Beiträge zur Chemie der Pyrrolpigmente, 38. Mitt.: Zur Assoziation von Gallenpigmenten

The long standing problem of solvent dependent absorption spectra of certain bile pigments such as bilirubindimethylester has been solved by measurement of molecular masses by means of vapour pressure osmometry. Using this method and the investigation of the concentration and temperature dependence of the absorption spectra on several model compounds an association equilibrium for pigments of the rubinoid structural type could be confirmed. Moreover the optical properties of the coexisting species and the corresponding equilibrium constants could be deduced by spectroscopic techniques. Verdinoid pigments lacking free carboxylic functions on the other hand tend to be monomeric in solution. A heteroassociated species involving equimolar amounts of a verdinoid and a rubinoid pigment could be verified existing on adsorbents like silicagel.

37. Mitt.:Falk, H., Thirring, K., Tetrahedron, im Druck.     

Synthesen von Heterocyclen, 135. Mitt.: Chinolizine und Indolizine,VI: eine Synthese von 2-Hydroxy-benzo[a] chinolizin-4-onen

Zusammenfassung 2-Hydroxy-6,7-dihydro-4H-benzo[a]chinolizin-4-one (3a—p) werden durch Kondensation von 1-Alkyl-3,4-dihydro-isochinolinen (1a—g) mit Malonsäure-bis-2,4,6-trichlorphenylestern (2a—e) erhalten. Die Ausbeuten sowie die erforderlichen Reaktionszeiten und Temperaturen sind stark von der Art der Substituenten abhängig.

---

Syntheses of heterocycles, CXXXV: Quinolizines and indolizines, VI. A synthesis of 2-hydroxy-4H-benzo[a]quinolizin-4-ones

The condensation of 1-alkyl-3.4-dihydro-isoquinolines (1a tog) with 2.4.6-trichlorophenyl malonates (2a—e) yields 2-hydroxy-6,7-dihydro-4H-benzo[a]quinolizin-4-ones (3a—p). Yields, required reaction-periods and temperatures are depending on the nature of the substituents present in the malonyl and isoquinoline residue.

     

Forced lattice vibrations: Part I

This is the First part of a two-part series on forced lattice vibrations in which a semi-infinite lattice of one-dimensional particles {x_n}_n≧1 is driven from one end by a particle x₀. This particle undergoes a given, periodically perturbed, uniform motion, _x0(_t) = _at + _h(_yt), where a and γ are constants and h(·) has period 2π. For a wide variety of restoring forces F (i.e., F′ > 0), numerical calculations indicate the existence of a sequence of thresholds γ₁ = γ₁(a, h, F) > γ₂ = γ₂(a,h,F) > … > γ_k = γ_k(a,h,F) > …, γ_k → 0, as k → ∞. If γ_k > γ > γ_k+1, a k-phase wave that is well described by the wave form, emerges and travels through the lattice. The goal of this series is to describe the emergence and calculate some properties of these wave forms. In Part I the authors first consider the case where F(x) = e^x (i.e., Toda forces) but h is arbitrary, and show how to compute a basic diagnostic (see J(λ), formula (1.26)) for the system in terms of the solution of an associated scalar Riemann-Hilbert problem, once a certain finite set of numbers is known. In another direction, the authors consider the case where F(x) is restoring but arbitrary, and h is small. Here the authors prove a general result, asserting that if there exists a sufficiently ample family of traveling-wave solutions of the doubly infinite lattice, then it is possible to construct time-periodic k-phase wave solutions with asymptotics in n of type (iii) for the driven system (i). In Part II, the authors prove that sufficiently ample families of traveling-wave solutions of the system (iv) exist in the cases γ > γ₁ and γ₁ > γ > γ₂ for general restoring forces F. In the case with Toda forces, F(x) = e^x, the authors prove that sufficiently ample families of traveling-wave solutions.     

Über lineare Unabhängigkeit

It is the aim of the present work to prove, under appropriate conditions, lower estimates for the dimension of w ₁ + ... + w _m over , wherew ₁,...,w _m are given real numbers. In particular, if this dimension ism, i.e. ifw ₁,...,w _m are linearly independent over , we are also interested in a quantitative version of this fact. Our qualitative theorems generalize a result of Nesterenko. Its formulation is quite similar to the axiomatization of methods for algebraic independence, as it became usual during the last decade.

     

Mössbauer studies on the series La1-xSrxFeO3

Mössbauer spectra have been recorded at 4.2 and 300 K on the series La_1–x Sr _x FeO₃, wherex varies from 0 to 1.0 in steps of 0.1. Neutron diffraction experiments have shown that the crystal structure is orthorhombic for 0x<0.3, rhombohedral for 0.4x0.7, and cubic for 0.8<x1.0. Mössbauer spectra at 4.2 K are composed of magnetic sextet components arising from different charge states of iron ions. In the orthorhombic and rhombohedral phases, the charge states Fe³⁺ and Fe⁵⁺ coexist. In the cubic phase, iron is present as Fe³⁺ and Fe⁴⁺ states. At 300 K, the samples are magnetically ordered in the range 0 x0.3 and the coexistence of Fe³⁺ and Fe⁵⁺ remains. For samples 0.4x1.0, the samples are paramagnetic. Fits to these spectra require two components, one corresponding to an Fe⁴⁺ state, the other being best described as an Fe³⁺ ion forx0.7 but forx>0.7 having a mean charge state which increases to 3.5 forx=1.0.     

Enlarged scaling ranges for the KS-entropy and the information dimension

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data. (c) 1996 American Institute of Physics.