Residual reduction algorithms for nonsymmetric saddle point problems

In this paper, we introduce and analyze Uzawa algorithms for non-symmetric saddle point systems. Convergence for the algorithms is established based on new spectral results about Schur complements. A new Uzawa type algorithm with optimal relaxation parameters at each new iteration is introduced and analyzed in a general framework. Numerical results supporting the efficiency of the algorithms are presented for finite element discretization of steady state Navier-Stokes equations.     

Valence isoelectronic substitution in the B8(-) and B9(-) molecular wheels by an Al dopant atom: umbrella-like structures of AlB7(-) and AlB8(-)

The structures and the electronic properties of two aluminum-doped boron clusters, AlB(7)(-) and AlB(8)(-), were investigated using photoelectron spectroscopy and ab initio calculations. The photoelectron spectra of AlB(7)(-) and AlB(8)(-) are both broad, suggesting significant geometry changes between the ground states of the anions and the neutrals. Unbiased global minimum searches were carried out and the calculated vertical electron detachment energies were used to compare with the experimental data. We found that the Al atom does not simply replace a B atom in the parent B(8)(-) and B(9)(-) planar clusters in AlB(7)(-) and AlB(8)(-). Instead, the global minima of the two doped-clusters are of umbrella shapes, featuring an Al atom interacting ionically with a hexagonal and heptagonal pyramidal B(7) (C(6v)) and B(8) (C(7v)) fragment, respectively. These unique umbrella-type structures are understood on the basis of the special stability of the quasi-planar B(7)(3-) and planar B(8)(2-) molecular wheels derived from double aromaticity.     

Comparison of luminescence ADP production assay and radiometric scintillation proximity assay for Cdc7 kinase

Several assay technologies have been successfully adapted and used in HTS to screen for protein kinase inhibitors; however, emerging comparative analysis studies report very low hit overlap between the different technologies, which challenges the working assumption that hit identification is not dependent on the assay method of choice. To help address this issue, we performed two screens on the cancer target, Cdc7-Dbf4 heterodimeric protein kinase, using a direct assay detection method measuring [(33)P]-phosphate incorporation into the substrate and an indirect method measuring residual ADP production using luminescence. We conducted the two screens under similar conditions, where in one, we measured [(33)P]-phosphate incorporation using scintillation proximity assay (SPA), and in the other, we detected luminescence signal of the ATP-dependent luciferase after regenerating ATP from residual ADP (LUM). Surprisingly, little or no correlation were observed between the positives identified by the two methods; at a threshold of 30% inhibition, 25 positives were identified in the LUM screen whereas the SPA screen only identified two positives, Tannic acid and Gentian violet, with Tannic acid being common to both. We tested 20 out of the 25 positive compounds in secondary confirmatory study and confirmed 12 compounds including Tannic acid as Cdc7-Dbf4 kinase inhibitors. Gentian violet, which was only positive in the SPA screen, inhibited luminescence detection and categorized as a false positive. This report demonstrates the strong impact in detection format on the success of a screening campaign and the importance of carefully designed confirmatory assays to eliminate those compounds that target the detection part of the assay.     

Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations

Any classical solution of the two-dimensional incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This paper studies solutions of a family of active scalar equations in which each component u _j of the velocity field u is determined by the scalar θ through \({u_j =\mathcal{R}\Lambda^{-1}P(\Lambda) \theta}\) , where \({\mathcal{R}}\) is a Riesz transform and Λ = (?Δ)^1/2. The two-dimensional Euler vorticity equation corresponds to the special case P(Λ) = I while the SQG equation corresponds to the case P(Λ) = Λ. We develop tools to bound \({\|\nabla u||_{L^\infty}}\) for a general class of operators P and establish the global regularity for the Loglog-Euler equation for which P(Λ) = (log(I + log(I ? Δ))) ^γ with 0 ≦ γ ≦ 1. In addition, a regularity criterion for the model corresponding to P(Λ) = Λ ^β with 0 ≦ β ≦ 1 is also obtained.     

Sensitivity Analysis for a Class of H 0 1 ${{H_{0}^{1}}}$ -Elliptic Variational Inequalities of the Second Kind

Set-Valued and Variational Analysis - We study the stability of solutions to ${H_{0}^{1}}$ -elliptic variational inequalities of the second kind that contain a non-differentiable Nemytskii...     

Global solutions for quasilinear parabolic problems

Results on the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous Dirichlet or Neumann boundary conditions are presented. Besides quasilinear parabolic equations, the method is also applicable to some weakly-coupled reaction-diffusion systems and to elliptic equations with nonlinear dynamic boundary conditions. Received December 21, 2000; accepted August 30, 2001.     

On the classification of complex vector bundles of stable rank

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle. Since deceased.     

Solutions of some singular integral equation

A singular integral equation with a Holderian second member function on [a,b] is considered and solved for four different type of kernels in the class of functions that are unbounded at the end points of the interval.