In functional analysis , a branch of mathematics , the Borelfunctionalcalculus is a functionalcalculus ... the kind of function of an operator which is allowed. The Borelfunctionalcalculus is more general than the continuous functionalcalculus . More precisely, the Borelfunctionalcalculus allows us ... section. The bounded functionalcalculus Formally, the bounded Borelfunctionalcalculus ... Borelfunctionalcalculus. This defines the functionalcalculus for bounded functions applied to possibly unbounded self adjoint operators. Using the bounded functionalcalculus, one can prove part of the Stone ... use the Borelfunctionalcalculus to abstractly solve some linear initial value problem s such as the heat equation, or Maxwell s equations. Existence of a functionalcalculus The existence of a mapping with the properties of a functionalcalculus requires proof. For the case of a bounded self adjoint operator T , the Borel existence of a Borelfunctionalcalculus can be shown in an elementary way as follows First pass from polynomial to continuous functionalcalculus by using the Stone Weierstrass ... T , the range of the continuous functionalcalculus h h T is the abelian C algebra C T generated by T . The Borelfunctionalcalculus has a larger range, that is the closure of C T in the weak operator topology , a still abelian von Neumann algebra . The general functionalcalculus We can also define the functionalcalculus for not necessarily bounded Borel functions h the result is an operator ... function s s sup 2 sup to T yields the operator T sup 2 sup . Using the functionalcalculus .... However, it is desirable to formulate the functionalcalculus in a way in which it is clear that it does ... functionalcalculus. Alternatively, the continuous calculus can be obtained via the Gelfand ... dom S math The operator S of the previous theorem is denoted h T . More generally, a Borelfunctional ... are given, this expression is purely formal. References references Category Functionalcalculus de ... more details
be. For technical accounts see holomorphic functionalcalculus continuous functionalcalculusBorelfunctionalcalculus . References Springer id F f042030 title Functionalcalculus DEFAULTSORT FunctionalCalculus Category Functionalcalculus de Funktionalkalk l nl Functionele calculus ...In mathematics , a functionalcalculus is a theory allowing one to apply mathematical function s to mathematical operator s. It is now a branch more accurately, several related areas of the field of functional analysis , connected with spectral theory . Historically, the term was also used synonymously with calculus of variations this usage is obsolete, but see functional derivative . Sometimes it is used in relation to types of functional equation , or in logic for systems of predicate calculus . If f is a function, say a numerical function of a real number , and M is an operator, there is no particular reason why the expression f M should make sense. If it does, then we are no longer using f on its original function domain . In the tradition of operational calculus , algebraic expressions in operators are handled irrespective of their meaning. This passes nearly unnoticed if we talk about squaring a matrix , though, which is the case of f x x sup 2 sup and M an n × n matrix mathematics matrix . The idea of a functionalcalculus is to create a principled approach to this kind of overloading of the notation. The most immediate case is to apply polynomial function s to a square matrix , extending what has just been discussed. In the finite dimensional case, the polynomial functionalcalculus yields quite a bit of information about the operator. For example, consider the family of polynomials which annihilates an operator T . This family is an ideal ring theory ideal in the ring ... calculus is not as informative in the infinite dimensional case. Consider the unilateral shift with the polynomials calculus the ideal defined above is now trivial. Thus one is interested in functional ... more details
Unreferenced date December 2009 In mathematics , the continuous functionalcalculus of operator theory and C algebra theory allows applications of continuous functions to normal elements of a C algebra. More precisely, Theorem . Let x be a normal operator normal element of a C algebra A with an identity element 1 then there is a unique mapping f f x defined for f a continuous function on the spectrum Sp x of x such that is a unit preserving morphism of C algebras such that 1 1 and x , where denotes the function z z on Sp x . The proof of this fact is almost immediate from the Gelfand representation it suffices to assume A is the C algebra of continuous functions on some compact space X and define math pi f f circ x. math Uniqueness follows from application of the Stone Weierstrass theorem . In particular, this implies that bounded self adjoint operators on a Hilbert space have a continuous functionalcalculus. For the case of self adjoint operator mathematics operator s on a Hilbert space of more interest is the Borelfunctionalcalculus . DEFAULTSORT Continuous FunctionalCalculus Category Functionalcalculus Category Continuous mappings de Stetiger Funktionalkalk l ... more details
