Let G be a connected reductive algebraic group defined over a non-Archimedean local field F . The study of Whittaker functions on G has a long history. For example, if G = GL(2), an explicit formula for the Whittaker function is well-known (See [5]). Shintani proved an explicit formula for the case G = GL(n) and expressed it by Schur polynomials in [16]. Casselman and Shalika generalized Shinta...

Estimates of the effects of treatment on cost from observational studies are subject to bias if there are unmeasured confounders. It is therefore advisable in practice to assess the potential magnitude of such biases. We derive a general adjustment formula for loglinear models of mean cost and explore special cases under plausible assumptions about the distribution of the unmeasured confounder....

Nitric oxide is an inorganic free radical gas, of formula *N=O (abbreviated as NO). The discovery in 1987/88 that vascular endothelial cells are able to synthesize NO from L-arginine as a transcellular signal [1-4] was initially received by most biologists with considerable scepticism. By now, however, the existence of the L-arginine:NO pathway has been thoroughly documented and its relevance i...

Theoretical studies of structures of neutral molecules and their anions as well as dissociative electron attachment properties are presented for the halomethanes of general formula CXnYm; XˆH, F; YˆCl, Br, I; nˆ 0,4; mˆ 4ÿn. The dissociative electron attachment seems to be the primary process resulting in toxicity of these species. The halomethane anions containing hydrogens are formed as radic...

The synthesis of original co-telomers based on 3,3,3-trifluoropropene (TFP) and vinylidene fluoride (VDF) with a general formula: RF-[CH2-CF2]n-[CH2-CH(CF3)]m-I (where n=1-63, m=2-640, and RF=(CF3)2CF) was achieved by sequential and random cotelomerizations in the presence of RFI. The radical cotelomerizations were initiated by thermal decomposition of different peroxide and persulfate initiato...

Let Gr be the affine Grassmannian for a connected complex reductive group G. Let CG be the complex vector space spanned by (equivalence classes of) Mirković-Vilonen cycles in Gr. The Beilinson-Drinfeld Grassmannian can be used to define a convolution product on MV-cycles, making CG into a commutative algebra. We show, in type A, that CG is isomorphic to C[N], the algebra of functions on the uni...

To analyze the standard intertwining operators for induced representations of a reductive group, one is naturally led to study certain integrals over the corresponding unipotent radical N . A Levi component M acts on N by the adjoint action, and so we may decompose the integral according to the Ad(M)-orbits. We treat unitary and classical cases in which M is the product G×H of two groups relate...

this study proposed a new discharge estimation method using a mean velocity formula derived from chiu’s 2d velocity formula of probabilistic entropy concept and the river bed shear stress of channel. in particular, we could calculate the mean velocity, which is hardly measurable in flooding natural rivers, in consideration of several factors reflecting basic hydraulic characteristics such as r...

In the current research work an attempt was made to develop "Melt in mouth pellets" (Meltlets(®)) containing 40% herbal extract of soy isoflavones that served to provide antioxidants activity in menopausal women. The process of extrusion-spheronization was optimized for extruder speed, extruder screen size, spheronization speed, and time. While doing so the herbal extract incorporated in the pe...

Prostate cancer is the second cause of cancer in males. The prophylactic pelvic irradiation is usually needed for treating prostate cancer patients with Subclinical Nodal Metestases. Currently, the physicians decide when to deliver pelvic irradiation in nodal negative patients mainly by using the Roach formula, which gives an approximate estimation of the risk of Subclinical Nodal Metestases. I...