Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for Re(si) sufficiently large, that has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. A heuristic definition of such series was given in [BB...

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.

In this study we examine the use of Multiscale Fourier Transforms (MFT) on the effect of image fusion and segmentation. The proposed method takes SPOT-PAN and SPOT-XS images to register using MFT technique to produce high quality fused image. The algorithm works iterativly from coarsest level of decomposition to the top level. This process applied to the all sub-bands in order to give best choi...

Medicine, BIDMC/Harvard Medical School, Boston, Massachusetts, USA Full list of author information is available at the end of the article Figure 1 DICE similarity coefficients obtained with and without the proposed motion correction approach in pre (5-3 scheme) and post contrast (4-3-2 scheme) T1w image series. Average DICE coefficients over each T1w image series (left column), and over each in...

Fractal Image Coder (FIC) makes use of the self-similarity inside a natural image to achieve high compression ratio and maintain good image quality. In FIC, the most important factor affecting the compression ratio and the image quality is the quantization of the contrast scaling and brightness offset coefficients. Most quantization methods treat the two coefficients independently and quantize ...

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 ...