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The purpose of this paper is to develop an equivariant intersection theory for actions of linear algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology groups which have all the functorial properties of ordinary Chow groups. In addition, they enjoy(More)
The primary goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames(More)
A complex frame is a collection of vectors that span C and define measurements, called intensity measurements, on vectors in C . In purely mathematical terms, the problem of phase retrieval is to recover a complex vector from its intensity measurements, namely the modulus of its inner product with these frame vectors. We show that any vector is uniquely(More)
Here ĜG(X) is the completion of the equivariant Grothendieck group of coherent sheaves along the augmentation ideal of the representation ring R(G), and the groups CH iG(X) are the equivariant Chow groups defined in [EG2]. The map τ G has the same functorial properties as the nonequivariant Riemann-Roch map of [BFM] and [F, Theorem 18.3]. IfG acts freely,(More)
Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group AX, natural with respect to pullbacks. These classes are analogous to topological characteristic classes(More)
The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete varieties. In addition, our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes(More)
AIMS To determine prevalence and incidence estimates for clinically recognized cases of Type 1 diabetes from the Life For a Child Program (LFAC) with onset < 26 years in six representative districts, and the capital, of Rwanda. METHODS Cases were identified from the LFAC registry and visits to district hospitals. Denominators were calculated from(More)