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We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.
      
For the case of positive characteristic we use the classification of finite irreducible groups generated by pseudoreflections due to Kantor, Wagner, Zalesski? and Sere?kin.
      
In the interesting case when the group is of Coxeter typeDn (n≥4) we use higher polarization operators introduced by Wallach.
      
We also use known results about canonical bases forUq2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.
      
We use invariant theory to compute the exact number of nonzero idempotents of an arbitrary 2-dimensional real division algebra.
      
For this, we use a variant of classical Morse theory.
      
We use this to disprove a conjecture of Kwon and Lusztig stating the irreducibility of quantum Weyl group actions of Artin's braid group Bn on the zero-weight spaces of all simple Usln-modules for n≥4.
      
We shall construct a generating set of a nonfinitely generated Ga-invariant ring given in Freudenburg's counterexample by making use of an integral sequence which was constructed inductively by Freudenburg.
      
Then we show how to use loop groups and hypercohomology to write explicit hamiltonians.
      
Extending this theory, we show how to use correlations between two processes to predict one from the other.
      
Extending this theory, we show how to use correlations between two processes to predict one from the other.
      
The method we use is a combination of the smoothing effect of the operator ?t + ?x(2j+1) and a gauge transformation performed on a linear system, which allows us to consider initial data with arbitrary size.
      
The Discrete Wavelet Transform (DWT) is of considerable practical use in image and signal processing applications.
      
For example, significant compression can be achieved through the use of the DWT.
      
We use these unitary operators to provide an interesting class of scaling functions.
      
We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes the result of Hansson and Brezis-Wainger for Wnk/k as a special case.
      
We prove properties of B-splines and exponential Euler splines and use these properties to estimate the Riesz bounds of the Wilson bases.
      
The first one is based on the use of the generalized Calderón reproducing formula and multidimensional fractional integrals with a Bessel function in the kernel.
      
We use the decomposition of a group into double cosets and a graph theoretic indexing scheme to derive algorithms that generalize the Cooley-Tukey FFT to arbitrary finite group.
      
Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions of Lp functions converge to the functions almost everywhere and in Lp for 1>amp;lt;p>amp;lt;∞.
      
 

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