One of these was the property, an essential universal true of the species, but not in the definition ( in modern terms, some examples would be grammatical language, a property of man, or a spectral pattern characteristic of an element, both of which are defined in other ways ).

Andrzej Wajda's films offer insightful analyses of the universal element of the Polish experience-the struggle to maintain dignity under the most trying circumstances.

The AWMT paper did not describe any automatic search, nor any universal metadata scheme such as a standard library classification or a hypertext element set like the Dublin core.

Neon is abundant on a universal scale ; it is the fifth most abundant chemical element in the universe by mass, after hydrogen, helium, oxygen, and carbon ( see chemical element ).

The " human element " is based on universal opportunities to make faulty decisions, to adopt a non-cooperative attitude, and to induce others to follow suit.

The universal quantifier y will include every single element in the domain, including our infamous barber x.

The dual notion is that of a terminal object ( also called terminal element ): T is terminal if for every object X in C there exists a single morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.

* MEDINA, a universal pre -/ postprocessor for finite element analysis of T-Systems.

Instead of positing a rich innate and universal syntactic structure ( see Universal Grammar ), Van Valin suggests that the only truly universal parts of a sentence are its nucleus, generally a predicating element such as a verb or adjective, and the arguments, normally noun phrases, that the nucleus requires.

By this time, it had long been universal practice among machine tool builders to build these machine element s into most bench lathes or engine lathes.

A key element Watt explores is the decline in importance of the philosophy of classical antiquities, with its various strains of idealistic thought that viewed human experience as composed of universal Platonic " forms " with an innate perfection.

A molecular assembler is also a key element of the plot of the computer game Deus Ex ( called a " universal constructor " in the game ).

In the limit as, these relations approach the relations for the universal enveloping algebra U ( G ), where and as q → 1, where the element,, of the Cartan subalgebra satisfies for all h in the Cartan subalgebra.

In particular, there is a universal bundle which is a subbundle of the trivial bundle, and which has the property that the fiber over each point is the n element subset of classified by p.

It is a quotient of the universal enveloping algebra of the Heisenberg algebra, the Lie algebra of the Heisenberg group, by setting the element 1 of

In mathematics, a Casimir invariant or Casimir operator is a distinguished element of the centre of the universal enveloping algebra of a Lie algebra.

He embraced a programme that included annual parliaments and universal suffrage, promoted openly and with none of the conspiratorial element of the old Jacobin clubs.

For example, the universal C *- algebra generated by a unitary element u has presentation < u | u * u

Any C *- algebra generated by a unitary element is the homomorphic image of this universal C *- algebra.

The universal call to holiness is an important element in the spirituality of Opus Dei, which emphasizes the sanctification of the lay people.

# finally, that the same most universal idea of being, this generator and formal element of all acquired cognitions, cannot itself be acquired, but must be innate in us, implanted by God in our nature.

* Universal constructions are functorial in nature: if one can carry out the construction for every object in a category C then one obtains a functor on C. Furthermore, this functor is a right or left adjoint to the functor U used in the definition of the universal property.

Universal constructions are more general than adjoint functor pairs: a universal construction is like an optimization problem ; it gives rise to an adjoint pair if and only if this problem has a solution for every object of C ( equivalently, every object of D ).

If we let be the inclusion functor from CHaus into Top, maps from to ( for in CHaus ) correspond bijectively to maps from to ( by considering their restriction to and using the universal property of ).

This is rather vague, though suggestive, and can be made precise in the language of category theory: a construction is most efficient if it satisfies a universal property, and is formulaic if it defines a functor.

As stated earlier, an adjunction between categories C and D gives rise to a family of universal morphisms, one for each object in C and one for each object in D. Conversely, if there exists a universal morphism to a functor G: C → D from every object of D, then G has a left adjoint.

The product in is given by a universal morphism from the functor to the object in.

A space M is a fine moduli space for the functor F if M represents F, i. e., the functor of points Hom (−, M ) is naturally isomorphic to F. This implies that M carries a universal family ; this family is the family on M corresponding to the identity map 1 < sub > M </ sub > ∈ Hom ( M, M ).

A space M is a coarse moduli space for the functor F if there exists a natural transformation τ: F → Hom (−, M ) and τ is universal among such natural transformations.

This is the universal property expressing that the functor sending X to its universal enveloping algebra is left adjoint to the functor sending a unital associative algebra A to its Lie algebra A < sub > L </ sub >.

It is the free algebra on V, in the sense of being left adjoint to the forgetful functor from algebras to vector spaces: it is the " most general " algebra containing V, in the sense of the corresponding universal property ( see below ).

Unlike many algebraic categories, the forgetful functor U: Top → Set does not create or reflect limits since there will typically be non-universal cones in Top covering universal cones in Set.

There is also a universal coefficient theorem for cohomology involving the Ext functor, stating that there is a natural short exact sequence

The choice of a ( normalised ) cleavage for a fibred E-category F specifies, for each morphism f: T → S in E, a functor f < sup >*</ sup >: F < sub > S </ sub > → F < sub > T </ sub >: on objects f < sup >*</ sup > is simply the inverse image by the corresponding transport morphism, and on morphisms it is defined in a natural manner by the defining universal property of cartesian morphisms.

Let C be a category with binary products and let Y and Z be objects of C. The exponential object Z < sup > Y </ sup > can be defined as a universal morphism from the functor –× Y to Z.

This gives rise to the alternate description: the left Kan extension of along consists of a functor and a natural transformation which are universal with respect to this specification, in the sense that for any other functor and natural transformation, a unique natural transformation exists and fits into a commutative diagram:

The function F is called universal if the following property holds: for every computable function f of a single variable there is a string w such that for all x, F ( w x ) = f ( x ); here w x represents the concatenation of the two strings w and x.

For F that are universal, such a p can generally be seen both as the concatenation of a program part and a data part, and as a single program for the function F.

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

Let F be a prefix-free universal computable function.

Namely φ is universal for homomorphisms from G to an abelian group H: for any abelian group H and homomorphism of groups f: G → H there exists a unique homomorphism F: G < sup > ab </ sup > → H such that.

According to the law of universal gravitation, the attractive force ( F ) between two bodies is proportional to the product of their masses ( m < sub > 1 </ sub > and m < sub > 2 </ sub >), and inversely proportional to the square of the distance, r, ( inverse-square law ) between them:

Under an assumption of constant gravity, Newton's law of universal gravitation simplifies to F = mg, where m is the mass of the body and g is a constant vector with an average magnitude of 9. 81 m / s < sup > 2 </ sup >.

Any collection of objects and morphisms defines a ( possibly large ) directed graph G. If we let J be the free category generated by G, there is a universal diagram F: J → C whose image contains G. The limit ( or colimit ) of this diagram is the same as the limit ( or colimit ) of the original collection of objects and morphisms.

Such an isomorphism uniquely determines a universal cone to F.

A given diagram F: J → C may or may not have a limit ( or colimit ) in C. Indeed, there may not even be a cone to F, let alone a universal cone.

* A limit of F is a universal morphism from Δ to F.

* A colimit of F is a universal morphism from F to Δ.

which assigns each diagram its limit and each natural transformation η: F → G the unique morphism lim η: lim F → lim G commuting with the corresponding universal cones.

which is natural in the variables N and F. The counit of this adjunction is simply the universal cone from lim F to F. If the index category J is connected ( and nonempty ) then the unit of the adjunction is an isomorphism so that lim is a left inverse of Δ.