Let g be a complex semisimple Lie algebra, and let G be a complex semisimple group with trivial center whose root system is dual to that of g. We establish a graded algebra isomorphism H q (Xλ,C) ∼= Sg e/Iλ, where Xλ is an arbitrary spherical Schubert variety in the loop Grassmannian for G, and Iλ is an appropriate ideal in the symmetric algebra of g, the centralizer of a principal nilpotent in...

Semidiscrete finite element methods for a semilinear parabolic equation in Rd, d < 3, were considered by Johnson, Larsson, Thomée, and Wahlbin. With h the discretization parameter, it was proved that, for compatible and bounded initial data in Ha, the convergence rate is essentially 0(h2+a) for t positive, and for a = 0 this was seen to be best possible. Here we shall show that for 0 < a < 2 th...

Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose Ah(M) is a Uh(g)-equivariant quantization of the function algebra A(M) on M . We develop a method of restricting Ah(M) to the Uh(g)-equivariant quantization on Gorbits in M . We are concerned with those quantizations that may be simultaneously represented as subalgebras in U∗ h(g) and quotients of Ah(M). It turns out...

Alveolar surfactant is known to exist in several morphologic forms or subtypes which have been separated from bronchoalveolar lavage fluid (BAL) by two types of methods-differential centrifugation (DC) and equilibrium buoyant density gradient centrifugation (EBDC). DC separates BAL into large aggregates (LA) and small aggregates (SA); EBDC separates BAL into three peaks called ultraheavy (UH), ...