He went on to introduce the étale cohomology theory of schemes, providing the key tools for proving the Weil conjectures, as well as crystalline cohomology and algebraic de Rham cohomology to complement it.

His key contributions include topological tensor products of topological vector spaces, the theory of nuclear spaces as foundational for Schwartz distributions, and the application of L < sup > p </ sup > spaces in studying linear maps between topological vector spaces.

Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

Shannon's work on information theory showed that to achieve so called perfect secrecy, it is necessary for the key length to be at least as large as the message to be transmitted and only used once ( this algorithm is called the One-time pad ).

Functors and natural transformations (' naturality ') are the key concepts in category theory.

John Tomlinson provides a critique of cultural imperialism theory that relies on some of the key points.

During the first years in power, under Lenin's rule, the Central Committee was the key decision-making body in both practice and theory, and decisions were made through majority votes.

A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.

His work was a key aspect of Hermann Weyl and John von Neumann's work on the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation and his namesake Hilbert space plays an important part in quantum theory.

EP is closely linked to sociobiology, but there are key differences between them including the emphasis on domain-specific rather than domain-general mechanisms, the relevance of measures of current fitness, the importance of mismatch theory, and psychology rather than behaviour.

" Mulvey argues that Lacan's psychoanalytic theory is the key to understanding how film creates such a space for female sexual objectification and exploitation through the combination of the patriarchal order of society, and ' looking ' in itself as a pleasurable act of voyeurism, as " the cinema satisfies a primordial wish for pleasurable looking.

Labor, not labor power, is the key factor of production for Marx and the basis for Marx's labor theory of value.

Hayek is widely recognized for having introduced the time dimension to the equilibrium construction and for his key role in helping inspire the fields of growth theory, information economics, and the theory of spontaneous order.

The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.

2 ) Some researchers ( e. g., Engel and Askanas ) advocate the theory that sIBM is a degenerative disorder related to aging of the muscle fibres and that abnormal, potentially pathogenic protein accumulations in myofibers play a key causative role in s-IBM ( apparently before the immune system comes into play ).

The key points where the theory of Karma in Jainism differs from the other religions such as theistic traditions of Hinduism, can be stated as follows:

In newly introduced doctrine, The Conduct of the Aerial Air War in 1935, Wever rejected the theory of Douhet and outlined five key points to air strategy:

One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its " infinitesimal group " and which has since become known as its Lie algebra.

Ventris ' initial theory was that Etruscan and Linear B were related and that this might provide a key to decipherment.

Along with reading musical notation, students learn rhythmic techniques like controlling tempo and recognizing time signatures, as well as the theory of harmony, including chords and key signatures.

A key aspect that affected the Bolshevik regime was the backward economic conditions in Russia that were considered unfavourable to orthodox Marxist theory of communist revolution.

In terms of political theory, he deemphasized virtue ( a core value of republicanism ) and emphasized widespread ownership of property ( a key element of liberalism ).

The key to our method is provided by the detailed analysis of the relation between mathematical languages and mathematical structures which lies at the bottom of contemporary model theory.

Let us not try to key them out at this stage of the game, and let us just call them Bombus.

In the second game of the Falcons 1999 season, running back Jamaal Anderson, who had been a key player in the Falcons ' 1998 success, suffered a season-ending knee injury.

The card would indicate which game functions, such as changing the view or vehicle speed, were assigned to each key.

One of the key clauses was that companies who made Nintendo games were not allowed to make that game on a competing system for a period of two years.

In a key game late in the 2005 season, Steve Smith was ejected for touching an official.

Similar versions of the game are played, using the same premise, but using a different ' key word '.

Other key members of the development team included Bill Trost, who created the history, lore and major characters of Norrath ( including Everquest protagonist Firiona Vie ), Geoffrey " GZ " Zatkin who implemented the spell system, and artist Milo D. Cooper, who did the original character modeling in the game.

* Gene therapy is an important plot key in the game Bioshock where the game contents refer to plasmids and splicers.

The key game in the Royals ' comeback was Game 6.

The MVS ( Multi Video System ), as the Neo Geo was known to the coin-operated arcade game industry, offered arcade operators the ability to put up to six different arcade titles into a single cabinet, a key economic consideration for operators with limited floorspace.

The key point is that if no one else is keen to bet, then the most a player can raise by ( in a limit game ) is one single bet.

Live spots at the end of the game are called survivors and play a key role in the analysis of Sprouts.

The game is also seen as having been key to expanding the Mario series into non-platforming games, where the main goal in platform games is when the hero has to rescue the damsel in distress ; this diversity has led to it become the best-selling game franchise of all time.

According to Roger Staubach, the Cowboys ' game plan was to neutralize the Dolphins ' key offensive and defensive players — Paul Warfield and Nick Buoniconti.

Since the running game was the key to the Cowboys ' offense, they wanted to take the quick-reacting Buoniconti out of each play.

Tight End Stu Voigt was also a key element of the passing game, with 23 receptions for 318 yards and two touchdowns.

The key play in the game occurred when the Dolphins were in control and were leading the Raiders 19-14 midway through the fourth quarter.

On third down, 49ers linebacker Dan Bunz made probably the key defensive play of the game.

Just like the 49ers in the NFC title game, the Chargers advanced to the Super Bowl despite the fact that the Steelers had outgained them in many key statistical categories such as total plays ( 80 – 47 ), total offensive yards ( 415 – 226 ), and time of possession ( 37: 13 – 22: 47 ).

However, New England took advantage of several key Jacksonville miscues in a game dominated by defense.

All gaming machines in Victoria have an information screen accessible to the user by pressing the ' i key ' button, showing the game rules, paytable, return to player percentage, and the top and bottom five combinations, with the odds shown.

The popular Minesweeper game under older versions of Microsoft Windows had a cheat mode triggered by entering the comment < tt > xyzzy < tt >, then pressing the key sequence shift and then enter, which turned a single pixel in the top-left corner of the entire screen into a small black or white dot depending on whether or not the mouse pointer is over a mine .< ref > This easter egg was present in all Windows versions through Windows XP Service Pack 2, but under Windows 95, 98 and NT 4. 0 the pixel was visible only if the standard Explorer desktop was not running.