In this fashion, one can prove many important theorems in the class of compact spaces, that do not hold in the context of non-compact ones.

The space M × C is compactified over the compact set C, and after Kaluza-Klein decomposition we have an effective field theory over M. A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten.

A compact space is a stronger condition: in the context of Riemannian manifolds, it is equivalent to being bounded and geodesically complete.

In the context of mountain biking the term compact crankset, or micro drive, refers to smaller triple cranksets, giving a small benefit in weight at the expense of increased wear and also giving the bike better clearance over obstacles.

In the context of road cycling, compact drivetrain typically refers to double cranksets with a smaller ( usually 110mm ) bolt circle diameter than the standard 130mm or Campagnolo's 135mm.

Thus a context in which the Hodge dual is very often seen is the exterior algebra of the cotangent bundle ( i. e. the space of differential forms on a manifold ) where it can be used to construct the codifferential from the exterior derivative, and thus the Laplace-de Rham operator, which leads to the Hodge decomposition of differential forms in the case of compact Riemannian manifolds.

That algorithm was extended to a complete parsing algorithm to accommodate indirect ( by comparing previously computed context with current context ) as well as direct left-recursion in polynomial time, and to generate compact polynomial-size representations of the potentially exponential number of parse trees for highly ambiguous grammars by Frost, Hafiz and Callaghan in 2007.

One can define positive-definite functions on any locally compact abelian topological group ; Bochner's theorem extends to this context.

It's solid as a Mercedes, still compact and light in the context of 1974 barrier busters, fast, reasonably economical of fuel, precise-handling, and quick-stopping: its engine and drivetrain are both sporty and refined.

In an astronomical context, relativistic beaming commonly occurs in two oppositely-directed relativistic jets of plasma that originate from a central compact object that is accreting matter.

A compact disc with 16 million lines of open-source code, accompanying the book, provides the context for all the presented examples.

In the Canadian context, compact theory posits that Confederation was an agreement between the two founding peoples, French and English, and that therefore Quebec should have special veto powers relating to its position in the federal structure.

His first ( pre-IHÉS ) breakthrough in algebraic geometry was the Grothendieck – Hirzebruch – Riemann – Roch theorem, a far-reaching generalisation of the Hirzebruch – Riemann – Roch theorem proved algebraically ; in this context he also introduced K-theory.

Lebesgue presents the problem of integration in its historical context, addressing Cauchy, Dirichlet, and Riemann.

Pierre Deligne proved a precise Riemann – Hilbert correspondence in this general context ( a major point being to say what ' Fuchsian ' means ).

Perhaps one of the most striking applications of systoles is in the context of the Schottky problem, by P. Buser and P. Sarnak, who distinguished the Jacobians of Riemann surfaces among principally polarized abelian varieties, laying the foundation for systolic arithmetic.

In a marching band context, the player prepares for the crash by holding the cymbals parallel a few inches apart, with the surfaces vertical, one at waist height and the other some distance above it.

In the context of joints, displacement implies that the joint surfaces are not in anatomical alignment.

R-functions are used in computer graphics and geometric modeling in the context of implicit surfaces and the function representation.

The automorphism group of an object X in a category C is denoted Aut < sub > C </ sub >( X ), or simply Aut ( X ) if the category is clear from context.

In this case the relation from X to Y is the subset G of X × Y, and " from X to Y " must always be either specified or implied by the context when referring to the relation.

* On a computer running Microsoft Windows, Mac OS X, or Unix running the X Window System, clicking the secondary mouse button ( usually the right button ) opens a context menu for the region that is under the mouse pointer.

* On systems that support one-button mice, context menus are typically opened by pressing and holding the primary mouse button ( this works on the icons in the Dock on Mac OS X ) or by pressing a keyboard / mouse button combination ( e. g. Ctrl-mouse click in Mac OS ).

* X agrees that enforcement in a particular social context is legitimate.

Often the code needed to get from an X window to a DPS context was much more complicated than the entire rest of the DPS interface.

Some people with chest pain have normal or minimal narrowing of heart arteries ; in these patients, vasospasm is a more likely cause for the pain, sometimes in the context of Prinzmetal's angina and syndrome X.

* X Window System protocols and architecture for context

The only difference between homology and cohomology is that in cohomology the chain complexes depend in a contravariant manner on X, and that therefore the homology groups ( which are called cohomology groups in this context and denoted by H < sup > n </ sup >) form contravariant functors from the category that X belongs to into the category of abelian groups or modules.

* Mac OS X Services – A Mac OS X Service to delete the resource fork of a file through context menu

In this context, it shows that if we assume there is a formal sentence ( X → Y ), where X itself is equivalent to ( X → Y ), then we can prove Y with a formal proof.

Baldwin's next book-length essay, No Name in the Street, also discussed his own experience in the context of the later 1960s, specifically the assassinations of three of his personal friends: Medgar Evers, Malcolm X, and Martin Luther King, Jr.

In this context, the elements of X are called arguments of f. For each argument x, the corresponding unique y in the codomain is called the function value at x or the image of x under f. It is written as f ( x ).

If the column headings in a relational database table are divided into three disjoint groupings X, Y, and Z, then, in the context of a particular row, we can refer to the data beneath each group of headings as x, y, and z respectively.

