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.     

Global regularity for vortex patches

We present a proof of Chemin's [4] result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth.Partially supported by a National Science Foundation Postdoctoral FellowshipPartially supported by the National Science Foundation     

Scaling Exponents for Active Scalars

We provide bounds for Dirichlet quotients and for generalized structure functions for 3D active scalars and Navier–Stokes equations. These bounds put constraints on the possible extent of anomalous scaling.     

Scattering for Schrödinger operators in a class of domains with non-compact boundaries

Schrödinger operators in a class of domains with asymptotic cones are considered. A generalized Fourier transform representing the absolutely continuous part of the Schrödinger operator as multiplication by $\text{¦ξ¦}{}^2$ in the asymptotic cone is constructed. Wave operators relating the free Laplacian to Schrödinger operators are computed using the generalized Fourier transform. The wave operators relating Schrödinger operators acting in domains with the same asymptotic cone are computed and shown to be complete.     

SPECTROFLUOROMETRIC DETERMINATION OF Mg-PROTOPORPHYRIN MONOESTER AND LONGER WAVELENGTH METALLOPORPHYRINS IN THE PRESENCE OF Zn-PROTOPORPHYRIN*

Abstract. Greening tissues accumulate Mg-protoporphyrin monoester and a group of metalloporphyrins that exhibit fluorescence emission and excitation properties which are red-shifted with respect to Mg-protoporphyrin monoester. These metalloporphyrins are collectively termed longer wavelength metalloporphyrins and are presumed to be metabolic intermediates between Mg-protoporphyrin monoester (MPE) and protochlorophyllide. The longer wavelength metalloporphyrins, together with Mg-protoporphyrin monoester, are referred to as the MPE-equivalent. During the study of the biosynthesis of the components of the MPE-equivalent and the study of their conversion to protochlorophyllide in vitro, it was observed that Zn-protoporphyrin and its monoester were also formed. The latter compounds interfered with the determination of the MPE-equivalent. Simultaneous equations were derived and solved to yield an equation which permitted the determination of the amount of MPE-equivalent in the presence of Zn-protoporphyrins from the fluorescence emission spectrum of the mixture. Such determinations were made without prior segregation of the metalloporphyrins.