In mathematics, a building ( also Tits building, Bruhat – Tits building, named after François Bruhat and Jacques Tits ) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces.

He was both an influential researcher and teacher, with students such as Bernard Malgrange, Jacques-Louis Lions, François Bruhat and Alexander Grothendieck.

In mathematics, the Bruhat decomposition ( named after François Bruhat ) G = BWB into cells can be regarded as a general expression of the principle of Gauss – Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices — but with exceptional cases.

This can be seen directly, but is also a special case of general results on ireducibility of induced representations due to François Bruhat and George Mackey, relying on the Bruhat decomposition G = B B s B where s is the Weyl group element.

The map taking w to BwB is an isomorphism from the set of elements of W to the set of double cosets of B ; this is the Bruhat decomposition G = BWB.

Iwahori – Matsumoto, Borel – Tits and Bruhat – Tits demonstrated that in analogy with Tits ' construction of spherical buildings, affine buildings can also be constructed from certain groups, namely, reductive algebraic groups over a local non-Archimedean field.

* The Bruhat decomposition G = BWB of a semisimple algebraic group into double cosets of a Borel subgroup can be regarded as a general expression of the principle of Gauss – Jordan elimination, which generically writes a matrix as the product of an upper triangular matrix with a lower triangular matrix — but with exceptional cases.

Georges Bruhat asked him to come back to the École Normale Supérieure, where he finally obtained a chair in 1952.

On 31 July 2012, the Bruhat Bengaluru Mahanagara Palike ( BBMP ) council passed a resolution to bring Electronics City within the limits of Greater Bangalore.

In the Bruhat decomposition of the flag variety of a Lie group, the fundamental class corresponds to the top-dimension Schubert cell, or equivalently the longest element of a Coxeter group.

In the special case when the hyperplanes arise from a root system, the resulting poset is the corresponding Weyl group with the weak Bruhat order.

The college also has industrial interactions with companies like ABB, Indian Space Research Organisation ( ISRO ), Bruhat Bengaluru Mahanagara Palike ( BBMP ), DELL, WIPRO, Gas Turbine Research Establishment ( GTRE ) and the Indian Railways.

More generally, any group with a ( B, N ) pair has a Bruhat decomposition.

In this case, we can take B to be the subgroup of upper triangular invertible matrices, so Bruhat decomposition says that one can write any invertible matrix A as a product U < sub > 1 </ sub > PU < sub > 2 </ sub > where U < sub > 1 </ sub > and U < sub > 2 </ sub > are upper triangular, and P is a permutation matrix.

The cells in the Bruhat decomposition correspond to the Schubert cell decomposition of Grassmannians.

The number of cells in a given dimension of the Bruhat decomposition are the coefficients of the q-polynomial of the associated Dynkin diagram.

* Birkhoff factorization, a special case of the Bruhat decomposition for affine groups.

In 2011, the Bruhat Bangalore Mahanagara Palike announced that the road would be widened in several places and underpasses and flyovers would be built at major junctions.

In 2006, the Bruhat Bengaluru Mahanagara Palike ( BBMP ), the third level of government, passed a resolution to implement the proposed name change.

The Physiocrats were partially influenced by Chinese agrarianism ; leading physiocrats like François Quesnay were avid Confucianists that advocated China's agrarian policies.

Pseudonyms adopted by authors are sometimes transposed forms of their names ; thus " Calvinus " becomes " Alcuinus " ( here V = U ) or " François Rabelais " = " Alcofribas Nasier ".

Major academic sculptors of France are represented in the sculpture of the Arc de Triomphe: Jean-Pierre Cortot ; François Rude ; Antoine Étex ; James Pradier and Philippe Joseph Henri Lemaire.

This was inaugurated by Montalembert, but its literary advocates were chiefly Dom Gueranger, a learned Benedictine monk, abbot of Solesmes, and Louis François Veuillot ( 1813 – 1883 ) of the Univers ; and it succeeded in suppressing them everywhere, the last diocese to surrender being Orleans in 1875.

The best known composers from this period are Joseph Haydn, Wolfgang Amadeus Mozart, and Ludwig van Beethoven ; other notable names include Luigi Boccherini, Muzio Clementi, Antonio Soler, Antonio Salieri, François Joseph Gossec, Johann Stamitz, Carl Friedrich Abel, Carl Philipp Emanuel Bach, and Christoph Willibald Gluck.

