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Connes and has
The Baum – Connes conjecture, now a long-standing problem, has been joined by others in a group known as the isomorphism conjectures in K-theory.
The leading direction in noncommutative geometry has been laid by French mathematician Alain Connes since his involvement from about 1979.
Some of the theory developed by Alain Connes to handle noncommutative geometry at a technical level has roots in older attempts, in particular in ergodic theory.
In 1993, in collaboration with Alain Connes, Rovelli has proposed a solution to this problem called the thermal time hypothesis.
In a development that has given substantive force to this approach to the Riemann hypothesis through functional analysis, Alain Connes has formulated a trace formula that is actually equivalent to a generalized Riemann hypothesis.
More recent work by Alain Connes has gone much further into the functional-analytic background, providing a trace formula the validity of which is equivalent to such a generalized Riemann hypothesis.

Connes and work
This theorem led naturally to the question of injectivity of von-Neumann algebras in general, which culminated in work by Alain Connes relating injectivity to hyperfiniteness.
Duality first appeared for actions of the reals in the work of Connes and Takesaki on the classification of Type III factors.

Connes and theory
One of the main starting points of the Alain Connes ' direction in noncommutative geometry is his spectacular discovery ( and independently by Boris Tsygan ) of a very important new homology theory associated to noncommutative associative algebras and noncommutative operator algebras, namely the cyclic homology and its relations to the algebraic K-theory ( primarily via Connes-Chern character map ).

Connes and geometry
* Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.
* Alain Connes ( 1994 ) Noncommutative geometry.
* 1986: A. Connes publishes his fundamental paper on non-commutative geometry.
* 1990: A. Connes and H. Moscovici prove the local index formula in the context of non-commutative geometry.
One can think of the deformed object as an algebra of functions on a " noncommutative space ", in the spirit of the noncommutative geometry of Alain Connes.
In the 1980s, mathematicians, most notably Alain Connes, developed noncommutative geometry.
The result of quantization leads to the study of noncommutative geometry whereby Connes emphasized C *- algebras.

Connes and .
Alain Connes (; born 1 April 1947 ) is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.
Alain Connes is one of the leading specialists on operator algebras.
Connes was awarded the Fields Medal in 1982, the Crafoord Prize in 2001 and the gold medal of the CNRS in 2004.
* Jean-Pierre Changeux, Alain Connes, M. B. DeBevoise ( translator ): Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998, ISBN 978-0691004051
Some of the mathematicians who were involved in the selection and presentation of the seven problems were Atiyah, Bombieri, Connes, Deligne, Fefferman, Milnor, Mumford, Wiles, and Witten.
Its recipients to date are Ian Agol, Manindra Agrawal, Yves Benoist, Manjul Bhargava, Danny Calegari, Alain Connes, Nils Dencker, Alex Eskin, David Gabai, Ben Green, Christopher Hacon, Richard Hamilton, Michael Harris, Jeremy Kahn, Laurent Lafforgue, Gérard Laumon, Vladimir Markovic, James McKernan, Ngô Bảo Châu, Jonathan Pila, Jean-François Quint, Oded Schramm, Stanislav Smirnov, Terence Tao, Clifford Taubes, Richard Taylor, Claire Voisin, Jean-Loup Waldspurger, Andrew Wiles, and Edward Witten.
Jean Bourgain, Alain Connes, Pierre Deligne, Mikhail Gromov, Alexandre Grothendieck, Oscar Lanford III, Laurent Lafforgue, Maxim Kontsevich, Dennis Sullivan and René Thom.
* Chamseddine, A., A. Connes ( 1996 ) " The spectral action principle ," Comm.
* Chamseddine, A., A. Connes, M. Marcolli ( 2007 ) " Gravity and the Standard Model with neutrino mixing ," Adv.
* Alain Connes official website with downloadable papers.
Elva Ruby Connes Miller ( October 5, 1907 – July 28, 1996 ), who recorded under the name " Mrs. Miller ", was an American singer who gained some fame in the 1960s for her series of shrill and off-key renditions of then-popular songs such as " Moon River ", " Monday, Monday ", " A Lover's Concerto " and " Downtown ".
Connes was born in Joplin, Missouri, to Edward and Ada ( Martin ) Connes.
Alain Connes and Vaughan Jones, both Fields Medalists, are Distinguished Professors of Mathematics at the university.
* Connes, Alain ; Symétries Galoisiennes & Renormalisation, Poincaré Seminar ( Paris, Oct. 12, 2002 ), published in: Duplantier, Bertrand ; Rivasseau, Vincent ( Eds.
French mathematician Alain Connes ( Fields medallist 1982 ) describe the mathematical underlying structure ( the Hopf algebra ) of renormalization, and its link to the Riemann-Hilbert problem.