no footnotes date March 2012 In mathematics , holomorphic functionalcalculus is functionalcalculus .... Motivation Need for a general functionalcalculus In this section T will be assumed to be a n ... T sup 0 sup I , the identity matrix . This is the polynomial functionalcalculus . It is a homomorphism ... T geq 1. , math Thus a more general functionalcalculus is needed. Functionalcalculus and the spectrum ... out to be an enabling condition such that the functionalcalculus map math f rightarrow f T , math has certain desirable properties. Functionalcalculus for a bounded operator Image Functionalcalculus ... component s and the corresponding path . Image Functionalcalculus illustration3.png thumb ... defined, this proposed functionalcalculus implies the following necessary conditions As the scalar ... mapping is holomorphic on the complement of T . So, to obtain a non trivial functionalcalculus, must enclose, at least part of, T . The functionalcalculus should be well defined in the sense that f T is independent of . The full definition of the functionalcalculus is as follows For T L ... of the functionalcalculus, &fnof is assumed to be holomorphic in an open neighborhood of . It will be shown ... z 1 ,d zeta. math The holomorphic functionalcalculus is similar in that the resolvent mapping plays a crucial role in obtaining properties one requires from a nice functionalcalculus. This subsection ... is complex differentiable at each z sub 1 sub T so the integral in the expression of functionalcalculus .... This property will be used in subsequent arguments for the functionalcalculus. To verify this claim ... is contained in the outside of . Hence, for the definition of the functionalcalculus, indeed a suitable ... has not been shown is that the definition of the functionalcalculus is unambiguous, i.e. does not depend ... g 0. , math Main argument The well definedness of functionalcalculus now follows as an easy consequence ... of Jordan curves satisfying the assumption given for the functionalcalculus. We wish to show ... more details
Borel may refer to Armand Borel 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 Armand BorelBorel 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
About the branch of mathematics other uses Calculus disambiguation pp move indef Merge from Infinitesimal calculus discuss Talk Calculus Merge with infinitesimal calculus date May 2011 CalculusCalculus Latin , wikt en calculus Latin calculus , a small stone used for counting is a branch of mathematics ... education . It has two major branches, differential calculus and integral calculus , which are related by the fundamental theorem of calculus . Calculus is the study of change, ref citation title Calculus ... in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis . Calculus has widespread applications in science ... alone is insufficient. Calculus has historically been called the calculus of infinitesimal s , or infinitesimal calculus . More generally, calculus plural calculi refers to any method or system of calculation ... calculi are propositional calculus , variational calculus , lambda calculus , pi calculus , and join calculus . History Attention leave dates as they are. We re not really that bothered, as the majority of Wikipedia dates state BC . Just think of it as Before Cronholm Main History of calculus Ancient File GodfreyKneller IsaacNewton 1689.jpg thumb 200px right Isaac Newton developed the use of calculus ... of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. Calculations of volumes and areas, one goal of integral calculus, can be found ... of integral calculus. ref Archimedes, Method , in The Works of Archimedes ISBN 978 0 521 66160 ... the volume of a sphere . ref cite book title Calculus Early Transcendentals edition 3 first1 Dennis ... many components of calculus such as the Taylor series , infinite series approximations, an integral .... Some consider the Yuktibh to be the first text on calculus. ref http www history.mcs.st andrews.ac.uk ... width 30em max width 30 cellspacing 5 style text align left The calculus was the first achievement ... more details
wiktionarypar functional Generally, functional refers to something able to fulfill its purpose or function. Functionalism architecture Functionalism and Functional form , movements in architecture architectural design Functional group , certain atomic combinations that occur in various molecules, e.g. carbonyl, amine Functional symptom , sometimes used in medicine to describe symptoms that have no current visible organic basis Functional classification , a classification system for roads in the United States. In mathematics and computer science Functional mathematics , a term applied to certain scalar valued functions in mathematics and computer science . Functional analysis Linear functional , a type of functional often simply called a functional in the context of functional analysis In an ontology information science ontology , functional is a property or relation that can only hold a single value for a given individual Functional programming , a programming paradigm based on mathematical functions rather than changes in variable states In software engineering Functional design , a paradigm used to simplify the design of hardware and software devices Functional model , a structured representation of functions, activities or processes in systems and software engineering See also Function disambiguation Functionalism disambiguation Functional group disambiguation Functional grammar disambiguation disambig ru ... 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 algebra that contains the open sets of X this is known as the algebra of Borel set s. 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 ... that a locally finite Borel measure automatically satisfies C for every compact set ... 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 measurable set E is also a Lebesgue measurable 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 measurable set . References cite book author J. D. Pryce title Basic methods of functional analysis series Hutchinson University Library publisher Hutchinson ... pages 158 184 DEFAULTSORT Borel Measure Category Measures measure theory de Borelma fr mesure de Borel homonymie it Misura di Borel nl Borelmaat pl Miara borelowska pt Medida de Borel sv Borelm tt uk ... 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
