Generalizations of these theories form the basis for understanding the closely related phenomenon of superfluidity, because they fall into the Lambda transition universality class, but the extent to which similar generalizations can be applied to unconventional superconductors as well is still controversial.

Generalizations of Cauchy sequences in more abstract uniform spaces exist in the form of Cauchy filter and Cauchy net.

In the theory of quadratic forms, the parabola is the graph of the quadratic form ( or other scalings ), while the elliptic paraboloid is the graph of the positive-definite quadratic form ( or scalings ) and the hyperbolic paraboloid is the graph of the indefinite quadratic form Generalizations to more variables yield further such objects.

Generalizations that are weak generally have more exceptions ( the number of exceptions to the generalization need not be a minority of cases ) and vice versa.

Generalizations to sinusoids of other phases, and to complex exponentials, are also common ; see plane wave.

Note that by definition, a linear combination involves only finitely many vectors ( except as described in Generalizations below ).

Generalizations of the Gauss – Bonnet theorem to n-dimensional Riemannian manifolds were found in the 1940s, by Allendoerfer, Weil, and Chern ; see generalized Gauss – Bonnet theorem and Chern – Weil homomorphism.

Generalizations of Bertrand's Postulate have also been obtained by elementary methods.

Tulsi was admitted by the Indian Institute of Science ( IISc )., where he wrote a 33-page long Ph. D. thesis on " Generalizations of the Quantum Search Algorithm ".

Generalizations have been studied by D. G. Higman ( coherent configurations ) and B. Weisfeiler ( distance regular graphs ).

Generalizations include those for classifying foliations, and the classifying toposes for logical theories of the predicate calculus in intuitionistic logic that take the place of a ' space of models '.

Generalizations of the absolute value for real numbers occur in a wide variety of mathematical settings.

Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

Generalizations of compactness include H-closed and the property of being an H-set in a parent space.

Generalizations are possible to metrics other than Euclidean.

Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order.

Generalizations of this definition are possible, for instance to complex manifolds and algebraic varieties.

Generalizations.

See " Introduction to Methods and Generalizations " in T. Janssen and G. Redeker ( Eds ) ( 1999 ).

Generalizations of Noether's theorem to superspaces are also available.

** 1. 31 Knowledge of Principles and Generalizations

Ma, Generalizations of tic-tac-toe,.

Generalizations to higher dimensions are also possible.

and Arora, K., " Generalizations of Dixon's theorem on the sum of a 3F2 ", Math.

Generalizations of these approaches underlie the path integral formulation of quantum mechanics, and is used for calculating geodesic motion in general relativity.

Generalizations to N =( 2, 0 ) supersymmetry have also appeared.

It is possible to posit the existence of an oracle which computes a non-computable function, such as the answer to the halting problem or some equivalent.

He was forced, by his extreme empiricism, to posit the existence of God in order to explain our experience of coherence, even though on an empirical understanding of raw sense data, such a conclusion did not follow.

Realists posit the existence of independent, abstract universals to account for attribute agreement.

Conceptualists posit that universals exist only in the mind, or when conceptualized, denying the independent existence of universals.

Rather, Searle simply claims that to posit the existence of something that is like a " thought " in every way except for the fact that no one can ever be aware of it ( can never, indeed, " think " it ) is an incoherent concept.

Therefore, the TAG differs from Thomistic and Evidentialist arguments, which posit the probable existence of God in order to avoid an infinite regress of causes or motions, to explain life on Earth, and so on.

For example, Einstein's theory of general relativity has static solutions in which space containing a gravitational field is ( locally ) described by three-dimensional elliptic geometry, but the theory does not posit the existence of a fourth spatial dimension, or even suggest any way in which the existence of a higher-dimensional space could be detected.

We could posit a rule stating that creating the charge required an input of energy E < sub > 1 </ sub >= qV < sub > 1 </ sub > and destroying it released E < sub > 2 </ sub >= qV < sub > 2 </ sub >, which would seem natural since qV measures the extra energy stored in the electric field because of the existence of a charge at a certain point.

This belief was in some ways similar to Gnostic Christian theology ; notably, both are dualistic, that is, they posit opposing gods, forces, or principles: one higher, spiritual, and " good ", and the other lower, material, and " evil " ( compare Manichaeism ), in contrast to the orthodox Christian view that " evil " has no independent existence, but is a privation or lack of " good ", a view shared by the eminent Jewish theologian Moses Maimonides.

Some extensions of present physics posit the existence of extra dimensions of space.

To establish its premises, dialectical monism may posit a Universal Dialectic, which is seen as the fundamental principle of existence.

Buddhists posit neither an ultimate beginning or final end to the universe, but see the universe as something in flux, passing in and out of existence, parallel to an infinite number of other universes doing the same thing.

The 19th-century Irish physicist George Johnstone Stoney, the first person to posit the existence of the electron, resided in Dundrum for much of his adult life.

His study of Sanskrit with Pandit Ramlochan at Nadiya led him to posit the existence of the Indo-European family of languages.

Most of which posit the existence of an elixir or the Golden Elixir that when ingested gives the drinker eternal life.