Richness of isomerism in labile octahedral Werner-type cobalt(II) complexes demonstrated by 19F NMR spectroscopy: structure and stability

The cobalt(II) complexes [CoL2(R2-Py)2] (1-4) where HLA = 1,1,1-trifluoro-5,5-dimethyl-2,4-hexanedione, R2-Py = 4-methylpyridine (1), HLB = 4,4,4-trifluoro-1-(2-thienyl)-1,3-butanedione, R2-Py = 4-methylpyridine (2), 4-phenylpyridine (3) and S-(-)-1-(4-pyridyl)ethanol (4) were prepared by two-step reactions. X-ray structure analysis of [CoLA2(CH3-Py)2] revealed the {trans(N)-trans(CF3)-trans} configuration for the complex obtained by crystallization from ethanol. A dynamic equilibrium between the five possible stereoisomers was observed for each complex 1-4 in solution by 19F NMR spectroscopy. The criteria used for full NMR assignment (180-265 K) include comparison of integral ratios, cis(N) and trans(N) differentiation in presence of the chiral amine [S-(-)-1-(4-pyridyl)ethanol], effect of solvent polarity on the relative stabilities of the five isomers and observation of trans influences in a mixture of complexes. Thermodynamic parameters for the equilibria between the isomers of 2 in CD2Cl2 (DeltaHi,j, DeltaSi,j and Ki,j) were obtained from signal integrals. The two trans(N) isomers are slightly more stable than the three cis(N) isomers at low temperature [DeltaGdegreesi,j (max) = 2.8 kJ mol(-1) at 179.8 K], but this stability difference almost vanishes with increasing temperature [DeltaGdegreesi,j (max) = 1.0 kJ mol(-1) at 265.0 K]. The values found for DeltaHdegreesi,j are relatively small and largely entropy compensated.     

Far-infrared absorption by collisionally interacting nitrogen and methane molecules

Quantum line shape calculations of the rototranslational enhancement spectra of nitrogen-methane gaseous mixtures are reported. The calculations are based on a recent theoretical dipole function for interacting N(2) and CH(4) molecules, which accounts for the long-range induction mechanisms: multipolar inductions and dispersion force-induced dipoles. Multipolar induction alone was often found to approximate the actual dipole surfaces of pairs of interacting linear molecules reasonably well. However, in the case of the N(2)-CH(4) pair, the absorption spectra calculated with such a dipole function still show a substantial intensity defect at the high frequencies (>250 cm(-1)) when compared to existing measurements at temperatures from 126 to 297 K, much as was previously reported.     

Consequences of the Kramers-Kronig relations for light diffraction on thick gratings

Diffraction of monochromatic light on a grating leads to the attenuation of the transmitted beam of diffraction order zero. In the case of a thick grating the diffraction efficiency, and hence the effective attenuation coefficient, is a fast-varying function of the Bragg mismatch angle. According to Kramers-Kronig theory, the transmitted beam encounters a phase shift that also depends on the mismatch angle. This phase shift is measured for holographic gratings in a photoaddressable block copolymer and compared with analytical calculations.     

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     

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.