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His construction of new cohomology theories has left deep consequences for algebraic number theory, algebraic topology, and representation theory.
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construction and new
but, as a second-look safeguard, each new project must undergo a Board of Estimate public hearing before construction proceeds.
Issuing bonds for plant construction has brought new industries to certain regions.
Fifty-two companies started or committed themselves to new plant construction, totaling 1,418,000 square feet and representing an investment of $11,900,000 ; ;
They are conscious of this state's new feeling of optimism and assurance and are definitely impressed by the number of new plants and construction projects in Rhode Island.
Service at these levels of production and utilization will eventually require the construction of about 379,900 miles of new roads and 6,000 miles of new trails, along with the reconstruction to higher standards of about 105,000 miles of roads and 10,500 miles of trails.
About 26,500 miles of existing trails will be replaced in service by the construction of new roads.
On the other hand, the new authority of $3,825 million proposed for missile procurement ( excluding research and construction ) in 1961 is $581 million higher than for 1960.
Board members indicated Monday night this would be done by an advisory poll to be taken on Nov. 15, the same date as a $581,000 bond election for the construction of three new elementary schools.
Louis H. Grenier, clerk of the board, said that the appeals will be reviewed in December at the time the board is visiting new construction sites in the town for assessment purposes.
The Defence Minister of Serbia, Dragan Šutanovac, stated in a 2011 meeting in Luanda that Serbia would negotiate with the Angolan military authorities for the construction of a new military hospital in Angola.
The Armenian Government is working toward closing the Armenian Nuclear Power Plant and has already made an agreement with Russian " businessmen " about the construction and operation and ownage of a new Nuclear power plant.
Fixed fees are usually based on a project's allocated construction cost and can range between 4 and 12 % of new construction cost, for commercial and institutional projects, depending on a project's size and complexity.
Under Title III of the ADA, all " new construction " ( construction, modification or alterations ) after the effective date of the ADA ( approximately July 1992 ) must be fully compliant with the Americans With Disabilities Act Accessibility Guidelines ( ADAAG ) found in the Code of Federal Regulations at 28 C. F. R., Part 36, Appendix " A ".
In the early 19th century, many new enterprises sprang up in the railroad and construction industries.
Johnson, in the face of the national mania over new railroad construction, and in response to the need in his own district for additional mode of transportation, found himself moderating in his opposition to them.
The restoration of London progressed through the later half of the 880s and is believed to have revolved around a new street plan, added fortifications in addition to the existing Roman walls, and, some believe, the construction of matching fortifications on the South bank of the River Thames.
The Falcons play their home games at the Georgia Dome in downtown Atlanta, but construction is likely to begin in 2014 on a new stadium with play beginning in the 2017 season.
In February 2010 a new main sponsor was found: construction works service provider BUKO from Beverwijk.
New construction benefited the whole economy, as the development of the tourism sector also spawned new businesses such as restaurants, bars and other tourist-oriented enterprises.
, the construction rate of new housing units was 6. 5 new units per 1000 residents.
construction and cohomology
In topology, by applying the same construction to vector bundles, Michael Atiyah and Friedrich Hirzebruch defined K ( X ) for a topological space X in 1959, and using the Bott periodicity theorem they made it the basis of an extraordinary cohomology theory.
As we now know, the route towards their proof, and other advances, lay in the construction of étale cohomology.
Technically speaking it enabled the construction of the sought-after étale cohomology ( as well as other refined theories such as flat cohomology and crystalline cohomology ).
In mathematics, the plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups.
In singular cohomology, the cup product is a construction giving a product on the graded cohomology ring H < sup >∗</ sup >( X ) of a topological space X.
In mathematics, the Chern – Weil homomorphism is a basic construction in the Chern – Weil theory, relating for a smooth manifold M the curvature of M to the de Rham cohomology groups of M, i. e., geometry to topology.
is a cohomology operation in topological K-theory, or any allied operation in algebraic K-theory or other types of algebraic construction, defined on a pattern introduced by Frank Adams.
