sr sv mile Borel ... more details
lunar crater data latitude 22.3 N or S S longitude 26.4 E or W E diameter 5 km depth 1.0 km colong 334 eponym mile Borel F. E. E. Borel Borel is a tiny lunar impact crater located in the southeast part of Mare Serenitatis . To the northeast is the crater Le Monnier crater Le Monnier . Borel was previously identified as Le Monnier C before being named by the International Astronomical Union IAU . This is a roughly circular, cup shaped formation with inner floors that slope down to the mid point of the crater. The interior has a higher albedo than the surrounding dark lunar mare . References Lunar crater references Moon crater stub Category Impact craters on the Moon da Borel m nekrater de Borel Mondkrater fa fr Borel crat re ... more details
In mathematics , a Borel set is any set in a topological space that can be formed from open set s or, equivalently ... intersection set theory intersection , and relative complement . Borel sets are named after mile Borel . For a topological space X , the collection of all Borel sets on X forms a sigma algebra &sigma algebra , known as the Borel algebra or Borel sigma algebra &sigma algebra . The Borel algebra on X is the smallest algebra containing all open sets or, equivalently, all closed sets . Borel sets ... sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure . Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory . In some contexts, Borel sets are defined to be generated ... s, but can be different in more pathological mathematics pathological spaces. Generating the Borel algebra In the case X is a metric space, the Borel algebra in the first sense may be described generatively ... that the Borel algebra is G sup sub 1 sub sup , where sub 1 sub is the first uncountable ordinal first uncountable ordinal number . That is, the Borel algebra can be generated from the class of open ... under countable unions. Note that for each Borel set B , there is some countable ordinal &alpha ... varies over all Borel sets, &alpha sub B sub will vary over all the countable ordinals, and thus the first ordinal at which all the Borel sets are obtained is &omega sub 1 sub , the first uncountable ... , is the Borel algebra on the set of real number s. It is the algebra on which the Borel measure ... is by definition also a measure on the Borel algebra. The Borel algebra on the reals is the smallest ..., the power of the continuum . So, the total number of Borel sets is less than or equal to math aleph 1 times 2 aleph 0 , 2 aleph 0 , math . Standard Borel spaces and Kuratowski theorems This section is linked from Kazimierz Kuratowski The following is one of a number of theorems of Kuratowski on Borel ... more details
File Petrus Borel.jpg thumb right Petrus Borel French literature small Petrus Borel 26 June 1809 14 July 1859 was a French writer of the Romantic movement . Born Joseph Pierre Borel dHauterive at Lyon , the 12 of 14 children of an ironmonger, he studied architecture in Paris but abandoned it for literature. Nicknamed le Lycanthrope wolfman , and the center of the circle of Bohemianism Bohemians in Paris, he was noted for extravagant and eccentric writing, foreshadowing Surrealism . He was not commercially successful though, and eventually was found a minor civil service post by his friends, including Th ophile Gautier . He died at Mostaganem in Algeria . He was the subject of a biography by Enid Starkie , Petrus Borel The Lycanthrope 1954 . Works Rhapsodies 1831 Champavert, contes immoraux 1833 Madame Putiphar 1839 External links http poesie.webnet.fr auteurs borel.html Text of selected Borel poems in French http www.horrormasters.com Text a0193.pdf Text of Andreas Vesalius the Anatomist Persondata Metadata see Wikipedia Persondata . NAME Borel, Petrus ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 26 June 1809 PLACE OF BIRTH DATE OF DEATH 14 July 1859 PLACE OF DEATH DEFAULTSORT Borel, Petrus Category French poets Category 1809 births Category 1859 deaths de Joseph Pierre Borel d Hauterive es Petrus Borel fr P trus Borel it Petrus Borel nl P trus Borel sv P trus Borel ... more details
