Towards a Certified Version of the Encyclopedia of Triangle Centers

Triangle centers such as the center of gravity, the circumcenter, the orthocenter are well studied by geometers. Recently, under the guidance of Clark Kimberling, an electronic encyclopedia of triangle centers (ETC) has been developed, it contains more than 7000 centers and many properties of these points. In this paper, we describe how we created a certified version of ETC such that some of the properties described come along with a computer checked proof of its validity.     

Surface reduction of freely floating smectic bubbles

Elongated freely floating smectic bubbles are observed during their relaxation to equilibrium sphere shape. Unlike soap bubbles that perform weakly damped oscillations into equilibrium, this relaxation is overdamped in smectics by internal structure reorganisation processes. The bubble area reduction of centimetre-sized freely floating bubbles with few nanometres film thickness is recorded with high-speed optical imaging in microgravity and analysed quantitatively. We find a nearly linear reduction of the film area with time, driven by capillary forces and inhibited by smectic layer reorganisations. Characteristic times are in the milliseconds range, with little correlation to the film thickness and bubble size. Instead, the homogeneity of the films and the number and sizes of islands of excess layers that spontaneously form on the films appear to have crucial influence on the dynamics. The efficiency of this process sets the time scale of the film area shrinkage. We discuss the limitations of a minimalistic model that captures smectic layer reorganisation processes.     

Splitting kernels into small summands

Let λ be a regular cardinal. An epimorphism between abelian groups is λ -pure if it is projective with respect to abelian groups of size less than λ. We show that cotorsion groups A have λ-pure projective dimension greater than 1 for all uncountable λ ≤ |A/tA|, where tA denotes the torsion subgroup of A. For λ > |A/tA|, cotorsion groups A are λ-pure projective.     

Hexa-Coordinated Silicon Complexes Derived from Regioisomeric Aminotriphenylethanols and Their use as Dopants for Liquid Crystals

Abstract

Tridentate imine ligands that are obtained from the chiral, regioisomeric amino alcohols 2-amino-1,1,2-triphenyethanol and 2-amino-1,2,2-triphenylethanol serve for the formation of bis-chelated silicon complexes. Whereas the complex based on the former amino alcohol is obtained as a diastereomeric mixture, the complex that is derived from 2-amino-1,2,2-triphenylethanol forms in a completely diastereoselective manner, and its configuration is determined as (A,R,R), according to a crystal structure analysis. The new silicon complexes are found to be efficient dopants for the conversion of nematic liquid crystals into cholesteric phases.

GRAPHICAL ABSTRACT     

General Discussion on Thermal and Photodegradation and Stabilization

Indole-containing bifunctional monomers (diacids, dialcohols, and dialdehydes) were synthesized by using as the basic nucleus two indoles attached by a tetraethylene glycol chain. These monomers were used for the preparation of polyesters, poly-amides, and polyazomethines.     

Position-specific isotope analysis of the methyl group carbon in methylcobalamin for the investigation of biomethylation processes

In the environment, the methylation of metal(loid)s is a widespread phenomenon, which enhances both biomobility as well as mostly the toxicity of the precursory metal(loid)s. Different reaction mechanisms have been proposed for arsenic, but not really proven yet. Here, carbon isotope analysis can foster our understanding of these processes, as the extent of the isotopic fractionation allows to differentiate between different types of reaction, such as concerted (S_N2) or stepwise nucleophilic substitution (S_N1) as well as to determine the origin of the methyl group. However, for the determination of the kinetic isotope effect the initial isotopic value of the transferred methyl group has to be determined. To that end, we used hydroiodic acid for abstraction of the methyl group from methylcobalamin (CH₃Cob) or S-adenosyl methionine (SAM) and subsequent analysis of the formed methyl iodide by gas chromatography (GC) isotope ratio mass spectrometry (IRMS). In addition, three further independent methods have been investigated to determine the position-specific δ ¹³C value of CH₃Cob involving photolytic cleavage with different additives or thermolytic cleavage of the methyl-cobalt bonding and subsequent measurement of the formed methane by GC-IRMS. The thermolytic cleavage gave comparable results as the abstraction using HI. In contrast, photolysis led to an isotopic fractionation of about 7 to 9 ‰. Furthermore, we extended a recently developed method for the determination of carbon isotope ratios of organometal(loid)s in complex matrices using hydride generation for volatilization and matrix separation before heart-cut GC and IRMS to the analysis of the low boiling partly methylated arsenicals, which are formed in the course of arsenic methylation. Finally, we demonstrated the applicability of this methodology by investigation of carbon fractionation due to the methyl transfer from CH₃Cob to arsenic induced by glutathione.

Enantioselective Synthesis of (1R,2S) and (1S,2S) Dehydrocoronamic Acids

Thanks to the successive use of two esterases with different regioselectivities and conventional organic chemistry we have synthesized (1R,2S) and (1S,2S) dehydrocoronamic acids.     

Modern methods of identifying and determining ginsenosides

Ginsenosides are the main bioactive compounds of the Panax plant genus. Ginseng and its analogues are widely used to produce traditional medicines in China, Korea, Japan, United States, and the Russian Far East. For more than 40 years, many researchers developed methods of identifying and determining and ginsenosides in plant tissues, extracts, and commercial products. Various extraction methods were used to isolate these compounds from plant materials. The separation of ginsenosides was conducted with methods such as gas chromatography, thin-layer chromatography, and high-performance liquid chromatography (HPLC). The HPLC method was used predominantly. Spectrophotometric and fluorescent monitoring and, later, light scattering and mass-spectrometry coupled with HPLC were used to determine ginsenosides. The most recent variants of these methods are presented in this review, together with a critical evaluation of the published results.