Solvothermal Synthesis and Characterization of the New Iron Thioantimonates(III) [Fe(C6H18N4)]FeSbS4 and [Fe(C4H13N3)2]Fe2Sb4S10 Containing FeII and FeIII and Protein‐Analogous [2FeIII‐2S]2+ Clusters

The two new compounds [Fe(tren)]FeSbS₄ ( 1 ) (tren = tris(2‐aminoethyl)amine) and [Fe(dien)₂]Fe₂Sb₄S₁₀ ( 2 ) (dien = diethylendiamine) were prepared under solvothermal conditions and represent the first thioantimonates(III) with iron cations integrated into the anionic network. In both compounds Fe³⁺ is part of a [2Fe^III‐2S] cluster which is often found in ferredoxines. In addition, Fe²⁺ ions are present which are surrounded by the organic ligands. In ( 1 ) the Fe²⁺ ion is also part of the thioantimonate(III) network whereas in ( 2 ) the Fe²⁺ ion is isolated. In both compounds the primary SbS₃ units are interconnected into one‐dimensional chains. The mixed‐valent character of [Fe(tren)]FeSbS₄ was unambiguously determined with Mössbauer spectroscopy. Both compounds exhibit paramagnetic behaviour and for ( 1 ) a deviation from linearity is observed due to a strong zero‐field splitting. Both compounds decompose in one single step.     

Chloracylierung und Bromacylierung von Carbonylverbindungen: Eine in Vergessenheit geratene Carbonylreaktion. I. Präparative Anwendungsbreite

Chloroacylation and bromoacylation of carbonyl compounds: A forgotten carbonyl reaction. I. Scope of the reaction Aliphatic, α,β-unsaturated and aromatic aldehydes as well as aliphatic ketones react with acyl halides to (α-haloalkyl)esters. These bifunctional derivates contain two leaving groups of different reactivity. The scope of this scarcely of this scarcely known carbonyl reaction is discussed.     

Hausdorff-summability of power series II

Let H _x a regular Hausdorff method and P(w)=∑ a_k w^k a power series with positive radius of convergence. A theorem of Okada states that P(w) is summable (H _x ) for w in a certain starshaped region G(H _x ,P). We call G=G(H _x ,P) the exact region of summability for P if summability cannot hold for any w \( \in \bar G\) Okada's theorem is said to be sharp for H_x if G(H_x,P) is the exact region of summability for any P. Three items are treated: 1. Criteria for Okada's theorem to be sharp are given in terms of the distribution function X (t) and the Mellin transform \(D(z) = \int\limits_0^1 {t^z d\chi (t)} \) . 2. When is Okada's theorem sharp for product methods? 3. Special classes of functions P(w) are indicated such that G(H_x, P) is the exact region of summability for any H_x. We use the notations of “Hausdorff-Summability of Power Series I” referred as “I”.     

A note on the hilbertfunction of a one-dimensional Cohen-Macaulay ring

In this note we give examples of one-dimensional noetherian local integral domains with the property that the number of generators of the square of the maximal ideal is less than the embedding dimension. On the other hand we show that if \((R,m)\) is a local one-dimensional Cohen-Macaulay ring, then \((m^n )\) for all n such that μ \((m^n )\) < m(R). Here μ denotes the minimal number of generators of an ideal and m(R) the multiplicity of R. A similar statement was conjectured by D. Sally in [5], Our main result 2.1 generalizes Prop. 2.6. in [6].     

Summierbarkeit der geometrischen Reihe auf vorgeschriebenen Mengen

In this paper we are concerned with the summability of the geometric series by matrix methods. We prove the following theorem: Suppose M_o:={z:|z|<1}, M₁, M₂, is a collection of countably many Lebesgue measureable, disjoint sets. For k=1,2, let f_k be a prescribed function, analytic on . Then there exists a triangular matrix , such that the V-transform {_n(z)} of the geometric series has the following properties: {_n(z)} converges compactly to on M_o; for k=1,2, there are sets B_k, such that has Lebesgue-measure zero and _n(z)f_k(z) for zB_k; if there is a set B^*, such that B^*M^* has Lebesgue-measure zero and {_n(z)} diverges for zB^*.     

Detection of stress whitening in plastics with the help of X-ray dark field imaging

The processing of thermoplastics can induce a wide range of defects such as stress whitening, cavitation and porosity, which can adversely affect the reliability of the final products. Hence, fast and effective non-destructive detection methods for such defects are highly important for quality assurance on production lines. In this paper, X-ray dark field imaging is presented as a new non-destructive testing method that allows the visualization of stress whitening or cavitation efficiently. The performance of the method is demonstrated for the case of an injection-moulded polyvinylidene fluoride part that exhibits stress whitening. Whereas the stress whitening could not be detected by conventional X-ray imaging, it was localized by an X-ray dark field image acquired within a few minutes. Once the precise location of the stress whitening was known, it was possible to verify the result by local micro X-ray computed tomography and by a micro section image.