technical date November 2011 In mathematics, Borel isomorphism is a Borel measurable bijective function from one Polish space to another Polish space. Borel isomorphisms are closed under composition and under taking of inverses. The set of Borel isomorphisms from a Polish space to itself apparently forms a group under composition. Borel isomorphisms on Polish spaces are analogous to homeomorphism s on topological space s both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous , instead of both being Borel measurable. References Alexander S. Kechris , Classical Descriptive Set Theory , Springer Verlag, 1995 External links Borel Spaces, by S. K. Berberian http www.ma.utexas.edu mp arc c 02 02 156.pdf Real Analysis and Probability , page 487, Second edition, by R. M. Dudley http ebooks.cambridge.org chapter.jsf?bid CBO9780511755347&cid CBO9780511755347A091 A course on Borel sets by Sashi Mohan Srivastava http books.google.com books?id FhYGYJtMwcUC&pg PA169 Category Measure theory ... more details
Use dmy dates date May 2011 Notability date October 2008 Pascale Borel is a French pop singer. She was a member of the French pop group Mikado band in the 1980s. External links http www.pascaleborel.fr Official Website Fr icon http www.myspace.com pascaleborel Official Myspace page Fr icon Persondata Metadata see Wikipedia Persondata . NAME Borel, Pascale ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Borel, Pascale Category French female singers Category Year of birth missing living people Category Living people France singer stub fr Pascale Borel ... more details
for the French writer of the nineteenth century Petrus Borel Pierre Borel Petrus Borellius ca. 1620 &ndash 1671 ref DSB first Eduard last Farber title Borel, Pierre volume 2 pages 305 306 ref was a French savant a chemist and reputed Alchemy alchemist , physician, and botanist. He concerned himself with an eclectic range of subjects optics , ancient history, philology and bibliography. His biographers have tended to deplore his spreading of himself over so many areas. Life Borel was born in Castres Tarn Castres . He became a doctor of medicine at the University of Montpellier in 1640. In 1654 he became physician to the King of France, Louis XIV . In 1663 he married Esther de Bonnafous. In 1674 he became a member of the Acad mie fran aise . He died in Paris . Works Les antiquit s de Castres , 1649 Bibliotheca chimica , 1654 Tr sor de recherches et d antiquit s gauloises et fran aises , 1655 Historiarium et observationum medico physicarum centuriae IV De vero telescopii inventore , 1655. References references Marie Rose Carre, A Man between Two Worlds Pierre Borel and His Discours nouveau prouvant la pluralit des mondes of 1657 , Isis, Vol. 65, No. 3 Sep., 1974 , pp. 322 335 Pierre Chabbert, Pierre Borel 1620 ? 1671 , Revue d histoire des sciences 21 1968 , 303 43. External links fr icon http 209.85.135.104 search?q cache ZUsG1QXu1ngJ cehm.toulouse.free.fr fichier T63.doc 22Pierre Borel 22 Chabbert&hl en&gl uk&ct clnk&cd 10 Persondata Metadata see Wikipedia Persondata . NAME Borel, Pierre ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1620 PLACE OF BIRTH DATE OF DEATH 1689 PLACE OF DEATH DEFAULTSORT Borel, Pierre Category 1620 births Category 1689 deaths Category French scholars es Pierre Borel fr Pierre Borel sv Pierre Borel ... more details
Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Borel symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered September 11, 1999 designations yes mp name 16065 alt names 1999 RE35 named after mile Borel mp category orbit ref epoch May 14, 2008 aphelion 2.7780647 perihelion 2.5413151 semimajor eccentricity 0.0445070 period 1584.3274108 avg speed inclination 3.43914 asc node 61.12973 mean anomaly 108.56741 arg peri 165.95241 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 15.2 16065 Borel 1999 RE35 is a main belt asteroid discovered on September 11, 1999 by P. G. Comba at Prescott Observatory Prescott . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 16065 Borel JPL Small Body Database Browser on 16065 Borel MinorPlanets Navigator 16064 1999 RH27 16066 1999 RN39 MinorPlanets Footer DEFAULTSORT Borel Category Main Belt asteroids Category Asteroids named for people Category Discoveries by Paul G. Comba Category Astronomical objects discovered in 1999 beltasteroid stub de 16065 Borel fa it 16065 Borel pl 16065 Borel pt 16065 Borel uk 16065 vi 16065 Borel yo 16065 Borel ... more details
