Lower bounds for blow-up time in a nonlinear parabolic problem

For a parabolic problem with a gradient nonlinearity which was introduced by Chipot and Weissler [M. Chipot, F.B. Weissler, Some blow up results for a nonlinear parabolic problem with a gradient term, SIAM J. Math. Anal. 20 (1989) 886-907] (see also [B. Kawohl, L.A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989) 207-217]), the question of blow-up is investigated. Specifically, if the solution blows up, a lower bound for the time of blow-up is derived     

X‐ray photoelectron spectroscopic chemical state quantification of mixed nickel metal,oxide and hydroxide systems

Quantitative chemical state X‐ray photoelectron spectroscopic analysis of mixed nickel metal, oxide, hydroxide and oxyhydroxide systems is challenging due to the complexity of the Ni 2p peak shapes resulting from multiplet splitting, shake‐up and plasmon loss structures. Quantification of mixed nickel chemical states and the qualitative determination of low concentrations of Ni(III) species are demonstrated via an approach based on standard spectra from quality reference samples (Ni, NiO, Ni(OH)₂, NiOOH), subtraction of these spectra, and data analysis that integrates information from the Ni 2p spectrum and the O 1s spectra. Quantification of a commercial nickel powder and a thin nickel oxide film grown at 1‐Torr O₂ and 300 °C for 20 min is demonstrated. The effect of uncertain relative sensitivity factors (e.g. Ni 2.67 ± 0.54) is discussed, as is the depth of measurement for thin film analysis based on calculated inelastic mean free paths. Copyright © 2009 John Wiley & Sons, Ltd.     

Total synthesis and antimalarial activity of symplostatin 4

The first total synthesis of symplostatin 4, a marine cyanobacterium-derived natural product, is described. Notable features of the route include the efficient preparation of three key fragments and final assembly to the natural product via sequential imide and amide couplings. Symplostatin 4 was also demonstrated to possess significant antimalarial activity (ED(50) of 74 nM against Plasmodium falciparum, strain 3D7).     

Double k-sets in symplectic generalized quadrangles

In classical projective geometry, a double six of lines consists of 12 lines ? ₁, ? ₂, . . . , ? ₆, m ₁, m ₂, . . . , m ₆ such that the ? _i are pairwise skew, the m _i are pairwise skew, and ? _i meets m _j if and only if i ≠ j. In the 1960s Hirschfeld studied this configuration in finite projective spaces PG(3, q) showing they exist for almost all values of q, with a couple of exceptions when q is too small. We will be considering double-k sets in the symplectic geometry W(q), which is constructed from PG(3, q) using an alternating bilinear form. This geometry is an example of a generalized quadrangle, which means it has the nice property that if we take any line ? and any point P not on ?, then there is exactly one line through P meeting ?. We will discuss all of this in detail, including all of the basic definitions needed to understand the problem, and give a result classifying which values of k and q allow us to construct a double k-set of lines in W(q).     

The existence of soliton metrics for nilpotent Lie groups

We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation U v = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac–Moody algebras to analyze the solution spaces for such linear systems. An application to the existence of soliton metrics on certain filiform Lie groups is given.     

Isoperimetric inequalities for polarization and virtual mass

This paper is the continuation of a previous investigation. Here representations for the components of the virtual mass and polarization tensors in terms of boundary integrals are given and new isoperimetric inequalities for star-shaped bodies are derived. Research supported by NSF Grant, MCS 8300842. Research supported by Natural Sciences and Engineering Research Council Canada.     

Some overdetermined boundary value problems for harmonic functions

Summary In this paper we study various overdetermined problems involving harmonic functions. In particular, we show that if the second eigenfunctionu ₂ of the Stekloff eigenvalue problem in a bounded simply connected plane domain has a constant value of u ₂ on , then is a disk

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Résumé Cet article est consacré à l'étude de certains problèmes surdéterminés pour des fonctions harmoniques. En particulier, nous montrons que si le gradient de la seconde fonction propre du problème de Stekloff défini dans un domaine borné, simplement connexe du plan, a son module constant sur la frontière , alors est nécessairement un disque.