On an inverse problem for acoustic and seismic waves

Two basic inverse problems for determining the constitutive relation in an attenuating medium from given absorption behavior of plane waves in the medium are dealt with in the frequency domain by methods of complex analysis. In particular the case of a prescribed constant internal friction function over the seismic frequencies is considered in detail.     

Kurvenintegrale und Begründung der Funktionentheorie

Ohne Zusammenfassung     

Alternative charge stabilisation and a changing reactivity of 1,3,5-triazine based starburst compounds as studied by in situ ESR/UV–vis–NIR spectroelectrochemistry

The role of the chemical structure in an alternative charge stabilisation and a changing reactivity of star-shaped compounds with a central triazine ring linked to aryl groups like thiophene, furan or ethylenedioxythiophene synthesized by a Stille cross-coupling procedure, is followed by spectroelectrochemical measurements. While cathodic reduction leads to stable anion radicals with a delocalised spin on the central triazine moiety, dimerisation and oligomerisation occurs upon anodic oxidation. The stability of the charged states in the polymer film increased substantially using an EDOT (3,4-ethylenedioxythiophene) side group. The location of the charged states on the molecules has been proved by computations. These star-shaped molecules are excellent model structures for studies of the competition of dimerisation and oligomerisation processes based on the variation of the electron and spin distribution in the molecules.     

Eigenschaften harmonischer Reihen mit zeichenfester Summe in Räumen höherer Stufenzahl

Ohne Zusammenfassung Herrn JOHANN RADON zum sechzigsten Geburtstage     

Relationships between strain,microstructure and oxide growth at the nano‐ and microscale

In the present article, the relationships between oxidation processes, surface strains and the microstructure of duplex stainless steels were investigated. Specimens were oxidized at 500 °C under secondary vacuum for 1 h to form a thin oxide film (thickness in the range of 20–50 nm). Such specimens were considered as the model system for developing novel methods of analysis in understanding the behavior of passive films. The interfacial strain field after oxidation was measured experimentally at the microscale using the point grid method. On the other hand, the chemical composition of the oxide film was determined at the submicroscopic scale by means of local scanning Auger spectroscopy (with a spot diameter of 50 nm). Local variations of the chemical composition of the oxide film were analyzed according to the specimen microstructure and the strain field. Copyright © 2008 John Wiley & Sons, Ltd.     

A new L-curve for ill-posed problems

The truncated singular value decomposition is a popular method for the solution of linear ill-posed problems. The method requires the choice of a truncation index, which affects the quality of the computed approximate solution. This paper proposes that an L-curve, which is determined by how well the given data (right-hand side) can be approximated by a linear combination of the first (few) left singular vectors (or functions), be used as an aid for determining the truncation index.     

Identification of complex,naturally occurring flavonoid glycosides in kale (Brassica oleracea var. sabellica) by high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry

Kale is a member of the Brassicaceae family and has a complex profile of flavonoid glycosides. Therefore, kale is a suitable matrix to discuss in a comprehensive study the different fragmentation patterns of flavonoid glycosides. The wide variety of glycosylation and acylation patterns determines the health‐promoting effects of these glycosides. The aim of this study is to investigate the naturally occurring flavonoids in kale. A total of 71 flavonoid glycosides of quercetin, kaempferol and isorhamnetin were identified using a high‐performance liquid chromatography diode‐array detection/electrospray ionization multi‐stage mass spectrometry (HPLC‐DAD/ESI‐MSⁿ) method. Of these 71 flavonol glycosides, 27 were non‐acylated, 30 were monoacylated and 14 were diacylated. Non‐acylated flavonol glycosides were present as mono‐, di‐, tri‐ and tetraglycosides. This is the first time that the occurrence of four different fragmentation patterns of non‐acylated flavonol triglycosides has been reported in one matrix simultaneously. In addition, 44 flavonol glycosides were acylated with p‐coumaric, caffeic, ferulic, hydroxyferulic or sinapic acid. While monoacylated glycosides existed as di‐, tri‐ and tetraglycosides, diacylated glycosides occurred as tetra‐ and pentaglycosides. To the best of our knowledge, 28 compounds in kale are reported here for the first time. These include three acylated isorhamnetin glycosides (isorhamnetin‐3‐O‐sinapoyl‐sophoroside‐7‐O‐D‐glucoside, isorhamnetin‐3‐O‐feruloyl‐sophoroside‐7‐O‐diglucoside and isorhamnetin‐3‐O‐disinapoyl‐triglucoside‐7‐O‐diglucoside) and seven non‐acylated isorhamnetin glycosides. Copyright © 2010 John Wiley & Sons, Ltd.     

On the theory of convolution equations of the third kind, II

Existence results of Part I of the paper are generalized to two types of autoconvolution equations of the third kind having free terms with nonzero values at x=0 like the well-known Bernstein-Doetsch equation for the Jacobian theta zero functions. Also uniqueness results for the linear convolution equations in Part I of the paper are extended to more general function spaces. Further, a special class of integro-differential equations with autoconvolution integral and two classes of the linear singular Abel-Volterra equations are dealt with.     

Ein Beweis des Hauptsatzes der Theorie der Matrizes

Ohne Zusammenfassung