Eigenschaften harmonischer Reihen mit zeichenfester Summe in Räumen höherer Stufenzahl

Ohne Zusammenfassung Herrn JOHANN RADON zum sechzigsten Geburtstage     

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     

Hexafluoroacetone as a Protecting and Activating Reagent. N- and O-Glycosylation of Isoserine and Isocysteine

Starting from HFA-protected malic and thiomalic acid a series of O- and N-glycoconjugates suitable for peptide and depsipeptide modification has been synthesized.     

Über dieC-Summierbarkeit der Laplaceschen Reihe auf der Überkugel und gewisser Hermitescher Reihen

Ohne Zusammenfassung