In this paper we present an application possibility of the affine plane of order $n$, in the planning experiment, taking samples as his point. In this case are needed $n^2$ samples. The usefulness of the support of experimental planning in a finite affine plane consists in avoiding the partial repetition combinations within a proof. Reviewed when planning cannot directly drawn over an affine plane. In this case indicated how the problem can be completed, and when completed can he, with intent to drawn on an affine plane.
Authors: Antoine Balan
Comments: 4 pages, written in french
The symplectic Dirac operator is defined over a spin Kaehler manifold. The corresponding Schrödinger-Lichnerowicz formula is proved.
The same mathematical equation connects the circle to the square, the sphere to the cube, the hyper-sphere to the hyper-cube, another also connects the ellipse to the rectangle, the ellipsoid to a rectangular parallelepiped, the hyper-ellipsoid To the rectangular hyper-parallelepiped.
The understanding of these equations has taken us very far in a universe so familiar to mathematicians, the universe of periodic functions, and that of geometric forms with rounded ends revealing an infinity of new mathematical constants associated with them.