A Formalism for Differential Rotation

Rotation operator formalism for open-shell omplexes

Differential Tannakian Formalism

1.1. Definition. Let C be an abelian category. The derivative D(C) of C is defined as follows: The objects are exact sequences 0 −→ X0 iX −−→ X1 πX −−→ X0 −→ 0 of C, and the morphisms from such an object are morphisms of exact sequences whose two X parts coincide. The category D(C) is again abelian. An exact functor F : C1 −→ C2 gives rise to an induced (exact) functor D(F ) : D(C1) −→ D(C2). W...

Linear Potentials and Galactic Rotation Curves -formalism

In the first paper in this series we presented a typical set of galactic rotation curves associated with the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-l...

Orthomax Rotation Problem. a Differential Equation Approach1)

In the present paper the ORTHOMAX rotation problem is reconsidered. It is shown that its solution can be presented as a steepest ascent flow on the manifold of orthogonal matrices. A matrix formulation of the ORTHOMAX problem is given as an initial value problem for matrix differential equation of first order. The solution can be found by any available ODE numerical integrator. Thus the paper p...

Differential Rotation in F Stars

Differential rotation can be detected in single line profiles of stars rotating more rapidly than about v sin i = 10 km s with the Fourier transform technique. This allows to search for differential rotation in large samples to look for correlations between differential rotation and other stellar parameters. I analyze the fraction of differentially rotating stars as a function of color, rotatio...