Since the definition of the spectrum does not mention any properties of B ( X ) except those that any such algebra has, the notion of a spectrum may be generalised to this context by using the same definition verbatim.

It is often misattributed to St. Augustine of Hippo, but seems to have been first used in the 17th century by the Archbishop of Split ( Spalato ) Marco Antonio de Dominis ( 1560-1624 ), in book 4, chapter 8 ( p. 676 of the first volume ) of his De republica ecclesiastica libri X ( London, 1617 ), where it appears in context as follows: Quod si in ipsa radice, hoc est sede, vel potius solio Romani pontificis haec abominationis lues purgaretur et ex communi ecclesiae consilio consensuque auferretur hic metus, depressa scilicet hac petra scandali ac ad normae canonicae iustitiam complanata, haberemus ecclesiae atrium aequabile levigatum ac pulcherrimis sanctuarii gemmis splendidissimum.

Rodolfo Llinás, for example, proposed that consciousness results from recurrent thalamo-cortical resonance where the specific thalamocortical systems ( content ) and the non-specific ( centromedial thalamus ) thalamocortical systems ( context ) interact in the gamma band frequency via temporal coincidence.

Examples include Lock, Stock and Two Smoking Barrels ( 1998 ) ( wherein the slang is translated via subtitles in one scene ); The Limey ( 1999 ); Sexy Beast ( 2000 ); Snatch ( 2000 ); Ocean's Eleven ( 2001 ); and Austin Powers in Goldmember ( 2002 ); It's All Gone Pete Tong ( 2004 ), after BBC radio disc jockey Pete Tong whose name is used in this context as rhyming slang for " wrong "; Green Street Hooligans ( 2005 ).

Context menus are opened via various forms of user interaction that target a region of the GUI that supports context menus.

But this would create more spelling inconsistencies ( such as the break / brake example above ) that would need to be resolved via the linguistic context, as they are in the spoken language.

In his vision of a solution to this " vertigo ," Lyotard opposes the assumptions of universality, consensus, and generality that he identified within the thought of Humanistic, Neo-Kantian philosophers like Jürgen Habermas and proposes a continuation of experimentation and diversity to be assessed pragmatically in the context of language games rather than via appeal to a resurrected series of transcendentals and metaphysical unities.

While tracing garbage collectors can impact efficiency severely via context switching and cache line faults, they collect relatively infrequently, while accessing objects is done continually.

But in the context of micrometer measurements, its nonzero nature becomes noticeable ( via amplification ), in a way that students sometimes find surprisingly odd ( counterintuitive ).

Scholarly and commercial exchanges, increasingly communicated via the Internet, have also resulted in an exchange of terminology, including Hmu and A Hmao people identifying as Hmong and, to a lesser extent, Hmong people accepting the designation " Miao ," within the context of China.

The " classic " interface is still available by a filing cabinet shaped icon, by an option in the " Edit -> Preferences -> Behavior " menu in Nautilus, in a folder's context menu, and by using the "-- browser " switch when started by a command via a launcher or shell.

* In River Out of Eden, Richard Dawkins discusses human ancestry in the context of a river of genes and shows that Mitochondrial Eve is one of the many common ancestors we can trace back to via different gene pathways.

* One of the most detailed histories of the machine tool industry from World War II through the early 1980s, relayed in the context of the social impact of evolving automation via NC and CNC.

* context help: context help for many languages can be downloaded via hotstuff.

For example, while Internet users may speak of having " met " someone that they have contacted via online chat or in an online gaming context, to say that they met someone " in real life " is to say that they literally encountered them in a common physical location.

The normative context was egalitarianism — consensus practices diminishing capricious power and augmenting freedom via collective regulation of distribution and change.

These Ext groups can also be computed via a projective resolution of ℤ, the advantage being that such a resolution only depends on G and not on M. We recall the definition of Ext more explicitly for this context.

In the context of Ehresmann connections, where the connection depends on a special notion of " horizontal lifting " of tangent spaces, one can define parallel transport via horizontal lifts.

A hardware interrupt causes the processor to save its state of execution via a context switch, and begins execution of an interrupt handler.

Players can choose to play minigames separate from the board game context via " Minigame Mode ".

The inauguration building in via Po, close to Piazza Castello, and the seats of power and other educational institutions of the City, coincided with the academic year 1720-1721, the first year of the reform of university studies passed by Victor Amadeus II in the context of a radical renewal at all levels of public administration and education.

Temporary inactivation of CA3 via GABA agonists prevented context induced reinstatement of lever pressing for intravenous cocaine.

Alternatively, the continuous calculus can be obtained via the Gelfand transform, in the context of commutative Banach algebras.

The Members ' Manual of the National Assembly outlines that this additional oath is to the people and constitution of Quebec, distinct from the Oath of Allegiance, which is an oath to the country via the Queen, though some saw the monarch, in that context, as representative of the Quebec State and not of Canada, taking into account Canada's " divisible " Crown.

In other words, he argues that we cannot now ( and never will ) be able to understand our own behavior in the same way as we understand objects in, for example, physics or chemistry: that is, by considering ourselves as things whose behaviour can be predicted via ' objective ', context free scientific laws.

In such cases the reading must be deduced from context or via furigana.