wiktionarypar calculusCalculus from Latin language Latin wikt en calculuscalculus Latin meaning pebble ... . Calculus may refer to In mathematics and computer science Calculus , also the calculus , short for differential calculus and integral calculus , which investigate motion and rates of change Logical calculus, a formal system that defines a language and rules to derive an expression from premises ... and integral calculus The calculus of sums and differences difference operator , also called the finite difference calculus, a discrete analogue of the calculus In symbolic logic the propositional calculus , specifies the rules of inference governing the logic of propositions the predicate calculus , specifies the rules of inference governing the logic of predicates a proof calculus , a framework for expressing systems of logical inference the sequent calculus , a proof calculus for first order logic Bondi k calculus Bondi k calculus , a method used in relativity theory Domain relational calculus , a calculus for the relational data model Epsilon calculus , a logical language which replaces quantifiers with the epsilon operator Functionalcalculus , a way to apply various types of functions to operators Join calculus , a theoretical model for distributed programming Lambda calculus ... Matrix calculus , a specialized notation for multivariable calculus over spaces of matrices Modal calculus , a common temporal logic used by formal verification methods such as model checking Non standard calculus , an approach to infinitesimal calculus using Robinson s infinitesimals Pi calculus ... Milner Refinement calculus , a way of refining models of programs into efficient programs Rho calculus , introduced as a general means to uniformly integrate rewriting and lambda calculus Schubert calculus , a branch of algebraic geometry Tuple calculus , a calculus for the relational data model, inspired the SQL language Umbral calculus , the combinatorics of certain operations on polynomials The calculus ... more details
Expand French Adrien Borel date April 2012 Adrien Borel 1886 1966 was a France French psychiatrist and psychoanalyst. Persondata Metadata see Wikipedia Persondata . NAME Borel, Adrien ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 1886 PLACE OF BIRTH DATE OF DEATH 1966 PLACE OF DEATH DEFAULTSORT Borel, Adrien Category 1886 births Category 1966 deaths Category French psychiatrists Category French psychoanalysts bg fr Adrien Borel France med bio stub ... 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 fa fr P trus Borel it Petrus Borel nl P trus Borel sv P trus 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
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 be 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 ... 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
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 . The Borel algebra on X is the smallest algebra containing all open sets or, equivalently, all closed sets . Borel sets are important ... 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 by the compact ... 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 as follows ... . math If i is a limit ordinal, set math G i bigcup j i G j. math We now claim that the Borel algebra ... ordinal number . That is, the Borel algebra can be generated from the class of open sets by iterating ... unions. Note that for each Borel set B , there is some countable ordinal &alpha sub B sub such that B ... 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 ordinal. Example An important example, especially in the probability theory theory of probability , is the Borel algebra on the set of real number s. It is the algebra on which the Borel measure is defined. Given a real ... also a measure on the Borel algebra. The Borel algebra on the reals is the smallest algebra on R ... . 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 ... 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
Notability Astro date February 2012 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 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 ... , Italy DATE OF DEATH January 21, 1993 PLACE OF DEATH DEFAULTSORT Borel, Felice Category 1914 births ... bg 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 s start succession box before Arnold Otto Aepli title President of the Swiss Council of States ... s end Persondata Metadata see Wikipedia Persondata . NAME Borel, Eugene ALTERNATIVE NAMES SHORT DESCRIPTION ... PLACE OF DEATH Bern , Switzerland DEFAULTSORT Borel, Eugene Category 1835 births Category 1892 ... 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
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
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
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 ?1960 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
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. Borel subgroups are one of the two key ingredients in understanding the structure of simple more generally, reductive group reductive algebraic groups, in Jacques Tits theory of groups with a B,N pair . Here the group B is a Borel subgroup and N is the normalizer of a maximal torus contained in B . The notion was introduced by Armand Borel , who played a leading role in the development of the theory of algebraic groups. Parabolic 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 ... h math , the Borel subalgebra is the direct sum of math mathfrak h math and the weight space s of math mathfrak g math with positive weight. A Lie subalgebra of math mathfrak g math containing a Borel ... Groups location New York publisher Springer year 1972 isbn 0 387 90108 6 cite book author A. Borel ... subgroup oldid 16195 first V.L. last Popov SpringerEOM title Borel subgroup id Borel subgroup oldid ... 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
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