An example of this is the equations of general relativity, where this symmetry is one of the defining features of the theory.

Although radial symmetry is usually given as a defining characteristic of radiates, a few members of the class Anthozoa, which are now considered as the most basal and oldest group of cnidarians, are actually bilateral symmetric.

A consequence of this potential energy function is that it is possible to shift the initial position of an electron by any lattice vector without changing any aspect of the problem, thereby defining a discrete symmetry.

In theoretical physics, explicit symmetry breaking is the breaking of a symmetry of a theory by terms in its defining equations of motion ( most typically, to the Lagrangian or the Hamiltonian ) that do not respect the symmetry.

In the latter, the defining equations respect the symmetry but the ground state ( vacuum ) of the theory breaks it.

By the symmetry of the defining formula, this shows that the resultant is a polynomial expression of the coefficients of both < var > P </ var > and < var > Q </ var >.

The Copenhagen Interpretation gives special status to measurement processes without clearly defining them or explaining their peculiar effects.

Unlike the force carriers of the other forces, gravitation plays a special role in general relativity in defining the spacetime in which events take place.

This extra distinction pays off when defining substitution ( without this distinction special provision has to be made to avoid variable capture ).

While civil law systems have traditionally put great pains in defining the notion of private property, how it may be acquired, transferred, or lost, socialist law systems provide for most property to be owned by the state or by agricultural co-operatives, and having special courts and laws for state enterprises.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations.

:" Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks.

The term is widely needed to support the more esoteric requirements of a number of disciplines including in philosophy when a concept is not available ; in biology when a genus is not available ; in law when a special and unique interpretation of a case or authority will be needed on-the-fly ; in town-planning where there is no existing use-case ; in intellectual property rights where there is no defining characteristic ; and in politics and societal norms where there is no real authority perceived.

Strictly speaking, the only true defining characteristic of the dory is that it is planked up with wide boards, " It should be well understood, that it is the dory's special mode of construction, not its hull shape, that sets it, and its related sub-types apart from other boats "

The terroir philosophy is predominately French, the flavour and character of the place defining the individuality and the special attributes of wines and combined with hundreds of years of the finest wine making traditions, terroir gives wines their distinctive taste and signature.

The third defining property implies as a special case that if f is a function and α a k-form, then because functions are forms of degree 0.

Reviewing the 2005 re-release of the album, Scott Alisoglu of Blabbermouth. net said that Alive or Just Breathing is " one special album " and that its release " marked a defining moment in metal.

These include waiting for death to occur before harvesting organs, expanding the definition of death, creating a special legal category for anencephalic infants, and defining them as non-persons.

Coalition governments were common with special interests defining the legislative agenda.

* The integrals defining C ( x ) and S ( x ) cannot be evaluated in the closed form in terms of elementary functions, except in special cases.

Based on Article 5 of the Constitution 1904, which says it believes the law allows political divisions with special or for reasons of administrative convenience or public service, legislation on indigenous territories in Panama began to be defined with the establishment of the Guna District of San Blas, in 1938, including areas of the provinces of Panama and Columbus, then, defining its boundaries and administration by Act No. 16 of 1953.

To see why the evolution equation defining the Ricci flow is indeed a kind of nonlinear diffusion equation, we can consider the special case of ( real ) two-manifolds in more detail.

Because signals and other causal influences cannot travel faster than light ( see special relativity and spooky action at a distance ), the light cone plays an essential role in defining the concept of causality-for a given event E, the set of events that lie on or inside the past light cone of E would also be the set of all events that could send a signal that would have time to reach E and influence it in some way.

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.

Christian democrats and liberal-centrists were undoubtedly the strongest factions within the party, but all four were mainstream for a special issue: for example liberals and liberal-centrists were highly influential over economic policy, Christian democrats led the party over ethical issues ( although there was a substantial minority promoting a more progressive outlook ), while social democrats had their say in defining the party's policy over labour market reform and, moreover, it is thanks to this group ( and to those around Tremonti, he himself a former Socialist ) that constitutional reform was at the top of Forza Italia's political agenda.

It expresses the value of the eta function as the limit of special Riemann sums associated to an integral known to be zero, using a relation between the partial sums of the Dirichlet series defining the eta and zeta functions for.

which is a quotient of the usual split short exact sequence defining the special linear group, namely

The defining feature of the Schizophora is the presence of a special structure that is used to help the emerging adult fly break free of the puparium ; this structure is an inflatable membranous sac called the ptilinum that protrudes from the face, above the antennae.

Opponents also cite problems with defining who is considered a journalist or news gatherer and who is not, and note that if journalists get special protection from the government, then they are getting special journalistic benefits from the government instead of acting in complete independence.

Even with the defining postulates of both Einstein's theory of general relativity and quantum theory being indisputably supported by rigorous and repeated empirical evidence and while they do not directly contradict each other theoretically ( at least with regard to their primary claims ), they have proven extremely difficult to incorporate into one consistent, cohesive model.

The publication of the 1996 anthology Rethinking linguistic relativity edited by sociolinguist John J. Gumperz and psycholinguist Stephen C. Levinson marked the entrance to a new period of linguistic relativity studies and a new way of defining the concept that focused on cognitive as well as social aspects of linguistic relativity.

Technically, general relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations.

This is the quantum version of the main property of Einstein's general relativity, where the solutions of the theory are not gravitational field living inside a spacetime, but are themselves defining spacetime.

For comparison, the Lagrangian defining general relativity is

Although diffeomorphism covariance is not the defining feature of general relativity

In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor ( or by defining a frame field ).

In general relativity, the geometric setting for physical phenomena is a Lorentzian manifold, which is physically interpreted as a curved spacetime, and which is mathematically specified by defining a metric tensor ( or by defining a frame field ).

A new South is emerging after the post-bellum years of hesitation, uncertainty, and lack of action from the Negro in defining his new role in the amorphously defined socio-political organizations of the white man.

The key to effective marketing is wrapped up in defining your company's marketing problems realistically.

`` A serious problem accompanying the technical-ladder approach is the difficulty of clearly defining responsibilities and standards of performance for each level.

Here the problem is essentially one of defining the word `` filling ''.

With the phylogenetic classification, the taxon Labyrinthodontia has been discarded as it is a paraphyletic group without unique defining features apart from shared primitive characteristics.

The President is also provided a variety of powers, like defining the policy of the country.

One of the defining characteristics of the order is the presence of phytomelan, a black pigment present in the seed coat, creating a dark crust.

Its triple point temperature of 83. 8058 K is a defining fixed point in the International Temperature Scale of 1990.

The defining characteristic of this family is the inflorescence: a simple or compound umbel.

The Spectrogram produced by such an instrument is a graphical display of the time varying pressure level and frequency profiles which give a specific acoustic signal its defining character.

An approach to defining what is meant by area is through axioms.

Some researchers state that the evidence-based approach to defining CAM is problematic because some CAM is tested, and research suggests that many mainstream medical techniques lack solid evidence.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes ' numerical definitions and representations.

Thus, ayahuasqueros and most others working with the brew maintain that the B. caapi vine is the defining ingredient, and that this beverage is not ayahuasca unless B. caapi is in the brew.

However, the defining recommendation indicates a change to a system similar to ISO 8601 and astronomical year numbering is likely in the future.

If this limit fails to exist then there is no oblique asymptote in that direction, even should the limit defining m exist.

Every Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

Conversely, if a Boolean ring A is given, we can turn it into a Boolean algebra by defining x ∨ y := x + y + ( x · y ) and x ∧ y := x · y.

Biopolymers often have a well-defined structure, though this is not a defining characteristic ( example: ligno-cellulose ):