Zwitterionic and anionic multinuclear pentacoordinate silicon(IV) complexes with bridging (R,R)-tartrato(4-) ligands and SiO5 skeletons: synthesis and reactivity in aqueous solution

Two nutrients in one molecule: A zwitterionic λ(5)Si,λ(5)Si'-disilicate (1) was synthesized and characterized. It contains ligands that exclusively derive from natural products ((R,R)-tartaric acid, choline). Hydrolysis of 1 yields 2, which shows a remarkable kinetic stability in water. Upon dissolution of 1 and 2 in water, the nutrients choline and orthosilicic acid are formed by hydrolysis.     

Systematic investigations of anthocyanin–metal interactions by Raman spectroscopy

The FT‐Raman spectra of the chloride salts of pelargonidin‐3‐glucoside, cyanidin‐3‐glucoside and delphinidin‐3‐glucoside, their structures at pH 5.0 and their interaction with aluminium and ferric ions are presented for the first time and discussed with regard to their spectroscopic response. Two marker bands at approximately 1510 and 1330/1350 cm⁻¹ and one band at approximately 1330/1350 cm⁻¹ were identified being characteristic for the formation of ferric and aluminium chelates, respectively, of cyanidin‐3‐glucoside and delphinidin‐3‐glucoside. In contrast, pelargonidin‐3‐glucoside, exhibiting one single hydroxyl group in the B‐ring, did not form metal chelates, which could be clearly demonstrated by missing marker bands. The formation of anthocyanin–metal chelates was also verified in model systems containing commercial sugar beet pectin and a pectic polysaccharide fraction isolated thereof, respectively. In addition, the absence of anthocyanin–metal chelates in systems prepared with citrate buffer was confirmed, and the effects of low and high methoxylated citrus pectins on chelate formation were studied. Copyright © 2012 John Wiley & Sons, Ltd.     

Variational calculus with sums of elementary tensors of fixed rank

In this article we introduce a calculus of variations for sums of elementary tensors and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the solution of a linear system in structured tensor format. Moreover, we discuss the solution of an eigenvalue problem with sums of elementary tensors. This example can be viewed as a prototype of a constrained minimization problem. For the numerical treatment, we suggest a method which has the same order of complexity as the popular alternating least square algorithm and demonstrate the rate of convergence in numerical tests.     

Investigations of the Marangoni effect on the regular structures in heated wavy liquid films

Formation and development of quasi-regular metastable structures within laminar-wavy falling films were studied. These structures emerge within the residual layer between large waves and could be one reason for the break up of the falling film. The temperature field of the film surface was visualised using IR-thermography. The film thickness was obtained from point measurements with the chromatic confocal imaging method and converted into a film thickness field, based on a quasi-steady assumption and IR thermography images. The thermo-capillary nature (Marangoni effect) of the regular structures was proven experimentally.     

Recent Progress with the SMILETRAP Penning Mass Spectrometer

The Penning trap mass spectrometer SMILETRAP has been considerably improved during the last two years. The helium pressure has been carefully stabilized and is now independent of irregular air pressure. The temperature of the hyperboloidal precision trap is stabilized to ±0.03°C. Remaining temperature instabilities are compensated by changes in the current of a warm coil surrounding the precision trap. The frequency synthesizer is now locked to GPS. This means that it is much easier to accurately measure resonances during several days. The improvements have demonstrated that in mass doublet measurements with an excitation time of 1 s it is possible to determine the mass of ions with q/A=1/2 at an uncertainty to a few times of 0.1 ppb, using selected rather than cooled ions. In routine measurements lasting for one day it is possible to reach a mass uncertainty of 1 ppb. The masses of the following particles and atoms have been measured with uncertainties in the region 0.3–2 ppb: p, ³H, ³He, ⁴He, ²²Ne, ²⁸Si, ³⁶Ar, ⁷⁶Ge, ⁷⁶Se, ⁸⁶Kr and ¹³³Cs. It has also been shown that though we are using a warm bore the trap pressure is sufficiently low to prevent electron capture from the rest gas for excitation times of 3 s and for ion charges as high as 50+. This revised version was published online in July 2006 with corrections to the Cover Date.     

Embedding Structures

 For any quasiordered set (`quoset') or topological space S, the set Sub S of all nonempty subquosets or subspaces is quasiordered by embeddability. Given any cardinal number n, denote by p _n and q _n the smallest size of spaces S such that each poset, respectively, quoset with n points is embeddable in Sub S. For finite n, we prove the inequalities n + 1 ≤p _n ≤q _n ≤p _n + l(n) + l(l(n)), where l(n) = min{k∈ℕ∣n≤2 ^k }. For the smallest size b _n of spaces S so that Sub S contains a principal filter isomorphic to the power set ?(n), we show n + l(n) − 1 ≤b _n ≤n + l(n) + l(l(n))+2. Since p _n ≤b _n , we thus improve recent results of McCluskey and McMaster who obtained p _n ≤n ². For infinite n, we obtain the equation b _n = p _n = q _n = n. Received: April 19, 1999 Final version received: February 21, 2000     

Finite Intervals in the Lattice of Topologies

We discuss the question whether every finite interval in the lattice of all topologies on some set is isomorphic to an interval in the lattice of all topologies on a finite set – or, equivalently, whether the finite intervals in lattices of topologies are, up to isomorphism, exactly the duals of finite intervals in lattices of quasiorders. The answer to this question is in the affirmative at least for finite atomistic lattices. Applying recent results about intervals in lattices of quasiorders, we see that, for example, the five-element modular but non-distributive lattice cannot be an interval in the lattice of topologies. We show that a finite lattice whose greatest element is the join of two atoms is an interval of T ₀-topologies iff it is the four-element Boolean lattice or the five-element non-modular lattice. But only the first of these two selfdual lattices is an interval of orders because order intervals are known to be dually locally distributive.