has and applied
Also under consideration is an increased investment in Cunard Eagle Airways which has applied to serve New York.
Electronics has been applied to medicine for many years in the form of such familiar equipment as the x-ray machine, the electrocardiograph, and the diathermy machine.
What does Tri-State actually want to do, now that it has the meters under franchise and certain phases of its piping system in the `` patent applied for '' stage??
This has an interesting analogy with the assumption stated by Philippoff that `` the deformational mechanics of elastic solids can be applied to flowing solutions ''.
Merchant has found that the same basic relationships which describe the geometry and force systems in the case of the cutting mechanism can also be applied to the discontinuous chip formation provided the proper values of instantaneous shear angle and instantaneous chip thickness or cross-sectional area are used.
Abnormal pressure, applied over a period of time, produces a change in the bony deposit, so a tooth functions normally in the new position into which it has been guided.
Knowledge gained from studying earthquake waves has been applied in various fields.
But since this is a world in which people disagree about ends and goals and concerning justice and injustice, and since, in a situation where direct action and economic pressure are called for, the justice of the matter has either not been clearly defined by law or the law is not effectively present, there has to be a morality of means applied in every case in which people take it upon themselves to use economic pressures or other forms of force.
It is also sufficient to show the Christian and any other champion of justice that he needs to make sure not only that his cause is just but also that his conduct is just, i.e., that, if economic pressure has to be resorted to, this be applied directly against those persons directly in the way of some salutary change in business or institutional practices, while, if injury fall upon others, it fall upon them indirectly and secondarily ( however inevitably ) and not by deliberate intent and direct action against them.
Levittown has applied science, business, and literature ; ;
The technique has been applied in the study of mathematics and logic since before Aristotle ( 384 – 322 B. C.
The practice of the Australian states — for example, New South Wales and Victoria — has been, when legislating to repeal some imperial statutes so far as they still applied in Australia, to provide that imperial statutes concerning the royal succession remain in force.
Some thinkers, for instance, have argued that the difference between fine art and applied art has more to do with the actual function of the object than any clear definitional difference.
The bond has strength because the adhesive is hard enough to resist flow when stress is applied to the bond.
Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the effective range of personal weapons.
Administrative law, as laid down by the Supreme Court of India, has also recognized two more grounds of judicial review which were recognized but not applied by English Courts viz.
Abeyance has never applied to earldoms, and only baronies have been called out of abeyance.
The anthropic principle has given rise to some confusion and controversy, partly because the phrase has been applied to several distinct ideas.
These contradictions are inherent in reason when it is applied to the world as it is in itself, independently of our perceptions of it ( this has to do with the distinction between phenomena and noumena ).
The term has also been applied to various things that relate to the region in which the grass grows:
Games played ( most often abbreviated as G or GP ) is a statistic used in team sports to indicate the total number of games in which a player has participated ( in any capacity ); the statistic is generally applied irrespective of whatever portion of the game is contested.
During the early centuries of Christianity the title " pope " was applied generally to all bishops ; it now has more specific meanings that vary between churches.

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