This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers.

Léger ’ s The Wedding, also shown at the Salon des Indépendants in 1912, gave form to the notion of simultaneity by presenting different motifs as occurring within a single temporal frame, where responses to the past and present interpenetrate with collective force.

It is by challenging the assumptions built into the common notion of simultaneity that logical consistency can be restored.

But in the theory of relativity, the notion of simultaneity is dependent on the observer.

According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed.

The notion of a great Elizabethan age depends largely on the builders, dramatists, poets, and musicians who were active during Elizabeth's reign.

The success of the De Leonist plan depends on achieving majority support among the people both in the workplaces and at the polls, in contrast to the Leninist notion that a small vanguard party should lead the working class to carry out the revolution.

In either approach, the fundamental notion is that of an isotropic subspace W. Each construction depends on an initial freedom in choosing this subspace.

An observer ’ s notion of what is ordered, what is random, and what is complex in its environment depends directly on its computational resources: the amount of raw measurement data, of memory, and of time available for estimation and inference.

The notion of measurability depends on the sigma algebras Σ and Τ.

The definition of an atlas depends on the notion of a chart.

:: Example: Nevertheless, the due process clause protects " property " interests ; and while the notion of property interest has been stretched quite far in certain contexts, e. g., Goldberg v. Kelly, 397 U. S. 254 ( 1970 ), it depends importantly on what interests are recognized under state law.

The definition of an attractor uses a metric on the phase space, but the resulting notion usually depends only on the topology of the phase space.

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.

Prison activists who buttress the notion of a prison industrial complex argue that these parties have a great interest in the expansion of the prison system since their development and prosperity directly depends on the number of inmates.

Calabresi took a different approach in his 1985 book, Ideals, Beliefs, Attitudes, and the Law, where he argued, " who is the cheapest avoider of a cost, depends on the valuations put on acts, activities and beliefs by the whole of our law and not on some objective or scientific notion ( 69 ).

The case that the assigned value depends on previous one is so common that many imperative languages, most notably C and the majority of its descendants, augment the notion of assignment by defining special binary operators like for convenience so that the example becomes.

Whether future expression is realis or irrealis depends not on any objective, ontological notion of future reality, but rather on the speaker's conviction that the predicted event will at some future moment constitute reality.

General position is a property of configurations of points, or more generally other subvarieties ( lines in general position, so no three concurrent, and the like ) – it is an extrinsic notion, which depends on an embedding as a subvariety.

The success of the De Leonist plan depends on achieving majority support among the people both in the workplaces and at the polls, in contrast to the Leninist notion that a small vanguard party should lead the working class to carry out the revolution.

This explanation depends on the notion that the economy faces more uncertainties in the distant future than in the near term.

Unruh demonstrated theoretically that the notion of vacuum depends on the path of the observer through spacetime.

The Unruh effect therefore means that the very notion of vacuum depends on the path of the observer through spacetime.

Each such map provides a way in which certain subsets of the manifold may be viewed as being like open subsets of but the usefulness of this notion depends on to what extent these notions agree when the domains of two such maps overlap.

Therefore, the appropriate notion of reduction depends on the complexity class being studied.

Specifically, Albert preserved Ockham ’ s notion of simple supposition: the direct reference of a term to the concept on which it depends when it signifies an extra-mental thing.

The definition of a ray depends upon the notion of betweenness for points on a line.

The use of an honor code depends on the notion that people ( at least within the community ) can be trusted to act honorably.

Finally, for the body and soul together, we have only the concept of their union, on which depends the notion of the soul's power to move the body and the body's power to act on the soul by causing its sensations and passions.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

In she has it in for George dominant stress will ordinarily be on in, where the notion of stored-up antipathy seems to center.

God knows what the African nations, who hold 25 per cent of the voting stock in the U.N. were thinking -- they may, for example, have been thinking of the U.S. abstention when the vote on Algerian freedom was before the Assembly -- but I think I have a fairly accurate notion of what the Negroes in the gallery were thinking.

( Pp. 228-229 ) in any event, it is obvious that the anti-trust laws did not prevent the formation of some of the greatest financial empires the world has ever known, held together by some of the most fantastic ideas, all based on the fundamental notion that a corporation is an individual who can trade and exchange goods without control by the government ''.

This leads Irenaeus to the somewhat startling notion that Adam and Eve died on the same day that they disobeyed, namely, on a Friday, as a parallel to the death of Christ on Good Friday ; ;

Alms are the fruits of a moral notion of the gift and of fortune on the one hand,

and of a notion of sacrifice, on the other.

This is similar to the notion of chivalry, but unlike that European concept, in i ' thar attention is focused on everything in existence.

Two works by Mauss in particular proved to have enduring relevance: Essay on the Gift, a seminal analysis of exchange and reciprocity, and his Huxley lecture on the notion of the person, the first comparative study of notions of person and selfhood cross-culturally.

Authors who use this formulation often speak of the choice function on A, but be advised that this is a slightly different notion of choice function.

Literary critics Barthes and Foucault suggest that readers should not rely on or look for the notion of one overarching voice when interpreting a written work, because of the complications inherent with a writer's title of " author.

There is thus, on the one hand, the notion of completeness of a deductive system and on the other hand that of completeness of a set of non-logical axioms.

# Deontological ethics, notions based on ' rules ' i. e. that there is an obligation to perform the ' right ' action, regardless of actual consequences ( epitomized by Kant's notion of the Categorical Imperative )

He argues that this casts doubt on the notion that recessions are caused by a reallocation of resources from industrial production to consumption, since he argues that the Austrian business cycle theory implies that net investment should be below zero during recessions.

The philosophy is founded on the notion that human society originates with the development of agriculture, and societies are based upon " people's natural prospensity to farm.

Dürer rejected Alberti's concept of an objective beauty, proposing a relativist notion of beauty based on variety.

Writers Michael Hardt & Antonio Negri have together in their books ( Empire & Multitude ) expanded on this idea of a disunified multitude: humans coming together for shared causes, but lacking the complete sameness of the notion of ' the people '.

Indeed, naive set theory might be said to be based on this notion.

His financial policies, based on the notion of balanced budgets, low taxes and laissez-faire, were suited to a developing capitalist society but could not respond effectively as economic and social conditions changed.

Nelson publicly encouraged this close bond with his officers and on 29 September 1798 described them as " We few, we happy few, we band of brothers ", echoing William Shakespeare's play Henry V. From this grew the notion of the Nelsonic Band of Brothers, a cadre of high-quality naval officers that served with Nelson for the remainder of his life.

When the Banach algebra A is the algebra L ( X ) of bounded linear operators on a complex Banach space X ( e. g., the algebra of square matrices ), the notion of the spectrum in A coincides with the usual one in the operator theory.