When over 25, 000 of these royalists — led by General Danican — assaulted Paris, Paul François Jean Nicolas, vicomte de Barras was appointed to defend the capital ; outnumbered five to one and disorganized, the Republicans were desperate.

In the 2009 European Parliament election the EFA got six MEPs elected: two from the SNP ( Ian Hudghton and Alyn Smith ), one from the PC ( Jill Evans ), one from the Party of the Corsican Nation ( PNC ; François Alfonsi ), one from the ERC ( Oriol Junqueras ) and Tatjana Ždanoka, individual member of the EFA from Latvia.

The day after that ( Tuesday ), Verdi's father took his newborn the three miles to Busseto, where the baby was recorded as Joseph Fortunin François ; the clerk wrote in French.

This was an early conception, and in early times the order in question was simply verbal ; some letters patent of Henry III of France in 1576 state that François de Montmorency was " prisoner in our castle of the Bastille in Paris by verbal command " of the late king Charles IX.

by J. F. Condon, continued to 1861, New Orleans, 1882 ) is the first scholarly treatment of the subject, along with François Barbé-Marbois ' Histoire de la Louisiane et de la cession de colonie par la France aux Etats-Unis ( Paris, 1829 ; in English, Philadelphia, 1830 ).

Later, with Nicolas Boileau and François de Malherbe, rhetoric is the instrument of the clarity of the comment and speech ; the literature that ensues from it is named " Sublime ".

François Rabelais gives tarau as the name of one of the games played by Gargantua in his Gargantua and Pantagruel ; this is likely the earliest attestation of the French form of the name.

In Europe, Art Cinema gains wider distribution and sees movements like la Nouvelle Vague ( The French New Wave ) featuring French filmmakers such as Roger Vadim, François Truffaut, Alain Resnais, and Jean-Luc Godard ; Cinéma Vérité documentary movement in Canada, France and the United States ; Swedish filmmaker Ingmar Bergman, Chilean filmmaker Alexandro Jodorowsky and Polish filmmakers Roman Polanski and Wojciech Jerzy Has produced original and offbeat masterpieces and the high-point of Italian filmmaking with Michelangelo Antonioni and Federico Fellini making some of their most known films during this period.

** François Duvalier, president of Haiti, dies ; his son Jean-Claude Duvalier follows him as president-for-life.

* February 21 – 26 – Seven Years ' War – At the Battle of Carrickfergus in the north of Ireland, a force of French troops under the command of privateer François Thurot captures and holds the town and castle of Carrickfergus before retiring ; the force is defeated ( and Thurot killed ) in a naval action in the Irish Sea on February 28.

Edward Bromhead, who knew John Boole through the Institution, helped George Boole with mathematics books ; and he was given the calculus text of Sylvestre François Lacroix by Rev.

Oscar I ( born Joseph François Oscar Bernadotte ; 4 July 1799 – 8 July 1859 ) was King of Sweden and Norway from 1844 to his death.

In April 1865 Louis François Janin proposed a double wire with diamond-shaped metal barbs ; he was granted a patent.

Journalist François Chalais also criticized The Story of O, claiming the novel glorified violence ; he described the novel as " bringing the Gestapo into the boudoir ".

The first fully developed constructed languages we know of, as well as the first constructed languages devised primarily as auxlangs, originated in the 19th century ; Solresol by François Sudre, a language based on musical notes, was the first to gain widespread attention although not, apparently, fluent speakers.

Patrice Lumumba was married to Pauline Lumumba and had five children ; François was the eldest followed by Patrice Junior, Julienne, Roland and Guy-Patrice Lumumba.

Other important early publications include: Edward H. Chamberlin's ( 1950 ) The Theory of Monopolistic Competition ; François Perroux's ( 1950 ) Economic Spaces: Theory and Application ; Torsten Hägerstrand's ( 1953 ) Innovationsförloppet ur Korologisk Synpunkt ; Edgar S. Dunn's ( 1954 ) The Location of Agricultural Production ; Martin J. Beckmann, C. B McGuire, and Clifford B. Winston's ( 1956 ) Studies in the Economics of Transportation ; Melvin L. Greenhut's ( 1956 ) Plant Location in Theory and Practice ; Gunnar Myrdal's ( 1957 ) Economic Theory and Underdeveloped Regions ; Albert O. Hirschman's ( 1958 ) The Strategy of Economic Development ; and Claude Ponsard's ( 1958 ) Histoire des Théorie Économique Spatiales.