The method of Hurwitz-Radon Matrices (MHR) enables interpolation of two-dimensional curves using different coefficients [gamma]: polynomial, sinusoidal, cosinusoidal, tangent, cotangent
, logarithmic, exponential, arcsin, arccos, arctan, arcctg or power function , also inverse functions.
We proceed to construct the phase space by building the cotangent
bundle, which is just the set of pairs consisting of a holonomy map and a divergence-free electric field.
According to the isomorphism (4), the Clifford algebra (40) can be isomorphically mapped to the exterior algebra of a cotangent
bundle [T.sup.*] M
The integral with the cotangent
kernel in (4.7) can be discretized by Wittich's method .
3792/pjaa.89.92 [c]2013 The Japan Academy cotangent
bundle of X is generically generated by its global sections, that is, [H.sup.0](X, [[OMEGA].sup.1.sub.X])[cross product][O.sub.X] [right arrow] [[OMEGA].sup.1.sub.X] is surjective at the generic point of X.
bundle of any compact smooth manifold is also a symplectic manifold in a natural way.
In 1870, Ernst Schering showed that a potential involving the hyperbolic cotangent
of the distance agrees with this law, .
Each codistribution [H.sub.[lambda]] for all [lambda] = 1, ..., k defines a corresponding subspace [B.sub.[lambda]] [subset] M such that [H.sub.[lambda]] is the cotangent
bundle of [B.sub.[lambda]] and dim [H.sub.[lambda]] = dim [B.sub.[lambda]] if and only if all [H.sub.[lambda]] are integrable.
The total space of the cotangent
bundle [T.sup.*][M.sub.I] is canonically diffeomorphic with the total space [T.sup.[dagger]][M.sub.I] of the affine dual of T[M.sub.I] [right arrow] [M.sub.I]
(From now on, it is to be understood that small and capital Latin indices run from 1 to 3, and that Greek indices run from 1 to 4.) As usual, we also define the dual, contravariant (i.e., cotangent
) counterparts of the basis vectors [g.sub.i], [e.sup.A], and [[omega][micro]], denoting them respectively as gi, [e.sub.A], and [[omega][micro]], according to the following relations: [g.sub.i], [g.sub.[micro]]
vector space at a point of ([M.sup.n], [A.sup.[omega]]) is defined in the next.
The average value of the cotangent
of the angle can be calculated as follows: