LetGn,r(K) be the Grassmannian manifold of k-dimensionalK-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine transforms, Rr′,r, Cr′,r and Sr′,r, from the L space L2(Gn,r(K)) to the space L 2(Gn,r′(K)), for r, r ′ ≤ n − 1. The L spaces are decomposed into irreducible representations of G with multiplicity free. We compute ...

Consider a root system of type BC1 on the real line R with general positive multiplicities. The Cherednik-Opdam transform defines a unitary operator from an L-space on R to a L-space of C-valued functions on R with the Harish-Chandra measure |c(λ)|dλ. By introducing a weight function of the form cosh(t) tanh t on R we find an orthogonal basis for the L-space on R consisting of even and odd func...

Let L be the Lie algebra of a simple algebraic group defined over F and let H be a split Cartan subalgebra of L. Let R = (X,Φ, Y,Φ∨) be the root datum of L, so that H = Y ⊗ F, and let 〈·, ·〉 : Φ × Φ∨ 7→ Z be the corresponding bilinear form. This bilinear form induces a linear form on the roots of L by defining α : h 7→ P i〈α, yi〉ti, where h = P i yi⊗ ti. Given a root α, we define the multiplici...

To evaluate the effects of the new resistant starch (RS) formula, PPB-R-203, on glucose homeostasis in healthy subjects and subjects with type 2 diabetes.A cohort consisting of 40 healthy participants received test and control diets and was checked for up to 3 hours post-meal. A randomized, 2-regimen, cross-over, comparative study was conducted in 44 subjects with type 2 diabetes and glycemic c...

Let R = Zq + uZq, where q = p s and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(xn − 1)-submodule of GR(R, l)[x]/(xn − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necess...

Determining the type of returns to scale (RTS) and identifying stability region for RTS of evaluating unit are appropriate abilities for forecasting the future the unit when its size is changed. This paper aims to introduce RTS sustainability of frontier decision making units (DMUs) in data envelopment analysis (DEA). Based on the importance of RTS in relation to decisions of managers, differen...

The flea beetle, Phyllotreta nemorum L. (Coleoptera: Chrysomelidae), is an intermediate specialist feeding on a small number of plants within the family Brassicaceae. The most commonly used host plant is Sinapis arvensis L., whereas the species is found more rarely on Cardaria draba (L.) Desv., Barbarea vulgaris R.Br., and cultivated radish ( Raphanus sativus L.). The interaction between flea b...