t h e o r y  o f  e v e y t h i n g

By Henryk Szubinski

 

data on a process to use the x,y,z formats for any direct displacement complication in coupling to the solar system sectors and solar exo planet systems..

 

projective basis in a parameter of short definitions

 

For other uses, see Ellipse (disambiguation).

An ellipse obtained as the intersection of a cone with a plane.

In mathematics, an ellipse (from Greek ἔλλειψις elleipsis, a “falling short”) is the finite or bounded case of a conic section, the geometric shape that results from cutting a circular conical or cylindrical surface with an oblique plane (the other two cases being the parabola and the hyperbola). It is also the locus of all points of the plane whose distances to two fixed points add to the same constant.

 

Ellipses also arise as images of a circle or a sphere under parallel

 

this common value in everything in the universe as basic to the large scale structures of the universe by fuse indicative motions of stars to their point reference positions by any short cut conal section into tow dismesional responses = to the non problems of any projective and any vector data

 1) By projection SHORT to DISPLACE projection=cobe

2) By Projection DISPLACE to SHORT projection=digital sky

3) the connective data on =large scale structures of their interactions..

 theese 3,2,1, formats are everywhere present…

projection, and some cases of perspective projection. Indeed, circles are special cases of ellipses. An ellipse is also the closed and bounded case of an implicit curve of degree 2, and of a rational curve of degree 2. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.

 

 

In dealing with a vector field X on a semi Riemannian manifold (p.ex. in general relativity), it is often useful to decompose the covariant derivative into its symmetric and skew-symmetric parts:

X_{a;b}=\frac{1}{2}h_{ab}+ F_{ab}

where

h_{ab}=(\mathcal{L}_X g)_{ab}=X_{a;b}+X_{b;a}

and

F_{ab}=\frac{1}{2}(X_{a;b}-X_{b;a})

Note that Xa are the covariant components of X.

 

By the data on how a indication of the same process to gain access into the laws of distribution by the process of active value sequencings of 4 x measurement systems as in a sequence to which the data on maintainment or survival of the human reference of a MIDI format

 

Mathematically, the condition for a vector field X to be projective is equivalent to the existence of a one-form ψ satisfying

X_{ab;c}\, =R_{abcd}X^d+2g_{a(b}\psi_{c)}

which is equivalent to

h_{ab;c}\, =2g_{ab}\psi_c+g_{ac}\psi_b+g_{bc}\psi_a

The set of all global projective vector fields over a connected or compact manifold forms a finite-dimensional Lie algebra denoted by P(M) (the projective algebra) and satisfies for connected manifolds the condition: \dim P(M) \le n(n+2). Here a projective vector field is uniquely determined by specifying the values of X, \nabla X and \nabla \nabla X (equivalently, specifying X, h, F and ψ) at any point of M. (For non-connected manifolds you need to specify these 3 in one point per connected component.) Projectives also satisfy the properties:

 

ptolematic projections as the referenciality of any value eliptical short displacement on every reference to projective universal value relations

 

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