It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2(C)–Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral grou...

I F we find it useful to distinguish short periods in the development of a science, the theory of invariants may easily enough be considered to have passed a milestone in 1887. In that year was published the second part of Gordan's Vorlesungen über Invariantentheorie. The plan of this work was dominated by the intent to expound and exemplify worthily the famous Gordan theorem on the finiteness ...

The newest progress on the study of the strangeness in the proton and in the lowest negative parity nucleon excited state N * (1535) is reviewed. Implications on the internal quark structure of the proton, N * (1535) and other baryons are discussed. The diquark cluster picture for the 5-quark components in baryons gives a natural explanation not only to the empirical indications for a positive ...

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kähler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conser...

Let Sn denote the full symmetric permutation group of degree n. For each a E e, let (J (a) be the corresponding permutation matrix, i.e., Q(a) = (0 iUU»)' If e is any subgroup of S n, then Q is a faithful representation of e whose c haracter, e, counts the number of fixed points . In trus note, we in vestigate a red uction of fr, the character of the rth Kronecker power of (J . The reduction of...

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...

We propose a non-Abelian generalization of the Clebsch parameterization for a vector in three dimensions. The construction is based on a group-theoretical reduction of the Chern-Simons form on a symmetric space. The formalism is then used to give a canonical (symplectic) discussion of non-Abelian fluid mechanics, analogous to the way the Abelian Clebsch parameterization allows a canonical descr...

The Schrödinger equation for the four-dimensional double singular oscillator is separable in Eulerian, doble polar and spheroidal coordinates in IR. It is shown that the coefficients for the expansion of double polar basis in terms of the Eulerian basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2) analytically continued to real values of their arguments. The coeff...

Self-adjusting computation is a language-based approach to writing programs that respond dynamically to input changes by maintaining a trace of the computation consistent with the input, thus also updating the output. For monotonic programs, i.e. where localized input changes cause localized changes in the computation, the trace can be repaired efficiently by insertions and deletions. However, ...

We approach concept learning as a heuristic search through a space of concepts for a concept that satisfies the learning task at hand The heuristics represent bias that the concept learning program employs when forming an inductive generalization. We present a model of bias adjustment and report our experience with an implementation of the model. A major objective in research on inductive conce...