Hartman, On the isometric immersions in

Euclidean space of manifolds with nonnegative sectional curvatures.

n are the set of points in 3-dimensional

Euclidean space. Then the Bezier curve with degree n is defined by

To this purpose, it is proposed that Cartesian geometry and a three-dimensional

Euclidean space are used to graph fNPV and calculate fIRR.

Minkowski spacetime or Minkowski space can be thought a combination of time dimension and

Euclidean space into a four-dimensional manifold.

In fact, it can be mentioned quite generally that new integrable equations have been obtained in the case of purely

Euclidean space from the Cartan system by exploiting the one-to-one correspondence between the Ablowitz-Kaup-Newell-Segur (AKNS) program [11, 12] and the classical theory of surfaces in three dimensions.

manifoldedness the chief possible manifoldednesses or spaces which he emphasizes are flat or

Euclidean space like that in which we live spherical & Pseudo spherical.

We choose a fibrewise smooth embedding j : [~.X] [right arrow] X x F, over X, for some

Euclidean space F.

Traditional methods describe the mechanical system in a flat

Euclidean space with local coordinate, and the problem caused by local coordinate is inevitable, such as the singularity and ambiguity caused by Euler angles [1].

Komori and Shirai in [16] defined weighted Morrey spaces in the

Euclidean space, which are the extension of Morrey spaces (see [17]) and showed the boundedness in these spaces of some important operators in harmonic analysis.

Subject to (Eq.) X, where X is an open convex subset of Rn (n-dimensional

Euclidean space), (Eq.) and (Eq.) are real-valued functions defined on X, are real-valued functions defined on X, and for each (Eq.) 0 for all x satisfying the constraints of (P).

This section has " topological defect according to partial

Euclidean space and SOM algorithm of manifold " the reason of issue, from a linearity or the approximate linear local data set that expands the training data acquisition according to the neighborhood structure of data gradually, carries on the evolution to train to the network that can avoid the local extremum and victory "topological defect " issue and finally studies and visualization data intrinsic lower-dimensional non-linear manifold structure.