Let K be a connected Lie group of compact type and let W(K ) denote the set of continuous paths in K, starting at the identity and with time-interval [0, 1]. Then W(K ) forms an infinite-dimensional group under the operation of pointwise multiplication. Let \ denote the Wiener measure on W(K ). We construct an analog of the Segal Bargmann transform for W(K ). Let KC be the complexification of K...

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

The mathematics behind Computerized Tomography (CT) is based on the study of the parallel beam transform P and the divergent beam transform D. Both of these map a function f in Rn into a function defined on the set of all lines in Rn, by integrating f along these lines. The parallel and divergent k-plane transforms are defined in a similar fashion by integration over k-planes (i.e., translates ...

in this research project, the nitrito nitro isomerization of [co (nh3)5no2]f2 complex has been studied. isomerization of this complex in the solid state follows a first order kinetics. the rate of isomerization at different temperatures was determined using a fourier transform lnfrared spectrophotometer. ? and ? are calculated at 298 k. the infrared, visible and ultraviolet spectra of this comp...

Gale transform was successfully used to classify polytopes with few vertices; that is, r-dimensional polytopes with r + k vertices, where k is small. In this paper, we use Gale transform to classify r-dimensional generic bar frameworks with r + k vertices, where k ≤ 4; as universally rigid, globally rigid or nonglobally rigid.

A (d, k) set is a subset of R containing a translate of every k-dimensional disc of diameter 1. We show that if (1 + √ 2)k−1 + k > d and k ≥ 2, then every (d, k) set has positive Lebesgue measure. This improves a result of Bourgain, who showed that the analogous statement holds when 2k−1 +k ≥ d and k ≥ 2. We obtain this improvement in two parts. First, we replace Bourgain’s main estimate with a...

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...