s is a time-frequency transform based on the concept of short-time fourier transform and wavelet transform. the main property of this transform that separate it from the discrete short-time fourier transform is variable frequency resolution. but in this transform the change of resolution of high frequencies to low frequencies is very high. so another transform as a modified s transform is intro...

0. Introduction 5 0.1. Objectives and main results 5 0.1.1. Affine Satake isomorphisms 5 0.1.2. Whittaker functions 6 0.1.3. The setting of the paper 7 0.2. Dunkl operators via DAHA 7 0.2.1. Families of Dunkl operators 8 0.3. The technique of spinors 9 0.3.1. Connections to AKZ 9 0.3.2. Isomorphism theorems 10 0.3.3. The localization functor 10 0.3.4. The Whittaker limit 11 0.4. On Langlands’ p...

Serre has asked if there are motives M with motivic Galois group of type G2 [Se3; pg 386]. This paper is the first step in a project to construct such a motive M , of rank 7 and weight 0, over the base field Q. Let G be the anisotropic form of G2 over Q, and let π = ⊗̂vπv be an automorphic representation of the adelic group G(A). At almost all primes p, the local representation πp is unramified ...

(From the Physiological Laboratory of Prof. Y. Satake, Tohoku University, Sendai.) (Received for publication, August 9, 1949) In the studies on the effect of eserine upon the augmented epinephrine secretion caused by KCl in non-anesthetized dogs, which were performed by the present writer in collaboration with Matumoto, Sasaki and Nuno kawa,1) we noticed that the epinephrine secretion rate from...

Braverman-Finkelberg [4] recently propose the geometric Satake correspondence for the affine Kac-Moody group Gaff . They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R /Zr correspond to weight spaces of representations of the Langlands dual group G∨aff at level r. When G = SL(l), the Uhlenbeck compactification...

We explain (following V. Drinfeld) how the G(C[[t]]) equivariant derived category of the affine Grassmannian can be described in terms of coherent sheaves on the Langlands dual Lie algebra equivariant with respect to the adjoint action, due to some old results of V. Ginzburg. The global cohomology functor corresponds under this identification to restriction to the Kostant slice. We extend this ...

Recent decade has seen an increasing use of the concepts of graph theory in the analysis of solids with heterogeneous microstructures. Generally, two approaches can be identified depending on whether the mechanical microscale properties are assumed deterministic or random. In the first case, work was focused primarily on the possibility of finding the effective continuum representation in terms...