Infobox architect name Fr d ric Borel nationality French birth date 1959 birth place Roanne , France death date death place Fr d ric Borel is a French architect, born in 1959 in Roanne France . He graduated from the cole sp ciale d architecture Paris in 1982, and then began to work with Christian de Portzamparc . He created his own agency in Paris in 1984. His buildings are examples of deconstructivism deconstructivist architecture. Some buildings Apartment building boulevard de Belleville, Paris 1989 Apartment building rue Oberkampf, Paris 1994 Apartment building rue Pelleport, Paris 1999 Tribunal, Narbonne 2004 National school of architecture Paris Val de Seine 2007 Image Poste de la rue Oberkampf Paris , architecte Fr d ric Borel.jpg thumb Apartment building rue Oberkampf Paris External links http www.fredericborel.fr Fr d ric Borel s website fr http www.archilab.org public 2000 catalog borel borelfr.htm Presentation of his work on the Archilad website archINFORM arch 7 Persondata Metadata see Wikipedia Persondata . NAME Borel, Frederic ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1959 PLACE OF BIRTH Roanne , France DATE OF DEATH PLACE OF DEATH DEFAULTSORT Borel, Frederic Category French architects Category Modernist architecture in France Category 1959 births Category Living people fr Fr d ric Borel ... more details
Infobox football biography name Felice Borel image fullname Felice Placido Borel II birth date April 5, 1914 birth place Nizza Monferrato , Italy currentclub clubnumber height convert 1.75 m ftin 0 abbr on position Forward years1 1932 1941 years2 1941 1942 years3 1942 1946 years4 1946 1947 years5 1948 1949 clubs1 Juventus F.C. Juventus clubs2 Torino F.C. Torino clubs3 Juventus F.C. Juventus clubs4 U.S. Alessandria Calcio 1912 Alessandria clubs5 S.S.C. Napoli Napoli caps1 206 goals1 118 caps2 25 goals2 7 caps3 27 goals3 10 caps4 1 goals4 0 caps5 1 goals5 0 nationalyears1 1933 1934 nationalteam1 Italian national football team Italy nationalcaps1 3 nationalgoals1 1 manageryears1 1942 1946 manageryears2 1946 1947 manageryears3 1948 1949 managerclubs1 Juventus F.C. Juventus managerclubs2 U.S. Alessandria Calcio 1912 Alessandria managerclubs3 S.S.C. Napoli Napoli Felice Placido Borel April 5, 1914, Nizza Monferrato &ndash January 21, 1993 was an Italy Italian football soccer football player who played as a striker. His older brother Aldo Borel played football professionally, spending 10 seasons in the Serie A , and their father Ernesto Borel played for OGC Nice , AS Cannes and Juventus F.C. in the 1900s and 1910s. To distinguish the brothers, Aldo was known as Borel I and Felice as Borel II . Borel was born in Nizza Monferrato , Italy . During his career, he played for Juventus F.C. Juventus and Torino F.C. Torino in Serie A and, in Serie B, for U.S. Alessandria Calcio 1912 Alessandria , and finally for S.S.C. Napoli , where he finished his career. During the 1958 59 season, he was technical ... Napoli managers Persondata Metadata see Wikipedia Persondata . NAME Borel, Felice ALTERNATIVE NAMES ... January 21, 1993 PLACE OF DEATH DEFAULTSORT Borel, Felice Category 1914 births Category 1993 deaths ... ca Felice Placido Borel de Felice Borel es Felice Borel fr Felice Borel id Felice Borel it Felice Borel pms Felice Borel pl Felice Borel ru , uk ... more details
unreferenced date May 2009 Infobox Person name Eug ne Borel image Eug ne Borel.gif caption Switzerland Swiss politician and founding director of the UPU . quotation Founder of the UPU . birth date birth date 1835 6 17 mf y birth place Neuch tel , Switzerland dead dead death date death date and age 1892 6 14 1835 6 17 mf y death place Bern , Switzerland Eug ne Borel June 17, 1835 June 14, 1892 was a Switzerland Swiss politician and member of the Swiss Federal Council 1872 1875 . Early life He was born in Neuch tel to Fran ois Victor and Louise Borel. He was educated at the humanistic high school in Neuch tel and then studied the law in Munich and Heidelberg . After finishing his studies he worked as a lawyer in Neuch tel. In 1861 he married Marie Gullaume. Borel became an auditor and translator in the National Council of Switzerland in 1860. In 1870 he was elected inquisitor for western Switzerland by the Federal Supreme Court of Switzerland