Symplectic Implosion

Let K be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian K-manifold a stratified space called the imploded cross-section. It bears a resemblance to symplectic reduction, but instead of quotienting by the entire group, it cuts the symmetries down to a maximal torus of K. We examine the nature of the singularities and describe in detail the imploded cross-section of the cotangent bundle of K, which turns out to be identical to an affine variety studied by Gelfand, Popov, Vinberg, and others. Finally we show that "quantization commutes with implosion".     

Hans Duistermaat’s contributions to Poisson geometry

Hans Duistermaat was scheduled to lecture in the 2010 School on Poisson Geometry at IMPA, but passed away suddenly. This is a record of a talk I gave at the 2010 Conference on Poisson Geometry (the week after the School) to share some of my memories of him and to give a brief assessment of his impact on the subject.     

Konzept eines rechnerkontrollierten und rechnergesteuerten analytischen Labors

Ohne Zusammenfassung

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Design of a computer-controlled laboratory in analytical chemistry

     

In vivo1H-magnetic resonance spectroscopy can detect metabolic changes in APP/PS1 mice after donepezil treatment

Background  

Donepezil improves cognitive functions in AD patients. Effects on the brain metabolites N-acetyl-L-aspartate, choline and myo-inositol levels have been reported in clinical studies using this drug. The APP/PS1 mouse coexpresses the mutated forms of human β-amyloid precursor protein (APP) and mutated human presenilin 1 (PS1). Consequently, the APP/PS1 mouse model reflects important features of the neurochemical profile in humans. In vivo magnetic resonance spectroscopy (¹H-MRS) was performed in fronto-parietal cortex and hippocampus (ctx/hipp) and in striatum (str). Metabolites were quantified using the LCModel and the final analysis was done using multivariate data analysis. The aim of this study was to investigate if multivariate data analysis could detect changes in the pattern of the metabolic profile after donepezil treatment.     

Moment maps and Riemannian symmetric pairs

We study Hamiltonian actions of a compact Lie group on a symplectic manifold in the presence of an involution on the group and an antisymplectic involution on the manifold. The fixed-point set of the involution on the manifold is a Lagrangian submanifold. We investigate its image under the moment map and conclude that the intersection with the Weyl chamber is an easily described subpolytope of the Kirwan polytope. Of special interest is the integral K?hler case, where much stronger results hold. In particular, we obtain convexity theorems for closures of orbits of the noncompact dual group (in the sense of the theory of symmetric pairs). In the abelian case these results were obtained earlier by Duistermaat. We derive explicit inequalities for polytopes associated with real flag varieties. Received: 8 February 1999 / in revised form: 25 October 1999 / Published online: 8 May 2000     

Auswertung digitaler Titrationskurven nach dem Tubbs-Verfahren

Zusammenfassung Das im Jahre 1954 von Tubbs für die graphische Auswertung registrierter Titrationskurven mit potentiometrischer Indikation beschriebene Verfahren läßt sich auch für digitale Titrationen anwenden. Durch Hyperbel-Approximation und Festlegung der Krümmungskreise in den Scheiteln der beiden eingeschriebenen Hyperbeln ergeben sich die gesuchten Mittelpunkte der kleinsten Krümmungskreise. Der Schnittpunkt der Verbindungsgeraden mit der approximierten Titrationskurve ergibt den Endpunkt. Das Verfahren wird vor allem an stärker unsymmetrischen Redox-Titrationen sowie an Simultantitrationen diskutiert und untersucht.

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Evaluation of digital potentiometric titrations by the tubbs method

Summary In 1954 Tubbs described a graphic method for locating the endpoint in recorded potentiometric titrations. Approximation of digital titration curves by hyperbolas and taking the curvature in the apex of each hyperbola leads to the centres of the smallest circles to be inscribed in the branches of the titration curve. The intersection of the straight line between these two points with the approximated titration curve gives the endpoint. This method is explained and discussed with non-symmetric redox titration curves and simultaneous titrations.

     

Rechnergesteuertes, selbstcalibrierendes Messen mit ionensensitiven Elektroden

Ohne Zusammenfassung

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Computer-controlled autocalibration and measurement using ion-sensitive electrodes

     

Introduction to Terahertz Raman spectroscopy

This work, intended for advanced undergraduate students, explains the basic concepts and an actual scientific use of Terahertz Raman spectroscopy, displaying some of the benefits of this versatile technique for structural analysis of molecules building up materials since this technique has been increasingly used for molecular characterization in chemistry. A good didactic example of the experimentally applied temperature dependence of molecular vibrations according to the Boltzmann distribution is the ratio of anti-Stokes to Stokes Raman peak intensity used to calculate the temperature of a nylon 6,6 sample. The comparison of the temperature of nylon 6,6 calculated from the experimentally determined anti-Stokes to Stokes peak intensity ratio in the Terahertz region with the temperature set with the help of a heating-freezing stage is discussed. The limitations of Terahertz Raman spectroscopy are also part of this fundamental discussion.     

Selective hydroformylation-hydrogenation tandem reaction of isoprene to 3-methylpentanal

The hydroformylation of isoprene catalysed by rhodium phosphine complexes usually yields a broad mixture of the monoaldehydes, the isomeric methylpentenals, as well as the dialdehyde 3-methyl-1,6-hexandial. Under usual reaction conditions the products of a consecutive hydrogenation are only formed as minor by-products. Surprisingly we discovered now a selective auto-tandem reaction consisting of a hydroformylation and a hydrogenation step if a rhodium complex with the chelate ligand bis(diphenylphosphino)ethane is used as catalyst. If branched aromatic solvents like cumene are applied the conversion of isoprene is nearly quantitatively and the yield of the tandem product 3-methylpentanal amounts to 85%.