Eine differentialtopologische Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie

The aim of this article is to compute the total (absolute) curvature, i.e. the mean value of the (absolute) Lipschitz-Killing-curvature, of an immersion f: MSⁿ of a compact manifold into the unit sphere in a differential topological manner. Through a generalization of KUIPERs treatment of immersions in Euclidean spaces it can be computed as the mean value of the number of critical points—weighted by (–1)^k (k=Index) resp.not weighted—of certain functions. These functions are the pullback via f of level-functions, which are defined almost everywhere on Sⁿ. Such a level-function is constructed by taking any oriented great circle as a leveling-scale and the orthogonal great (n–1)-spheres as level-surfaces.     

Anwendungen der differentialtopologischen Berechnung der Totalen Krümmung und Totalen Absolutkrümmung in der sphärischen Differentialgeometrie

In a previous article [16] we have shown how the total absolute (Lipschitz-Killing) curvature of the immersion f:MSⁿ of a compact manifold into a sphere can be computed in a differential topological manner as the mean-value of the number of critical points of certain level-functions. (And similar the total curvature.) (comp. [12], prob. 15) Now we consider the gradient vector field of the level-functions and achieve a relation between the total curvature and the Euler characteristic, of the manifold, which can be sharpened in some cases to inequalities. Moreover it leads to the formula of Allendoerfer-Weil for compact n-dim. submanifolds of the sphere Sⁿ.     

Hepatic Vitamin A Content Investigation Using Coherent Anti‐Stokes Raman Scattering Microscopy

Standard techniques for examining the distribution of vitamin A in liver either require staining or lead to rapid photobleaching of the molecule. A potentially better alternative approach is to use coherent anti‐Stokes Raman scattering (CARS) microscopy; a fast, label‐free, non‐disruptive imaging method that provides contrast based on molecular vibrations. This contribution evaluates the viability of CARS microscopy for imaging vitamin A within thick hepatic tissue under physiological conditions by tuning into its characteristic vibrational band in the fingerprint region. Additional information about the morphology and architecture of the tissue was acquired using second harmonic generation (SHG) and multi‐photon excited fluorescence (MPEF) to help mapping the intra‐lobular positions of the vitamin A droplets. We demonstrate the capability of our multimodal imaging framework to selectively image lipid‐soluble vitamin A droplets deep in bulk liver tissue with a high contrast while co‐registering a complementary morphological background that clearly visualizes hepatic lobules. The results obtained envisage the good prospect of the technique for in vivo studies assessing vitamin A distribution heterogeneity and how it is affected by the progression of hepatic diseases.     

Comparative Photostability Studies of BODIPY and Fluorescein Dyes by Using Fluorescence Correlation Spectroscopy

In single‐molecule applications, the photostability of fluorescent molecules is a key parameter. We apply fluorescence correlation spectroscopy to compare the photostability of four fluorescein and four borondipyrromethene (BODIPY) dyes of similar structure but different triplet yields. The latter class of dyes are more stable. In the kinetic analysis the, diffusion and photobleaching are treated as competitive processes. Corrections, which account for saturation and for experimental artefacts, are achieved solely by using experimental data. Photobleaching is found to occur mainly through the first excited singlet state S₁, in contrast to previous findings.     

A note on compact operators on matrix domains

We establish some identities or estimates for the operator norms and Hausdorff measures of noncompactness of linear operators given by infinite matrices that map the matrix domains of triangles in arbitrary BK spaces with AK, or in the spaces of all convergent or bounded sequences, into the spaces of all null, convergent or bounded sequences, or of all absolutely convergent series. Furthermore, we apply these results to the characterizations of compact operators on the matrix domains of triangles in the classical sequence spaces, and on the sequence spaces studied in [I. Djolovi?, Compact operators on the spaces and , J. Math. Anal. Appl. 318 (2) (2006) 658-666; I. Djolovi?, On the space of bounded Euler difference sequences and some classes of compact operators, Appl. Math. Comput. 182 (2) (2006) 1803-1811].     

A simple ion chromatography-mass spectrometry method for amino acid analysis in beer

The amino acid footprint of different beer samples was analyzed using ion chromatography coupled with electrospray ionization mass spectrometry. A tailor-made polymer-based cation-exchange resin was operated with a mass spectrometry-compatible eluent under isocratic conditions on a standard high-performance liquid chromatography system coupled to a single quadrupole mass spectrometer using formic acid as a volatile eluent ion source. The partially separated peaks of the isomeric pair isoleucine/leucine were processed according to their area response ratio using vertical peak splitting or Gaussian fit. Additionally, the chromatographic resolution of the isomers was optimized with an adjusted, solely aqueous mobile phase from 0.85 to 2.92. Ion suppression in the electrospray ion source was investigated for the derivatization-free method and found to be insignificant (recovery value 100 ± 15%) for 15 out of the 20 analytes. Quantitative results for various beer and mixed-beer beverages were found to be in high agreement with existing methods. Simultaneous photometric detection demonstrated the method's ability to successfully remove most of the interfering matrix compounds.     

Thermally induced gelling of oil-in-water emulsions comprising partially crystallized droplets: the impact of interfacial crystals

We produced triglyceride-in-water emulsions comprising partially crystallized droplets, stabilized by a mixture of protein and low molecular weight surfactant. The emulsions were emulsified in the melted state of the oil phase and stored at low temperature (4 degrees C) right after fabrication to induce oil crystallization. The systems were then warmed to room temperature for a short period of time and cooled again to 4 degrees C. Owing to this treatment referred to as temperature cycling or "tempering", the initially fluid emulsions turned into hard gels. We followed the bulk rheological properties of the materials during and after tempering. The storage modulus, G', exhibited a dramatic increase when tempering was applied. We showed that the systems evolved following two distinct regimes that depend on the average droplet size and on the surfactant-to-protein molar ratio. Gelling may involve partial coalescence of the droplets, i.e., film rupturing with no further shape relaxation because of the solid nature of the droplets. Alternatively, gelling may occur without film rupturing, and is reminiscent of a jamming transition induced by surface roughness. We discussed the origin of these two mechanisms in terms of the properties (size and protuberance) of the interfacial oil crystals.     

Electronically excited states of water clusters of 7-azaindole: structures, relative energies, and electronic nature of the excited states

The geometries of 1H-7-azaindole and the 1H-7-azaindole(H(2)O)(1-2) complexes and the respective 7H tautomers in their ground and two lowest electronically excited pi-pi(*) singlet states have been optimized by using the second-order approximated coupled cluster model within the resolution-of-the-identity approximation. Based on these optimized structures, adiabatic excitation spectra were computed by using the combined density functional theory/multireference configuration interaction method. Special attention was paid to comparison of the orientation of transition dipole moments and excited state permanent dipole moments, which can be determined accurately with rotationally resolved electronic Stark spectroscopy. The electronic nature of the lowest excited state is shown to change from L(b) to L(a) upon water complexation.