federal court . Politics In 1857 he was elected into the legislative branch Generalrat of the city of Neuch tel for the radical party, which is now the Free Democratic Party of Switzerland . He was elected to the city council in 1864, to the Grand Council of Neuch tel Grand Council of the canton of Neuch tel and in 1865 he became a member of the Swiss ... player in the founding of the Universal Postal Union UPU with the Treaty of Bern in 1874. Borel ... . Borel was sent there and, together with troops from Z rich , he managed to restore order. Borel ... Borel start box succession box before Arnold Otto Aepli title President of the Swiss Council of States ... end box Persondata Metadata see Wikipedia Persondata . NAME Borel, Eugene ALTERNATIVE NAMES SHORT ... 14, 1892 PLACE OF DEATH Bern , Switzerland DEFAULTSORT Borel, Eugene Category 1835 births Category 1892 ... Eug ne Borel de Eug ne Borel fr Eug ne Borel it Eug ne Borel la Eugenius Borel nl Eug ne Borel pt Eug ne Borel ru , ... more details
In mathematical logic , the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space elements of this algebra are called Borel sets . Each Borel set is assigned a unique countable ordinal number called the rank of the Borel set. The Borel hierarchy is of particular interest in descriptive set theory . One common use of the Borel hierarchy is to prove facts about the Borel sets using transfinite induction on rank. Properties of sets of small finite ranks are important in measure theory and Mathematical analysis analysis . Borel sets main Borel algebra The Borel algebra in an arbitrary topological space is the smallest collection of subsets of the space ... be shown that the Borel algebra is closed under countable intersections as well. A short proof that the Borel ... under complements and countable unions, and thus the Borel algebra is the intersection of all families ... for determining whether a set is Borel. A motivation for the Borel hierarchy is to provide a more explicit characterization of the Borel sets. In many cases, the Borel algebra does not contain all subsets of the space. If the space is an uncountable Polish space then there are many sets that are not Borel. If the space is a countable set with the discrete topology then every subset is Borel. Boldface hierarchy The Borel hierarchy or boldface Borel hierarchy on a space X consists of classes ... a Borel set could be constructed from open sets using complementation and countable unions. A Borel ... 1 mathbf Delta 0 alpha math . Moreover, a set is in this union if and only if it is Borel. For every .... Borel sets of small rank The classes of small rank are known by alternate names in classical descriptive ... G sub &delta sub sets . Lightface hierarchy The lightface Borel hierarchy is an effective version of the boldface Borel hierarchy. It is important in effective descriptive set theory and recursion theory . The lightface Borel hierarchy extends the arithmetical hierarchy of subsets of an effective Polish ... more details
Borel is a former settlement in Kern County, California Kern County , California . ref name CGN It was located convert 2.5 mi km 0 southwest of Vaughn, California Vaughn . ref name CGN California s Geographic Names 1005 ref A post office operated at Borel from 1904 to 1908. ref name CGN The name comes from the Borel Canal Construction Company . ref name CGN References reflist Kern County, California coord missing Kern County, California Category Former settlements in Kern County, California Category Former populated places in California KernCountyCA geo stub ... more details
quote box align right width 33 quote Borel, then an unknown young man, discovered that his summation .... Mittag Leffler listened politely to what Borel had to say and then, placing his hand upon the complete ... Mark Kac , quoted by harvtxt Reed Simon 1978 p 38 In mathematics, Borel summation is a summation method for divergent series , introduced by harvs txt first Emile last Borel year 1899 authorlink Emile Borel . There are several variations of this method that are also called Borel summation. Definition Let math y z sum k 0 infty y kz k math be a formal power series in z . Define the Borel ... Suppose that the Borel transform converges to an analytic function near 0 that can be analytic continuation ... that the following integral is well defined as an improper integral . Then the Borel sum of y is given by math int 0 infty e t mathcal B y tz , dt. math A slightly weaker form of Borel s summation method gives the Borel sum of y as math lim t rightarrow infty e t sum n frac t n n cdot sum k le ... 