A variational approach to strongly damped wave equations

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix--Haase, thus extending several known results and obtaining optimal analyticity angle.Comment: This is an extended version of an article appeared in \emph{Functional Analysis and Evolution Equations -- The G\"unter Lumer Volume}, edited by H. Amann et al., Birkh\"auser, Basel, 2008. In the latest submission to arXiv only some typos have been fixe

Perceived Sufficiency of Full-Field Digital Mammograms With and Without Irreversible Image Data Compression for Comparison with Next-Year Mammograms

Problems associated with the large file sizes of digital mammograms have impeded the integration of digital mammography with picture archiving and communications systems. Digital mammograms irreversibly compressed by the novel wavelet Access Over Network (AON) compression algorithm were compared with lossless-compressed digital mammograms in a blinded reader study to evaluate the perceived sufficiency of irreversibly compressed images for comparison with next-year mammograms. Fifteen radiologists compared the same 100 digital mammograms in three different comparison modes: lossless-compressed vs 20:1 irreversibly compressed images (mode 1), lossless-compressed vs 40:1 irreversibly compressed images (mode 2), and 20:1 irreversibly compressed images vs 40:1 irreversibly compressed images (mode 3). Compression levels were randomly assigned between monitors. For each mode, the less compressed of the two images was correctly identified no more frequently than would occur by chance if all images were identical in compression. Perceived sufficiency for comparison with next-year mammograms was achieved by 97.37% of the lossless-compressed images and 97.37% of the 20:1 irreversibly compressed images in mode 1, 97.67% of the lossless-compressed images and 97.67% of the 40:1 irreversibly compressed images in mode 2, and 99.33% of the 20:1 irreversibly compressed images and 99.19% of the 40:1 irreversibly compressed images in mode 3. In a random-effect analysis, the irreversibly compressed images were found to be noninferior to the lossless-compressed images. Digital mammograms irreversibly compressed by the wavelet AON compression algorithm were as frequently judged sufficient for comparison with next-year mammograms as lossless-compressed digital mammograms

Flame propagation in models of complex chemistry

Abstract. We consider models of laminar flames with Arrhenius kinetics in long thin tubes. In previous studies of a model of a one-step reaction of the form A → B, we identified certain conditions imposed on the initial temperature that guarantee a rough sense of flame propagation resulting in complete asymptotic burning of the fuel. We now extend these studies to a model of a two-step reaction of the form A → B → C, and to some models of one-step reactions with multiple species. We again identify sufficient conditions on the initial temperature that guarantee a rough sense of flame propagation and complete asymptotic burning. For these results to hold we need to add some restrictions on other parameters for technical reasons, but we show that our results nonetheless apply to a wide range of cases. 1