Some aspects of Aomoto’s generalized hypergeometric functions on Grassmannian spaces Gr(k+1, n+1) are reviewed. Particularly, their integral representations in terms of twisted homology and cohomology are clarified with an example of the Gr(2, 4) case which corresponds to Gauss’ hypergeometric functions. The cases of Gr(2, n + 1) in general lead to (n + 1)-point solutions of the Knizhnik-Zamolo...

Cherednik attached to an affineHecke algebramodule a compatible systemof difference equations, called quantum affine Knizhnik–Zamolodchikov (KZ) equations. In the case of a principal series module, we construct a basis of power series solutions of the quantum affine KZ equations. Relating the bases for different asymptotic sectors gives rise to a Weyl group cocycle, which we compute explicitly ...

Mixed layer (ML) gross (GOP) and net (NOP) oxygen production rates based on in situ mass balances of triple oxygen isotopes (TOI) and O2/Ar are influenced by vertical transport from below, a term traditionally difficult to constrain. Here we present a new approach to estimate vertical eddy diffusivity (Kz) based on density gradients in the upper thermocline and wind speed-based rates of turbule...

We pursue the definition of a KZ-doctrine in terms of a fully faithful adjoint string Dd m dD. We give the definition in any Gray-category. The concept of algebra is given as an adjunction with invertible counit. We show that these doctrines are instances of more general pseudomonads. The algebras for a pseudomonad are defined in more familiar terms and shown to be the same as the ones defined ...

Radiation-induced damage to the retina triggers leukostasis, retinal endothelial cell (REC) death, and subsequent hypoxia. Resultant ischemia leads to visual loss and compensatory retinal neovascularization (RNV). Using human RECs, we demonstrated that radiation induced leukocyte adhesion through mechanisms involving p38MAPK, p53, and ICAM-1 activation. Additional phenotypic changes included p3...

The Kz entropy, and the correlation dimension are commonly used measures of chaotic activity in com.plea: dynamic systems. The design and implem,entation of a massively parallel algorithm on the MasPar MP-2 for the computation of Kz entropy and the correlation dimension is presented. The algorithm is used to compute the Kz entropy and correlation dimension of experimental heart rate data. Exper...

Smallscale internal waves are numerically ray-traced through random 3-D Garrett and Munk (GM) internal wave backgrounds. Past ray-tracing investigations have considered only interactions with background vertical shear Vz = (Uz, Vz). Our numerical simulations indicate a non-negligible role for vertical divergence Wz. The spectral transfer of internalwave energy toward high vertical wavenumber kz...