On the Iwasawa Theory of p-Adic Lie Extensions

In this paper, the new techniques and results concerning the structure theory of modules over noncommutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions k of number fields k 'up to pseudo-isomorphism'. In particular, a close relationship is revealed between the Selmer group of Abelian varieties, the Galois group of the maximal Abelian unramified p-extension of k as well as the Galois group of the maximal Abelian p-extension unramified outside S where S is a certain finite setof places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.     

Concerning the one site resp. Two site coordination model for ketones in lis calculations

Model calculations (1) show that both coordination models for ketones (one site and two site model, resp.) are equally well suited for simulation of experimental LIS data.     

Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

     

Beiträge zur Konformationsanalyse der Aryl—Methoxy-Bindung

The lanthanide induced shifts of a series of methoxy-indanones and-indanols were recorded and interpreted in terms of hindered rotation about the aryl—methoxy bond. A planar conformation was found in all cases, the populations of the two planar positions being determined by the substituentortho to the methoxyl group. Some of the compounds are very suitable forNOE experiments; these measurements supported theLIS results. Moreover a semiempirical quantum-mechanical method [MINDO/3] was used to calculate the relative stabilities of the romaters of anisole; again the planar conformation is predicted to be the most stable one.

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Mit 5 Abbildungen

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Auszugsweise vorgetragen beim Österreichisch-Deutschen Chemikertreffen vom 26. bis 29. April 1976 in Salzburg, Österreich.     

Ein Modell zur Beschreibung der Lanthaniden-induzierten Verschiebungen bei zweizähnigen Liganden—1,3-Diole

The NMR-LIS data of the four diastereomeric 2-(hydroxyphenylmethyl)cyclohexanols1–4 are used to test two possible computational models for bidentate Eu(dpm)₃ complexes. A model taking into account the presence of two equivalent coordination centers by averaging the corresponding dipolar fields of both centers proved to be superior to the simpler one assuming only one dipolar field with a fictive coordination center at a point equidistant between the two actual coordination sites.

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Mit 3 Abbildungen     

The Use of Tikhonov Regularization in the Identification of Electrical Conductivities from Overdetermined Boundary Data

In this paper we consider the estimation of the electrical conductivity a in the partial differential equation div(a grad ? = 0 with the boundary condition ? = \(\tilde g\) from overdetermined boundary data \(a{{\partial \tilde u}\over \partial n}=\tilde h\) via Tikhonov regularization. We formulate this problem in an appropriate Hilbert space setting and prove stability and convergence of the Tikhonov regularized solutions in an appropriate set-valued sense. Conditions are given that guarantee convergence rates of Hölder type if the electrical conductivity is assumed to be smooth. Finally we consider the special important case that the parameter a is piecewise constant and may only attain a finite number of known values. This case is of special interest in applications (e.g. non-destructive testing).     

Model calculations on LIS,III. A simple force field model for Ln(III)-shift-reagent—Substrate complexes, 1. Carbinols

A force field type of calculation (FFLIS model, force field aided LIS calculation) is presented allowing to predict the lanthanide(III) positionand the relative LIS values for carbinol—Ln(III) complexes.II.:O. Hofer, Mh. Chem.110, 745 (1979).     

New Pyrrolo[1,2-a]azepine Type Alkaloids from Stemona and Stichoneuron (Stemonaceae)

Summary. Three new pyrroloazepine type alkaloids, stichoneurines A and B and 6-hydroxycroomine were isolated from the lipophilic root extracts of Stichoneuron caudatum and Stemona tuberosa collected in Thailand together with the already known croomine, tuberostemonine, and tuberostemonine A. The structures were elucidated by spectroscopic methods including H/H-COSY, HMQC, and HMBC. Information on the relative stereochemistries and conformational behaviour was obtained by analysis of the NOESY spectra. The formation of pyrroloazepine alkaloids in the genus Stichoneuron is reported for the first time and supports its affiliation to the family Stemonaceae. The occurrence of two different types of alkaloids, of the tuberostemonine and croomine series, in different geographical provenances of Stemona tuberosa is of special chemosystematic interest and may contribute to a more natural species delimitation within that complex group.     