1. The Borel transform is math mathcal B y t sum k 0 infty frac 1 k t k e t. math So the Borel sum .... The series math y z sum k 0 infty 1 kk z k math does not converge for any nonzero z . The Borel transform ... continued to all t 0. So the Borel sum is math int 0 infty e t mathcal B y tz , dt int 0 infty frac ... is Borel summable for all such z . This function has an asymptotic expansion as z tends to 0 that is given by the original divergent series. This is a typical example of the fact that Borel summation will sometimes correctly sum divergent asymptotic expansions. The Borel polygon The region where the power series of an analytic function is Borel summable was described as follows by Borel and Phragmen ... of the origin then it has a Borel sum at some point z if it can be analytically continued to a disc ... 0 z then it is Borel summable at z . The set of points z such that the function can be analytically ... number of singularities, called the Borel polygon. Its edges pass through the singular points ... more details
Infobox football biography name Aldo Borel fullname Aldo Giuseppe Borel image birth date birth date 1912 5 30 birth place Nice , France height height m 1.82 currentclub clubnumber position Midfielder youthyears1 youthclubs1 years1 1929 1931 years2 1931 1932 years3 1932 1933 years4 1933 1935 years5 1935 1938 years6 1938 1939 years7 1939 1940 years8 1940 1941 clubs1 Torino F.C. Torino clubs2 A.S. Casale Calcio Casale clubs3 ACF Fiorentina Fiorentina clubs4 U.S. Citt di Palermo Palermo clubs5 Juventus F.C. Juventus clubs6 Novara Calcio Novara clubs7 Savona 1907 F.B.C. Savona clubs8 Omegna Sportiva Omegna caps1 2 caps2 32 caps3 16 caps4 34 caps5 37 caps6 12 caps7 15 goals1 1 goals2 16 goals3 9 goals4 12 goals5 7 goals6 1 goals7 9 nationalyears1 nationalteam1 nationalcaps1 nationalgoals1 manageryears1 managerclubs1 pcupdate ntupdate Aldo Giuseppe Borel born May 30, 1912 in Nice , France was an Italy Italian professional Association football football player. His younger brother Felice Borel won the 1934 FIFA World Cup with Italy national football team , and their father Ernesto Borel played for OGC Nice , AS Cannes and Juventus F.C. in the 1900s and 1910s. To distinguish the brothers, Aldo was known as Borel I and Felice as Borel II . External links http www.playerhistory.com Default.aspx?page player details&playerID 94379 Career summary by playerhistory.com Persondata Metadata see Wikipedia Persondata . NAME Borel, Aldo ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH May 30, 1912 PLACE OF BIRTH Nice , France DATE OF DEATH February 28, 1979 PLACE OF DEATH Spain DEFAULTSORT Borel, Aldo Category 1912 births Category Year of death missing Category Italian footballers Category Serie A footballers Category Torino F.C. players Category A.S. Casale Calcio players Category ACF Fiorentina players Category U.S. Citt di Palermo players Category Juventus F.C. players Category Novara Calcio players Italy footy midfielder 1910s stub fr Aldo Borel it Aldo Giuseppe Borel ... more details
File Daniel Borel in 2008.jpg thumb Daniel Borel in 2008 Daniel Borel born February 14, 1950 ref name ForbesBio Citation needed date February 2010 is a Switzerland Swiss ref name NestleBio cite web url http www.nestle.com AllAbout Governance NestleManagement AllCvs BoardDirectors DanielBOREL.htm title Daniel Borel Nestle Board of Directors Bio publisher Nestle accessdate 13 February 2010 ref businessman and co founder of Logitech . In 1973 Daniel Borel earned an engineering degree in Physics from the cole Polytechnique F d rale de Lausanne in Switzerland, ref name BWBio and in 1977 received a Master of Science degree in Computer Science in 1977 from Stanford University . ref name ForbesBio cite web url http people.forbes.com profile daniel borel 49987 title Daniel Borel Profile Forbes publisher Forbes accessdate 13 February 2010 ref ref name BWBio Borel co founded Logitech at his father in law s farm in 1981 with Pierluigi Zappacosta and Giacomo Marini . ref name swissInfo cite news url http www.swissinfo.ch eng Mouse maker reveals how niche players succeed.html?cid 5136766 title Mouse maker reveals how niche players succeed last Allen first Matthew date April 20, 2006 publisher swissinfo accessdate 13 February 2010 location Switzerland ref He served as Logitech s Chairman 1982 to 2008, and served as the company s CEO from 1982 to 1988, ref name NestleBio ref name BWBio cite web ...