Over an algebraically closed field k of characteristic zero, the Drinfeld double Dn Taft algebra that is defined using a primitive nth root unity q?k for n?2 quasitriangular Hopf algebra. Kauffman and Radford have shown has ribbon element if only n odd, unique; however there been no explicit description this element. In work, we determine explicitly. For any n?2, use R-matrix to construct actio...

We quantize explicitly the Witt algebra in characteristic 0 equipped with its Lie bialgebra structures discovered by Taft. Then, we study the reduction modulo p of our formulas. This gives p − 1 families of polynomial noncocommutative deformations of a restricted enveloping algebra of a simple Lie algebra in charactristic p (of Cartan type). In particular, this yields new families of noncommuta...

Patients with active cirrhosis of the liver may show evidence of multiple system involvement (Read, Sherlock, and Harrison, 1963). The suggestion has also been made that in such patients autoimmune phenomena play an important part in the pathogenesis of the disease (Mackay, Taft, and Cowling, 1956). These findings prompted us to undertake an investigation into the frequency with which antinucle...

Three cases associating multiple congenital anomalies with a small extra metacentric chromosome have been reported by Fr0land, Holst, and Terelev (I963), Gustavson, Atkins, and Patricks (I964), and Taft, Dodge, and Atkins (I965). All three occurred in boys. Because this occurred in male patients only, the possibility that this extra small chromosome was associated with the X chromosome could no...

Assessing the sensitivity of water networks to noisy mass loads using Monte Carlo simulation Raymond R. Tan a,∗, Dominic C.Y. Foo b,1, Zainuddin A. Manan c a Chemical Engineering Department, De La Salle University-Manila, 2401 Taft Avenue, 1004 Manila, Philippines b Chemical Engineering Pilot Plant, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia c Department of Chemical Engineerin...

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference case is interpretation value map, classically element group. interpretations as states algebra, elements a Hilbert $C^{*} $-bimodule $\frac{1}{2}$ densities and dual algebra. examples complex valued functions $S_{3}$ $\mathbb{Z}$, Woronowicz's matrix quantum ...