Stereochemie von Metallocenen, 43. Mitt.: Torsionsisomere Biphenyl-tricarbonylchrom-Komplexe: Darstellung,Konformationsanalyse und Kinetik der Interkonversion

Complexation of methyl 3-nitro-2-(o-tolyl)-benzoate (2, ano-trisubstituted biphenyl) with hexacarbonyl chromium gave the isomeric Cr(CO)₃ complexes3 and4 both existing as two torsional isomersa andb, as seen by nmr. For the main product3 the preferred conformations of the two torsional isomersa andb were deduced by the lanthanide induced shift (LIS) technique. The activation energy for the interconversion process could be determined from kinetic measurements and especially from¹H-nmr coalescence temperature of the methylsignals. The barrier of 91±1.5 kJ/mol (21.7±0.3 kcal/mol) in3 reflects the interaction of theo-H-atom of the benzene ring passing the Cr(CO)₃ moiety of the benchrotrene ring during the interconversion.A partial optical resolution of3 was achieved by asymmetric reduction with a chiral lithium-aluminium hydride yielding (+)-3 with [] _D ²⁰ +30° (benzene) and the levorotatory alcohol (–)-7.

42. Mitt.:K. Schlögl undR. Schölm, Mh. Chem.109, 1227 (1978).     

X-ray structural analysis of tetrahydrofurofuran lignans

The crystal structures of two diastereomeric tetrahydrofurofuran lignans, diasesartemin (1) and episesartemin-B (2), were determined. The former one is of the classical axial-axial substitution type (the two aryl moieties of the 1,4-diaryl-tetrahydro-1H,3H-furo[3,4-c]furan in ax-ax position), the latter one belongs to the axial-equatorial type. Analysis of the X-ray results revealed that in both cases the substituents are attached in pseudo-equatorial positions due to a flip of the (slightly twisted) envelope conformation of the oxolane five-rings. In1 the oxygen atoms of the two five rings point against each other (overall boat conformation of the tetrahydrofurofuran system orendo-endo topology), in2 one ring is folded towards and the other one is folded away from the second ring (overall boat-chair conformation of the tetrahydrofurofuran system orendo-exo topology): as a consequence,all aryl substituents adopt a pseudo-equatorial position. The terms ax-ax, ax-eq, and eq-eq used throughout in the literature are therefore misleading as far as the true conformations are concerned. Analysis of the aromatic short wavelength CD couplet of1 by means of the coupled oscillator model shows that the X-ray derived geometry is compatible with the CD data in solution.

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Röntgenstrukturanalyse von Tetrahydrofurofuran-Lignanen

Zusammenfassung Es wurde die Kristallstruktur von zwei diastereomeren Tetrahydrofurofuran-Lignanen, Diasesartemin (1) und Episesartemin-B (2), bestimmt. Ersteres gehört dem klassischen axial-axial-substituierten Typ an (dabei sind die zwei Arylsubstituenten des 1,4-Diaryl-tetrahydro-1H,3H-furo[3,4-c]furans in ax-ax-Position), das zweite gehört zum axial-equatorial-Typ. Die Röntgenstrukturanalyse zeigte, daß die Aryl-Substituenten immer in pseudo-equatorialen Positionen stehen, da die Oxolan-Fünfringe eine entsprechende (leicht getwistete) Briefumschlag-Konformation einnehmen. In1 zeigen die Sauerstoffatome der beiden Ringe zueinander (insgesamt eine Boot-Konformation des Tetrahydrofurofuransystems bzw.endo-endo-Topologie), in2 ist ein Ring in Richtung zum, der andere Ring jedoch weg vom jeweils zweiten gegenüberliegenden gefaltet (insgesamt eine Boot-Sessel-Anordnung in der Tetrahydrofurofuran-Einheit bzw.endo-exo-Topologie): Eine Folge davon ist, daß alle Arylsubstituenten eine pseudo-equatoriale Position einnehmen. Die in der Literatur durchgehend verwendete Bezeichnung ax-ax, ax-eq oder eq-eq ist daher bezüglich der tatsächlichen Konformation mißverständlich. Die Analyse der kurzwelligen aromatischen CD-Banden von1 mittels des Modells der gekoppelten Oszillatoren zeigte, daß die Konformation aus der Röntgenstrukturanalyse mit den CD-Daten in Lösung in Übereinstimmung ist.