The significance of this construction begins with the following result, which belongs to the subject of cohomology of fiber bundles.
It was defined by in order to give an algebraic construction of the cohomology of the underlying topological spaces of compact Lie groups.
The construction of this differential on an exterior algebra makes sense for any Lie algebra, so is used to define Lie algebra cohomology for all Lie algebras.
More generally one uses a similar construction to define Lie algebra cohomology with coefficients in a module.
There are numerous variations on this construction, in which cohomology is used instead of homology, integration replaces intersection, Chern classes pulled back from the Deligne – Mumford space are also integrated, etc.
This construction of Floer homology explains the independence on the choice of the almost complex structure on M and the isomorphism to Floer homology provided from the ideas of Morse theory and pseudoholomorphic curves, where we must recognize the Poincare duality between homology and cohomology as the background.
construction and theories
As a technological discipline, computer vision seeks to apply its theories and models to the construction of computer vision systems.
Feminist theory, which emerged from these feminist movements, aims to understand the nature of gender inequality by examining women's social roles and lived experience ; it has developed theories in a variety of disciplines in order to respond to issues such as the social construction of sex and gender.
These included an aluminum honeycomb chassis construction and a " breadvan " body design that experimented with " kammback " aerodynamic theories.
There have been varying scientific and alternative theories about the Great Pyramid's construction techniques.
Many alternative, often contradictory, theories have been proposed regarding the pyramid's construction techniques.
The earliest advances occurred in the development of earth pressure theories for the construction of retaining walls.
Learning theories often inform instructional theory, and three general theoretical stances take part in this influence: behaviorism ( learning as response acquisition ), cognitivism ( learning as knowledge acquisition ), and constructivism ( learning as knowledge construction ).
Criticism of learning theories that underlie traditional educational practices claims there is no need for such a theory ; that the attempt to comprehend the process of learning through theory construction creates more problems and inhibits personal freedom.
Influenced by theories of social construction, White argues that culture is " reconstituted " through language.
) This limitation, however, in no way precludes the construction of mathematical theories that formalize large bodies of scientific knowledge.
Shelley's construction of Lionel Verney's immunity remains a subject of significant critical debate, but the novel certainly demonstrates a deep understanding of the history of medicine, specifically the development of the smallpox vaccine and the various nineteenth-century theories about the nature of contagion.
In the 1960s, Chomsky introduced two central ideas relevant to the construction and evaluation of grammatical theories.
It is used in certain speculative theories, such as on the construction of wormholes.
None of these theories refer back to the actual stonework, and it is only when you have done so, as John James did exhaustively in 1969, that you realize that the construction process was in fact simple and logical.
Although ultimately proving incapable of distinguishing between differing theories of aether-dragging, its construction provided important lessons for the design of Michelson and Morley's 1887 instrument.
Zerzan's theories draw on Theodor Adorno's concept of negative dialectics to construct a theory of civilization as the cumulative construction of alienation.
TOLC and TOBE together constitute an alternative construction on the neoclassical marginalist theories of consumption and production, respectively.
While a variety of theories exist, most have come to the conclusion that there was sharing of culture and construction methods both directions.
For example, with theories that include arithmetic, such constructions generally give models that include non-standard numbers, unless the construction method was specifically designed to avoid them.
Many theories for Tiwanaku's architecture construction have been proposed.
Nevertheless, more subtle arguments based on modern theories of phase equilibrium seem to confirm the Maxwell Equal Area construction and it remains a valid modification of the Van der Waals equation of state.
An important step in the construction of covariant string field theories ( preserving manifest Lorentz invariance ) was the construction of a covariant kinetic term.
Theories held by mainstream Egyptologists about the date of the construction of the Great Sphinx of Giza have been challenged and various alternative theories have been proposed – about the builder or the dating – to explain its construction.
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