Low-field one-dimensional and direction-dependent relaxation imaging of bovine articular cartilage

The structure of articular cartilage is separated into three layers of differently oriented collagen fibers, which is accompanied by a gradient of increasing glycosaminoglycan (GAG) and decreasing water concentration from the top layer towards the bone interface. The combined effect of these structural variations results in a change of the longitudinal and transverse relaxation times as a function of the distance from the cartilage surface. In this paper, this dependence is investigated at a magnetic field strength of 0.27 T with a one-dimensional depth resolution of 50 μm on bovine hip and stifle joint articular cartilage. By employing this method, advantage is taken of the increasing contrast of the longitudinal relaxation rate found at lower magnetic field strengths. Furthermore, evidence for an orientational dependence of relaxation times with respect to an axis normal to the surface plane is given, an observation that has recently been reported using high-field MRI and that was explained by preferential orientations of collagen bundles in each of the three cartilage zones. In order to quantify the extent of a further contrast mechanism and to estimate spatially dependent glycosaminoglycan concentrations, the data are supplemented by proton relaxation times that were acquired in bovine articular cartilage that was soaked in a 0.8 mM aqueous Gd++ solution.     

Characterization of Siegel cusp forms by the growth of their Fourier coefficients

We characterize all Siegel cusp forms of degree $n$ and large weight $k$ by the growth of their Fourier coefficients. More precisely we prove, among other related results, that if the Fourier coefficients of a modular form on the congruence subgroup $\Gamma _0^n(N)$ of square–free level $N$ satisfy the “Hecke bound” at the cusp $\infty $ , then it must be a cusp form, provided $k >2n+1$ .     

Kondensation von Naphtalaldehydsäure mit Methyl-m-tolylketon,Pinakolin und Acenaphtenon

Ohne ZusammenfassungIch schließe, indem ich meinem hochverehrten Lehrer, Herrn Prof. G. Goldschmiedt, für die liebenswürdige Hilfe, die er mir bei der Vollendung dieser Arbeit in Rat und Tat angedeihen ließ, den herzlichsten Dank ausspreche.     

Stereoselective Formation of Triphenylene Ketals

The oxidative trimerization of catechol ketals by MoCl₅ or MoCl₅/TiCl₄ mixtures leads preferentially to the all‐syn stereoisomer of the corresponding triphenylene ketal. The concomitant metal salts of the oxidative coupling most probably form a multinuclear template that directs the diastereoselectivity in a subsequent isomerization step under electrophilic conditions. Several functionalities can serve as coordination sites for the multinuclear metal chloro clusters. Suitable functional groups have to be stable towards the strong electrophilic and oxidizing conditions. Therefore, esters, nitriles, nitro derivatives, triazoles, and pyridines are successfully employed. Based on the flexibility and size of the substrate, different reagent mixtures lead to the stereoselective formation of the all‐syn derivatives.     

Verified bounds for singular values,in particular for the spectral norm of a matrix and its inverse

The singular value decomposition and spectral norm of a matrix are ubiquitous in numerical analysis. They are extensively used in proofs, but usually it is not necessary to compute them. However, there are some important applications in the realm of verified error bounds for the solution of ordinary and partial differential equations where reasonably tight error bounds for the spectral norm of a matrix are mandatory. We present various approaches to this together with some auxiliary useful estimates.     

Surface modification of epoxy‐functionalized acrylate colloids

A synthetic route towards surface modified, monodisperse, spherical particles is presented. The precursor particles exhibit epoxy‐functionalities which can be opened afterwards with an appropriate nucleophile. Via this route, dye labeled particles are obtained. Copyright © 2004 John Wiley & Sons, Ltd.