Hyperkähler Analogues of Kähler Quotients by Nicholas James Proudfoot Doctor of Philosophy in Mathematics University of California, Berkeley Professor Allen Knutson, Chair Let X be a Kähler manifold that is presented as a Kähler quotient of Cn by the linear action of a compact group G. We define the hyperkähler analogue M of X as a hyperkähler quotient of the cotangent bundle T ∗Cn by the induc...

In this paper we initiate a new approach consisting to characterize the commutativity of quotient ring $R/P$ by endomorphisms $R$ satisfying some algebraic identities involving prime ideal $P.$ Some well-known results concerning (semi-prime) rings have been improved.

For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Arm...

We investigate the Cox ring of a normal complete variety X with algebraic torus action. A first result relates the Cox ring of X to that of a maximal geometric quotient of X. As a consequence, we obtain a complete description of the Cox ring in terms of generators and relations for varieties with torus action of complexity one. Applied to smooth K-surfaces, this gives a description of the Cox r...

Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...

1. Sweetman S. C., Eds, In; Martindale ‘The complete drug reference, 33rd Edn., The Pharmaceutical Press, London, 2002, 209. 2. Perry, C.M., Barman Balfour, J.A. and Lamb, H.M., Drugs., 1999, 58, 683. 3. Lawrence M. T., Stephen J. .M., Maxine A.P., Current Medical Diagnosis and Treatment., 42nd Edn., The McGraw Hill Companies, Inc. India, 2003, 1525. TABLE 1: RESULTS OF ANALYSIS AND RECOVERY ST...