A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (Hn, In) are exhibited. For n = 1 we recover Clebsch sytem. All these systems are also integrable at the quantum level.

Abstract. In a recent paper [1] we have constructed the spin and tensor representations of SO(4) from which the invariant weight can be derived for the Barrett-Crane model in quantum gravity. By analogy with the SO(4) group, we present the complexified Clebsch-Gordan coefficients in order to construct the Biedenharn-Dolginov function for the SO(3,1) group and the spherical function as the Loren...

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules Lh(g) of the quantized enveloping algebras Uh(g). On them the quantum Lie bracket is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie alge...

The 1|1-supertransvectants are the osp(1|2)-invariant bilinear operations on weighted densities on the supercircle S, the projective version of R. These operations are analogues of the famous Gordan transvectants (or Rankin-Cohen brackets). We prove that supertransvectants coincide with the iterated Poisson and ghost Poisson brackets on R and apply this result to construct star-products.

A new method for linear regression analysis of interval-valued data is proposed. In particular, the linear relationship between an interval-valued response variable and a set of interval-valued explanatory variables is investigated by considering two regression models, one for the midpoints (the locations of the intervals) of the response and explanatory variables and the other one for the radi...

We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order √ log n, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order log log n. This is a noteworthy difference to orthonormal functions on the unit interval, wher...

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear...

A type of closed exterior algebra in R3 under the cross product is revealed to hold between differential forms from the three Whittaker scalar potentials, associated with the fields of a moving electron. A special algebraic structure is revealed in the context of Clebsch reparametrization of these scalars, and a special prescription for the construction of permutation invariant electromagnetic ...

turbulence structure on the gas side of a wavy stratified flow was experimentally investigated in a near horizontal 18.7 cm (h) 10 cm (w) 5.5m (l) rectangular duct.by applying the variable interval time averaging (vita) technique to the hot wire anemometer measurements frequency of occurrence of turbulent events were detected near the air-water interface. experimental results showed that freque...