Let $p\equiv 1\,(\mathrm{mod}\,9)$ be a prime number and $\zeta_3$ primitive cube root of unity. Then $\mathrm{k}=\mathbb{Q}(\sqrt[3]{p},\zeta_3)$ is pure metacyclic field with group $\mathrm{Gal}(\mathrm{k}/\mathbb{Q})\simeq S_3$. In the case that $\mathrm{k}$ possesses $3$-class $C_{\mathrm{k},3}$ type $(9,3)$, capitulation $3$-ideal classes in its unramified cyclic cubic extensions determine...

Acute chicken leukemia retroviruses, because of their capacity to readily transform hematopoietic cells in vitro, are ideal models to study the mechanisms governing the cell-type specificity of oncoproteins. Here we analyzed the transformation specificity of 2 acute chicken leukemia retroviruses, the Myb-Ets– encoding E26 virus and the ErbA/ErbBencoding avian erythroblastosis virus (AEV). While...

Acute chicken leukemia retroviruses, because of their capacity to readily transform hematopoietic cells in vitro, are ideal models to study the mechanisms governing the cell-type specificity of oncoproteins. Here we analyzed the transformation specificity of 2 acute chicken leukemia retroviruses, the Myb-Ets- encoding E26 virus and the ErbA/ErbB-encoding avian erythroblastosis virus (AEV). Whil...

Mouse embryonic stem (ES) cells, derived from the inner cell mass of blastocyst stage embryos, undergo programmed differentiation in vitro to form a primitive vasculature. This programmed differentiation proceeds through similar processes of vasculogenesis and angiogenesis found during early vascular development in vivo. Partially differentiated ES cell clumps or embryoid bodies (EBs) first for...

We study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to pr...

In this paper, we summarize our progress on two interaction techniques (point-based and ray-based) for haptic rendering. First, we describe a new point-based rendering technique that is computationally less expensive than previously proposed methods. We use a localized search procedure to reduce the number of computations and make it independent of the number polygons of the polyhedron. Second,...

We study prime and primitive ideals in a uniied setting applicable to quanti-zations (at nonroots of unity) of n n matrices, of Weyl algebras, and of Euclidean and symplectic spaces. The framework for this analysis is based upon certain iterated skew polynomial algebras A over innnite elds k of arbitrary characteristic. Our main result is the veriication, for A, of a characterization of primiti...

We study the algebra U ζ obtained via Lusztig's 'integral' form [Lu 1, 2] of the generic quantum algebra for the Lie algebra g = sl 2 modulo the two-sided ideal generated by K l − 1. We show that U ζ is a smash product of the quantum deformation of the restricted universal enveloping algebra u ζ of g and the ordinary universal enveloping algebra U of g, and we compute the primitive (= prime) id...

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian stabilizers and a well behaved orbit space. In this case, the spectrum of the crossed product is homeomorphic, via an induction map, to a quotient of the spe...

Phosphorus, as phosphate, plays a paramount role in biology. Since phosphate transfer reactions are an integral part of contemporary life, phosphate may have been incorporated into the initial molecules at the very beginning. To facilitate the studies into early phosphate utilization, we should look retrospectively to phosphate-rich molecules present in today's cells. Overlooked by origin of li...