Formally speaking, this means that there must be an algebra monomorphism from the de Rham cohomology of the closed n-manifold ...

The simplest example of a flat three-dimensional shape is ordinary infinite space — what mathematicians call Euclidean space — but there are other flat shapes to consider too. These shapes are harder ...

Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and ...

"You know you can fill space with cubes," Torquato said, "We were looking for another way." In the article "New Family of Tilings of Three-Dimensional Euclidean Space by Tetrahedra and Octahedra," he ...

over time draws out what is known as a three-dimensional Euclidean space—one which has comparable qualities to the universe overall. The shape created had those same qualities regardless of the ...

This advancement facilitates nonlinear interpolation and denoising within the high-dimensional ambient space (panel (d ... analysis methods often rely on Euclidean (linear) dependencies among ...