Study on the behavior of farthest points and farthest mapping;

We obtain that any surjective isometry between the unit spheres of normed space E and l~1(F)can be extended to be a linear isometry on the whole space E,and give an affirmative answer to the corresponding Tingley s problem.

We first obtain some sufficient conditions for an isometric mapping defined on the unit sphere(or ball)of aβ-normed space(0＜β■1)can bc extended to be a linear isometry on the whole space.

In the paper,based on the theories of linear algebra,the author introduces some properties about isometric fransformation and isometric mapping in N dimensional euclidean spac

The important precondition of Isomap is supposing that there is an isometric mapping between the data space and the parameter space.

The proposed approach utilizes geodesic distance to denote the difference between sample vectors,and then uses a new nonlinear dimensionality reduction algorithm:isometric mapping(ISOMAP) to find intrinsic geometry structure hiding in users keystroke patterns space.

Isomap is a representative nonlinear dimensionality reduction algorithm,which can discover low dimensional manifolds from high dimensional data.

The minimum mapping distance method,a novel global optimization algorithm of IC parametric yield,is proposed.

Isometries of the Preannihilators of Weakly Closed T(N)-Modules;