Примеры использования Infinite family на Английском языке и их переводы на Русский язык
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The simplest infinite family are the canonical pyramids of n sides.
Any number of half-twists may be introduced into the loop before linking,resulting in an infinite family of possibilities.
The twist knots are an infinite family of knots, and are considered the simplest type of knots after the torus knots.
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975.
Additionally there are many other examples of sporadic simplicial arrangements that do not fit into any known infinite family.
Tietze's graph is isomorphic to the graph J3,part of an infinite family of flower snarks introduced by R. Isaacs in 1975.
Another infinite family, elongated pyramids, consists of polyhedra that can be roughly described as a pyramid sitting on top of a prism with the same number of sides.
This theorem generalizes to projective groups of higher dimensions andgives an important infinite family PSL(n, q) of finite simple groups.
The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices.
The pretzel knot 7, 5, 3 is non-invertible, as are all pretzel knots of the form(2p+ 1),(2q+ 1),(2r+ 1), where p, q, and r are distinct integers,which is the infinite family proven to be non-invertible by Trotter.
The Kolakoski sequence is the prototype for an infinite family of other sequences that are each their own run-length encodings.
Squaregraphs may be characterized in several ways other than via their planar embeddings:They are the median graphs that do not contain as an induced subgraph any member of an infinite family of forbidden graphs.
They can be used to give examples of an infinite family of homeomorphic simply connected compact 4-manifolds no two of which are diffeomorphic.
In 1962 Ralph Fox conjectured that some knots were non-invertible, butit was not proved that non-invertible knots exist until Hale Trotter discovered an infinite family of pretzel knots that were non-invertible in 1963.
The only regular Euclidean compound honeycombs are an infinite family of compounds of cubic honeycombs, all sharing vertices and faces with another cubic honeycomb.
In mathematics, the Kolakoski sequence, sometimes also known as the Oldenburger-Kolakoski sequence, is an infinite sequence of symbols{1,2}that is its own run-length encoding and the prototype for an infinite family of related sequences.
Plummer(1992) used the Kleetope construction to provide an infinite family of examples of simplicial polyhedra with an even number of vertices that have no perfect matching.
You belong to a well-nigh infinite family of worlds, but your sphere is just as precisely administered and just as lovingly fostered as if it were the only inhabited world in all existence.”.
There are 44 such Schwarz triangles(5 with tetrahedral symmetry, 7 with octahedral symmetry and 32 with icosahedral symmetry),which, together with the infinite family of dihedral Schwarz triangles, can form almost all of the non-degenerate uniform polyhedra.
Lubotzky, Phillips and Sarnak show how to construct an infinite family of( p+ 1){\displaystyle(p+1)}-regular Ramanujan graphs, whenever p{\displaystyle p} is a prime number and p≡ 1( mod 4){\displaystyle p\equiv 1{\pmod{4.
More strongly, there exists a constant α<1(the shortness exponent) and an infinite family of polyhedral graphs such that the length of the longest simple path of an n-vertex graph in the family is Onα.
Figure 4 encapsulates an infinite family of order 2 setisets each composed of two triangles, P and Q. As shown, the latter can be hinged together to produce a compound triangle that has the same shape as P or Q, depending upon whether the hinge is fully open or fully closed.
Some constructions are based on infinite families of aperiodic sets of tiles.
This has been proven for all paths, caterpillars,and many other infinite families of trees.
Since projective planes are known to exist for all orders n which are powers of primes,these constructions provide infinite families of symmetric configurations.
They form one of the few known infinite families of cubic partial cubes, and(except for four sporadic examples) the only vertex-transitive cubic partial cubes.
Although several infinite families of cubic partial cubes are known, together with many other sporadic examples, the only known cubic partial cube that is not a planar graph is the Desargues graph.
Dual graphs of simplicial arrangements have been used to construct infinite families of 3-regular partial cubes, isomorphic to the graphs of simple zonohedra.
The classification theorem states that the list of finite simple groups consists of 18 countably infinite families, plus 26 exceptions that do not follow such a systematic pattern.
In 1975, Rufus Isaacs introduced two infinite families of snarks-the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark BDS stands for Blanuša Descartes Szekeres.