Examples of using Embeddings in English and their translations into Russian
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Flat embeddings are automatically linkless, but not vice versa.
For example this is always the case for embeddings of trees, which have a single face.
Isometric embeddings of graphs into hypercubes have an important application in chemical graph theory.
Thus, graphs of bounded pathwidth have embeddings of this type with linear volume.
Thus, their theory establishes fundamental connections between graph minors and topological embeddings of graphs.
Ustalov Joining Dictionaries and Word Embeddings for Ontology Induction pp.
Study of embeddings of G into the Cremona group is equivalent to study of G-birational geometry of rational G-Mori fiber spaces.
For an arbitrary K if ϕ is approximable by embeddings, then ϕ/c is approximable by embeddings.
Graph embeddings are also used to prove structural results about graphs, via graph minor theory and the graph structure theorem.
The set of faces of any one of these two embeddings is the set of Petrie polygons of the other embedding.
Ja'Ja'& Simon(1982) used Mac Lane's planarity criterion as part of a parallel algorithm for testing graph planarity andfinding planar embeddings.
The graphs that do not have knotless embeddings(that is, they are intrinsically knotted) include K7 and K3,3,1,1.
Moreover, since any function between discrete or indiscrete spaces is continuous, both of these functors give full embeddings of Set into Top.
The graphs that admit such embeddings were characterized by Djoković(1973) and Winkler(1984), and were later named partial cubes.
Like the graphs with planar covers, the graphs with projective plane embeddings can be characterized by forbidden minors.
The map ϕ is approximable by embeddings if and only if for each i 0,, k the i-th derivative ϕ(i) does not contain transversal self-intersections.
In category theory, there is no satisfactory and generally accepted definition of embeddings that is applicable in all categories.
A common special case are word embeddings, where the possible values of the categorical variable are the words in a language and words with similar meanings are to be assigned similar vectors.
Because of this characterization by Hamiltonian cycles, graphs that have two-page book embeddings are also known as subhamiltonian graphs.
Planar graphs that do not have two-page book embeddings may also be drawn in a similar way, by allowing their edges to be represented by multiple semicircles above and below the line.
It studies the embedding of graphs in surfaces,spatial embeddings of graphs, and graphs as topological spaces.
In the present paper we study embeddings of some spaces of functions of generalized bounded variation into classes of functions with given majorant of average modulus of continuity introduced by B.
The main result of this paper is an analogous criterion for approximability by embeddings of a cycle in the plane Theorem 1.3.S below, also generalizing Example 1.2.
When simultaneous embeddings with fixed edges do exist, they can be found in polynomial time for pairs of outerplanar graphs, and for Biconnected graphs, i.e. pairs of graphs whose intersection is biconnected.
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings into a book, a collection of half-planes all having the same line as their boundary.
The actual projective embeddings are complicated(see equations defining abelian varieties) when n> 1, and are really coextensive with the theory of theta-functions of several complex variables with fixed modulus.
A different method uses an inductive construction of 3-connected graphs to incrementally build planar embeddings of every 3-connected component of G and hence a planar embedding of G itself.
The class of trees that admit greedy embeddings into the Euclidean plane has been completely characterized, and a greedy embedding of a tree can be found in linear time when it exists.
Clearly, for investigation of approximability by embeddings of simplicial maps K G⊂ R2 it suffices to consider only the approximations f: K N.
Unger(1992) claimed that finding three-page embeddings with a fixed spine ordering can also be performed in polynomial time although his writeup of this result omits many details.