Примеры использования Injective на Английском языке и их переводы на Русский язык
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Isometries are always continuous and injective.
Projective and injective descriptions in the complex domain.
A function is called an embedding if it is both monotone and injective.
Injective hull Radical of a module Cosocle Robinson 1996, pp. 87.
Both with the help of plastic surgery, andthe best hardware and injective aesthetic procedures.
An automaton that is both injective and surjective is called a reversible cellular automaton.
For example, every function may be factored into the composition of a surjective function with an injective function.
Injective sheaves are acyclic, but for computations it is useful to have other examples of acyclic sheaves.
The category of fields is a reflective subcategory of the category of integral domains with injective ring homomorphisms as morphisms.
A requirement that ƒ be injective means that no label can be used a second time; the result is a sequence of labels without repetition.
In the terminology below, the case of sampling with replacement is termed"Any f",while the case of sampling without replacement is termed"Injective f.
Assume for a contradiction that f could be injective, which means the pieces of S cut out by the squares stack up in a non-overlapping way.
Injective f: After we choose an item, we set it aside, so we can't choose it again; hence we will end up with n distinct items.
This can often be used to prove that there are no(injective) homomorphisms between two concretely given groups.
Generally, an injective function f from an unordered set X to a cycle Y induces a unique cyclic order on X that makes f an embedding.
The companion terms monomorphism and epimorphism were originally introduced by Nicolas Bourbaki;Bourbaki uses monomorphism as shorthand for an injective function.
Or a smooth embedding, is defined to be an injective immersion which is an embedding in the topological sense mentioned above i.e. homeomorphism onto its image.
A convex metric space in which the closed balls have the 2-Helly property(that is, a space with Helly dimension 1, in the stronger variant of Hellydimension for infinite subcollections) is called injective or hyperconvex.
A metric space is injective if and only if it is an injective object in the category of metric spaces and metric maps.
An L(2,1)-coloring is a homomorphism into the complement of the path graph that is locally injective, meaning it is required to be injective on the neighbourhood of every vertex.
If ƒ must be injective, then the selection must involve n distinct elements of X, so it is a subset of X of size n, also called an n-combination.
The category of sheaves of abelian groups on a topological space X is an abelian category, and so it makes sense to ask when a morphism f:B→ C of sheaves is injective(a monomorphism) or surjective an epimorphism.
One also talks about injective objects in categories more general than module categories, for instance in functor categories or in categories of sheaves of OX-modules over some ringed space X.
It provides an example of a cellular automaton that is surjective(eachconfiguration has a predecessor) but not injective(it has sets of more than one configuration with the same successor), showing that the converse of the Garden of Eden theorem is not true.
Alloplant biomaterial, injective surgery, lesions of dermal integument, angiogenesis, phagocytosis, regeneration, augmentation, pigmentary exchange, injective contour plastics.
The formula is x n x( x- 1)⋯( x- n+ 1).{\displaystyle x^{\underline{ n}}= x( x-1)\ cdots(x-n+1).} Note that if n> x then one obtains a factor zero,so in this case there are no injective functions N→ X at all; this is just a restatement of the pigeonhole principle.
Requiring in addition ƒ to be injective means forbidding to put more than one ball in any one box, while requiring ƒ to be surjective means insisting that every box contain at least one ball.
In contrast to the classical reflexive spaces the class Ste of stereotype spaces is very wide(it contains, in particular, all Fréchet spaces and thus, all Banach spaces), it forms a closed monoidal category, and it admits standard operations(defined inside of Ste) of constructing new spaces, like taking closed subspaces, quotient spaces,projective and injective limits, the space of operators, tensor products, etc. The category Ste have applications in duality theory for non-commutative groups.
We say that H is an immersion minor of G if there exists an injective mapping from vertices in H to vertices in G where the images of adjacent elements of H are connected in G by edge-disjoint paths.
In a concrete category, an embedding is a morphism ƒ:A→ B which is an injective function from the underlying set of A to the underlying set of B and is also an initial morphism in the following sense: If g is a function from the underlying set of an object C to the underlying set of A, and if its composition with ƒ is a morphism ƒg: C→ B, then g itself is a morphism.