There are a few Lax matrices of the Clebsch system. Poles Baker-Akhiezer function determine class equivalent divisors on corresponding spectral curves. According to Riemann-Roch theorem, each has unique reduced representative. We discuss properties such divisor curve $3\times 3$ matrix having natural generalization $gl^*(n)$ case.

The body and spatial representations of rigid body motion correspond, respectively, to the convective and spatial representations of continuum dynamics. With a view to developing a unified computational approach for both types of problems, the discrete Clebsch approach of Cotter and Holm (6) for continuum mechanics is applied to derive (i) body and spatial representations of discrete time model...

Abstract We present sum rules for Clebsch–Gordan coefficients in the framework of SO (4) group-theoretical description hydrogen atom. The main results are obtained using properties Runge-Lenz-Pauli vector, particular expressing matrix elements powers its last component both spherical and parabolic basis. Connections with Stark effect diamagnetism atom outlined.

The zero distribution of orthogonal polynomials pn,N , n = 0, 1, . . . generated by recurrence coefficients an,N and bn,N depending on a parameter N has been recently considered by Kuijlaars and Van Assche under the assumption that an,N and bn,N behave like a(n/N) and b(n/N), respectively, where a(·) and b(·) are continuous functions. Here, we extend this result by allowing a(·) and b(·) to be ...

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.

In this paper we present a method for determining some variations of a singular trajectory of an affine control system. These variations provide necessary optimality conditions which may distinguish between maximizing and minimizing problems. The generalized Legendre-Clebsch conditions are an example of these type of conditions.