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 free We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra. The basic tool is the decomposition ofN pairs of free charged bosons with respect toglN and the commuting withglN Lie algebra of infinite matrices?l. Free quotients and the first betti number of some hyperbolic manifolds In all these cases we actually show that Γ=π1(M) has a finite index subgroup which is mapped onto a nonabelian free group. A theorem of Kostant states that the universal enveloping algebra of g is a free module over its center. A theorem of Richardson states that the algebra of regular functions ofG is a free module over the subalgebra of regular class functions. Finitely generated profinitely dense free groups in higher rank semi-simple groups Indeed, we will give a full classification of the manifoldsN(g, V) which are commutative spaces, using a characterization in terms of multiplicity-free actions. We prove that the socle of restriction is multiplicity free and moreover that the summands lie in distinct blocks. Transvection free groups and invariants of polynomial tensor exterior algebras By a case-free approach we give a precise description of the closure of a Steinberg fiber within a twisted wonderful compactification of a simple linear algebraic group. Of particular interest are spherical varieties which are smooth and affine since they form local models for multiplicity free Hamiltonian K-manifolds, K a maximal compact subgroup of G. We consider free affine actions of unipotent complex algebraic groups on Cn and prove that such actions admit an analytic geometric quotient if their degree is at most 2. Moreover, we classify free affine C2-actions on Cn of degree n - 1 and n - 2. We describe the main results obtained in a joint work with Athanasopoulos and Caffarelli on the regularity of viscosity solutions and of their free boundaries for a rather general class of parabolic phase transition problems. This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface $P \in {\Bbb R}^3$ to samples of such a field taken at scattered sites on P. STUDIES ON NOVEL NON-IMIDAZOLE HUMAN H4 RECEPTOR ANTAGONISTS USING GFA AND FREE-WILSON ANALYSIS Herein we describe 3D QSAR studies of non-imidazole Indolylpiperazines using GFA and Free Wilson Analysis. The same set of molecules was analyzed using the Free-Wilson analysis and a good correlation was obtained [r2 = 0.988]. Compounds 3-8 were also synthesized in good yields using microwave-mediated synthesis under solvent free conditions.

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2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社