&ticker LOGN VX&previousCapId 388005&previousTitle Logitech 20International 20S 20A title Daniel Borel ... us,en title Daniel Borel Executive Bios publisher Logitech accessdate 13 February 2010 ref and on the Nasdaq ... NestleBio Borel currently serves on the board of directors of Logitech and Nestl . ref name NestleBio ... Persondata . NAME Borel, Daniel ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 14 February 1950 PLACE OF BIRTH DATE OF DEATH PLACE OF DEATH DEFAULTSORT Borel, Daniel Category 1950 births Category ... alumni Switzerland bio stub de Daniel Borel fr Daniel Borel ru , ... more details
Infobox Company name Ernest Borel logo type foundation 1856 location city Le Noirmont location country Switzerland location modifies Headquarters entry locations of locations key people M.Jules Borel, Entrepreneur Founder area served industry Watch manufacturing products Wristwatches services revenue operating income net income num employees parent divisions subsid slogan Romance in heart homepage http www.ernestborel.ch dissolved footnotes intl yes Enter yes to change labels to international instead of US terminology Ernest Borel is a watch manufacturer founded in 1856 in Neuchatel, Switzerland. They have traditionally focused on export markets outside Europe. They won several awards in the late 19th century, including first place in the 1866 Neuchatel observatory timing accuracy competition. This was viewed by the company as an important marketing strategy for increasing the brand s value, since the Neuchatel observatory was famed at the time for its timekeeping accuracy. In 1876 they were ... Borel family until 1975 when, owing to the Quartz crisis affecting the entire Swiss watchmaking industry ... Cyma and Doxa S.A. Doxa . Ernest Borel SA is headquartered at their new factory premises at Le Noirmont ... Borel is Mr Raphael Bouillat, who has been at the helm of the company since 1997. Products Ernest Borel currently produces traditionally styled automatic and quartz movement wrist watches for men .... The manufacturer s life time warranty on movements, sets Ernest Borel apart from most competitors ... range from the low hundreds of USD up to the mid thousands of USD. Ernest Borel appears to be focussing their marketing on China at present, with the opening of a dedicated Ernest Borel shop in Beijing ... main Ernest Borel football Ernest Borel sponsored a football soccer football team which played in Hong ...? archives 24 Review of the Ernest Borel Deep Blue automatic.html http www.thewatchplaceonline.com ernest borel.htm DEFAULTSORT Borel, Ernest Category Watch manufacturing companies of Switzerland ... more details
Image Borel.jpg thumb right Borel share certificate of 1918 Etablissements Borel was a French aircraft manufacturer of the early twentieth century. It was founded by Gabriel Borel 1880 19?? and manufactured a number of monoplane designs between 1909 and 1914. The factory, located at Mourmelon was temporarily forced to close when the outbreak of World War I saw most of its workers conscripted into the army, but Borel re opened in November 1915 to produce military aircraft for France under licence from other manufacturers including Caudron , Nieuport and SPAD . After the war, Borel was restructured as the Soci t G n rale des Constructions Industrielles et M caniques SGCIM and attempted to re market one of its torpedo bomber designs as a civil transport. However, neither this nor two new generation fighter designs were able to keep the company in business. References cite book last Gunston first Bill title World Encyclopedia of Aircraft Manufacturers year 1993 publisher Naval Institute Press location Annapolis pages 54 55 Category Defunct aircraft manufacturers of France ... more details
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