Примеры использования Isometry на Английском языке и их переводы на Русский язык
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As isometry group these are all automorphisms.
Symmetry groups of objects are isometry groups.
Isomorphism and isometry of separable Hilbert spaces.
Isometry is a map which preserves distances.
It is a subgroup of the isometry group of the space concerned.
An isometry is a distance-preserving map between metric spaces.
Important subgroups of the isometry group are the Fuchsian groups.
The isometry group of the n-dimensional Euclidean space is the Euclidean group En.
A figure is achiral if and only if its symmetry group contains at least one orientation-reversing isometry.
Accordingly, analysis of isometry groups is analysis of possible symmetries.
The column" of order 2 elements" in the following tables shows the total number of isometry subgroups of types C2, Ci, Cs.
The Cayley transform provides an isometry between the half-plane model and the Poincaré disk model.
For example, the program" Pipe Isometry" allows pipelines to be entered with graphical support.
However, it is not vertex-transitive, and consequently not one of the Archimedean solids,as there are pairs of vertices such that there is no isometry of the solid which maps one into the other.
Roughly speaking, this theory says that the Dade isometry can be extended unless the groups involved have a certain precise structure.
The hyperboloid model of the n-dimensional hyperbolic space is closely related to the Beltrami-Klein model andto the Poincaré disk model as they are projective models in the sense that the isometry group is a subgroup of the projective group.
To define the third and last move U,apply an isometry to this ellipsoid so as to carry it over TS.
Two such isometry groups are of the same type(of the same wallpaper group) if they are the same up to an affine transformation of the plane.
Three, we create a stable safe zone by applying temporal inversion isometry to as much of space-time as we can isolate.
The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective plane OP2.
One open problem(as of 2006) is the completion of the Bargmann-Wigner programme for the isometry group SO(D- 2, 1) of the de Sitter spacetime dSD- 2.
A point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.
This total number is one of the characteristics helping to distinguish the various abstract group types, while their isometry type helps to distinguish the various isometry groups of the same abstract group.
In Euclidean geometry any isometry can be written as v↦ A v+ b{\displaystyle v\mapsto Av+b} with an orthogonal matrix A{\displaystyle A} and a vector b{\displaystyle b.
In the global sense, the Gromov-Hausdorff space is totally heterogeneous, i.e., its isometry group is trivial, but locally there are many nontrivial isometries. .
There are many infinite isometry groups; for example, the"cyclic group"(meaning that it is generated by one element- not to be confused with a torsion group) generated by a rotation by an irrational number of turns about an axis.
It is a subgroup of the full icosahedral symmetry group(as isometry group, not just as abstract group), with 4 of the 10 3-fold axes.
By extending these calculations Cartwright& Steger(2010) showed that the twenty-eight classes exhaust all possibilities for fake projective planes andthat there are altogether 50 examples determined up to isometry, or 100 fake projective planes up to biholomorphism.
However, it is not vertex-transitive,as it has different isometry at different vertices, making it a Johnson solid rather than an Archimedean solid.