no necessary assumptions for ANOVA is its full generality, but the

AI systems can solve very simple restricted versions of AI-complete problems, but never in their full generality.

Continuity of functions is one of the core concepts of topology, which is treated in full generality below.

Thus the no-cloning theorem holds in full generality.

In full generality, algebraic structures may involve an arbitrary number of sets and operations of higher arity, but this article focuses on binary operations on one or two sets.

In full generality, the exterior algebra can be defined for modules over a commutative ring, and for other structures of interest in abstract algebra.

Ten years after, in, Lamberto Cesari changed the continuity requirement in Tonelli's definition to a less restrictive integrability requirement, obtaining for the first time the class of functions of bounded variation of several variables in its full generality: as Jordan did before him, he applied the concept to resolve of a problem concerning the convergence of Fourier series, but for functions of two variables.

Finally, Anatoly Ivanovich Maltsev ( Анато ́ лий Ива ́ нович Ма ́ льцев, 1936 ) proved the Löwenheim – Skolem theorem in its full generality.

While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot merely be a single sheaf in the absence of some hypothesis of non-singularity on V. The formulation in full generality uses a derived category and Ext functors, to allow for the fact that K is now represented by a chain complex of sheaves, namely, the dualizing complex.

The cup product was introduced in work of J. W. Alexander, Eduard Čech and Hassler Whitney from 1935 – 1938, and, in full generality, by Samuel Eilenberg in 1944.

An understanding of the economy as consisting of linked sectors goes back to the French economist François Quesnay, but was developed in full generality by Léon Walras in 1874.

An understanding of the economy as consisting of linked sectors goes back to the French economist François Quesnay, but was developed in full generality by Léon Walras in 1874.

In full generality, the word link is essentially the same as the word knot – the context is that one has a submanifold M of a manifold N ( considered to be trivially embedded ) and a non-trivial embedding of M in N, non-trivial in the sense that the 2nd embedding is not isotopic to the 1st.

The theorem was first proven by for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by.

By restricting the generality of full dependent types type checking remains decidable.

The bitap algorithm for exact string searching, in full generality, looks like this when implemented in C:

Some systems can solve very simple restricted versions of these problems, but none can solve them in their full generality.

However, unlike subharmonic functions ( which are defined on a Riemannian manifold ) plurisubharmonic functions can be defined in full generality on complex spaces.

In full generality, the notion can be defined on an arbitrary complex manifold or even a complex space as follows.

Education, like access to autonomy and information for all, begins with all children having access to a full primary education free of gender inequality.

In the probabilistic setting, the inequality can be further generalized to its full strength.

The full inequality is an extension of this idea to dimensions.

The 140,414 Americans who gave `` the last full measure of devotion '' to prevent disunion, preserved individual freedom in the United States from the dangers of anarchy, inherent in confederations, which throughout history have proved fatal in the end to all associations composed primarily of sovereign states, and to the liberties of their people.

The greatest impact of the matching-fund principle has been in initially encouraging the poorest states and school districts to spend enough to obtain their full allocation of outside funds.

Hierocles, writing in the 5th century, states that Ammonius ' fundamental doctrine was that Plato and Aristotle were in full agreement with each other:

The ACT has internal self-government, but Australia's Constitution does not afford the territory government the full legislative independence provided to Australian states.

In medicine, consciousness is assessed by observing a patient's arousal and responsiveness, and can be seen as a continuum of states ranging from full alertness and comprehension, through disorientation, delirium, loss of meaningful communication, and finally loss of movement in response to painful stimuli.

The Zhou Dynasty began to bow to external and internal pressures in the 8th century BC, and the kingdom eventually broke apart into smaller states, beginning in the Spring and Autumn Period and reaching full expression in the Warring States period.

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

The Talmud states that the fetus is not yet a full human being until it has been born ( either the head or the body is mostly outside of the woman ), therefore killing a fetus is not murder, and abortion-in restricted circumstances-has always been legal under Jewish law.

" These are likely the same Cathari mentioned in Canon 8 of the First Ecumenical Council of Nicaea in 325 AD, which states "... f those called Cathari come over the Catholic faith, let them first make profession that they are willing to communicate full communion with the twice-married, and grant pardon to those who have lapsed ..."

* Associate member parties may include parties that do not have MEPs ( e. g., French Trotskyist parties which did not get elected in the 2004 European elections ), are from states that are not part of the European Union, or do not wish to be full members.

The dogmatic constitution states that the Pope has " full and supreme power of jurisdiction over the whole Church " ( chapter 3: 9 ); and that, when he " speaks ex cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals " ( chapter 4: 9 ).

Although the Holy See, as distinct from the Vatican City State, does not fulfil the long-established criteria in international law of statehood — having a permanent population, a defined territory, a stable government and the capacity to enter into relations with other states — its possession of full legal personality in international law is shown by the fact that it maintains diplomatic relations with 179 states, that it is a member-state in various intergovernmental international organizations, and that it is: " respected by the international community of sovereign States and treated as a subject of international law having the capacity to engage in diplomatic relations and to enter into binding agreements with one, several, or many states under international law that are largely geared to establish and preserving peace in the world.

Since there are many different reference ellipsoids the latitude of a feature on the surface is not unique: this is stressed in the ISO standard which states that " without the full specification of the coordinate reference system, coordinates ( that is latitude and longitude ) are ambiguous at best and meaningless at worst ".

Its main interests remain the development and maintenance of a credible capability to defend the nation's vital interests and development of the Macedonia Army in such a way that ensures their interoperability with the armed forces of NATO and the European Union member states and their capability to participate in the full range of Alliance missions.

Freud's description of subjective states, involving an unconscious mind full of primal impulses, and counterbalancing self-imposed restrictions, was combined by Carl Jung ( 1875 – 1961 ) with the idea of the collective unconscious, with which the conscious mind fought or embraced.

Some have questioned whether these criteria are sufficient, as they allow less-recognized entities like the Republic of China ( Taiwan ) to claim full status as states.

In the German-speaking states Michael Denis made the first full translation in 1768, inspiring the proto-nationalist poets Klopstock and Goethe, whose own German translation of a portion of Macpherson's work figures prominently in a climactic scene of The Sorrows of Young Werther ( 1774 ).

Note that a device designed primarily as a comparator may be better if, for instance, speed is important or a wide range of input voltages may be found, since such devices can quickly recover from full on or full off (" saturated ") states.

** Lack of voting representation in either House of the U. S. Congress, as the US Constitution provides these rights only to full states.

However, many Warring states era bamboo texts contain the symbols 「└」 and 「▄」 indicating the end of a chapter and full stop, respectively.

Qatar achieved full independence on 3 September 1971 in an atmosphere of cooperation with the United Kingdom, the United States of America and friendship with neighbouring states.

The Baltic states achieved full independence, and they quickly received diplomatic recognition from many nations.