Spiders of the genus Argiope , such as Argiope lobata, contain polyamine toxins that are potent but nonselective blockers of glutamate receptors. However, by very subtle modifications of the structure of native toxins, it is possible to obtain selectivity for subtypes of these receptors, as described by K. Strømgaard and co‐workers in their Communication on page 3087 ff.
The classical Fischer decomposition of polynomials on Euclidean space makes it possible to express any polynomial as a sum
of harmonic polynomials multiplied by powers of |x|2. A deformation of the Laplace operator was recently introduced by Ch.F. Dunkl. It has the property that the symmetry with
respect to the orthogonal group is broken to a finite subgroup generated by reflections (a Coxeter group). It was shown by
B. ?rsted and S. Ben Said that there is a deformation of the Fischer decomposition for polynomials with respect to the Dunkl
harmonic functions. In Clifford analysis, a Dunkl version of the Dirac operator was introduced and studied by P. Cerejeiras,
U. K?hler and G. Ren. The aim of the article is to describe an analogue of the Fischer decomposition for solutions of the
Dunkl Dirac operator. The main methods used are coming from representation theory, in particular, from ideas connected with
Howe dual pairs.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš to recall our long lasting cooperation on
many topics in mathematics
The work presented here is a part of the research project MSM 0021620839 and was supported also by the grant GA ČR 201/05/2117.
Received: October, 2007. Accepted: February, 2008. 相似文献
We are studying the Diophantine exponent μn,l defined for integers 1≤l<n and a vector α∈ℝn by letting
where is the scalar product, denotes the distance to the nearest integer and is the generalised cone consisting of all vectors with the height attained among the first l coordinates. We show that the exponent takes all values in the interval [l+1,∞), with the value n attained for almost all α. We calculate the Hausdorff dimension of the set of vectors α with μn,l(α)=μ for μ≥n. Finally, letting wn denote the exponent obtained by removing the restrictions on , we show that there are vectors α for which the gaps in the increasing sequence μn,1(α)≤...≤μn,n-1(α)≤wn(α) can be chosen to be arbitrary. 相似文献
We present a fiber-based method for generating vortex beams with a tunable value of orbital angular momentum from -1? to +1? per photon. We propose a new (to our knowledge) method to determine the modal content of the fiber and demonstrate high purity of the desired vortex state (97% after 20 m, even after bends and twists). This method has immediate utility for the multitude of applications in science and technology that exploit vortex light states. 相似文献
