Analytic torsion versus Reidemeister torsion on hyperbolic 3-manifolds with cusps

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of \(\mathrm{SL }_2(\mathbb {C})\) to the corresponding Reidemeister torsion. While the analytic torsion is a spectral invariant of the manifold, the Reidemeister torsion is of combinatorial nature. Our proof rests on an expression of the analytic torsion in terms of special values of Ruelle zeta functions as well as on recent work of Pere Menal-Ferrer and Joan Porti.     

Exponential growth of homological torsion for towers of congruence subgroups of Bianchi groups

In this paper we prove that for suitable sequences of subgroups of Bianchi groups, including the standard exhaustive sequences of a congruence subgroup, and even symmetric powers of the standard representation of $\mathrm{SL }_2(\mathbb {C})$ the size of the torsion part in the first integral homology grows exponentially. This extends results of Bergeron and Venkatesh to a case of non-uniform lattices. Our approach is geometric. For odd symmetric powers we obtain a modified statement.     

Fluorescent Vesicles Consisting of Galactose‐based Amphiphilic Copolymers with a π‐Conjugated Sequence Self‐assembled in Water

Fluorescent vesicles considered as a mimic of natural primitive cells are prepared from poly(3‐hexylthiophene)‐block‐poly(3‐O‐methacryloyl‐D‐galactopyranose) P3HT‐b‐PMAGP copolymers. The unique characteristic of such vesicular nanostructures is their architecture, which comprises a hydrophobic π‐conjugated P3HT wall stabilized by a hydrophilic PMAGP interface featuring glucose units. The results of this work offer a very efficient and straightforward method for engineering well‐controlled fluorescent nanoparticles (without the addition of dyes), which provide an excellent support to the study of carbohydrate‐protein interactions.

     

Acid-Catalyzed Transacetalization from Glycol to Pinacol Acetals

A one-pot transacetalization of glycol acetals, frequently used as protecting groups of the aldehyde function, into the more stable pinacol acetals is given. A clean transformation of aromatic and aliphatic substrates is possible with trifluoroacetic acid within 30 min at 0 °C. Glycol acetals derived from ketones (ketals) cannot be converted with this protocol. Deprotection of the pinacol acetals is possible with trifluoromethanesulfonic acid in the presence of water.     

Gas chromatographic determination of diethylcarbamazine (Hetrazan) in serum of laboratory rodents (author's transl)

After chloroform extraction in an alkaline solution, diethylcarbamazine (DEC) is measured in the presence of dipropylacetamid (internal standard), treated in the same manner, by a gas chromatographic procedure using a nitrogen detector in a 10% BDS column. Results can be easily reproduced for analysis of DEC in sera up to levels of 10 mg/1 and sensibility allows determination of approximately 0.5 mg/l levels on 50-microliter samples of serum. This method is suitable for pharmacokinetic studies.     

Glycopolymer-grafted polystyrene nanospheres

The synthesis and characterization of spherical sugar-containing polymer brushes consisting of PS cores onto which chains of sugar-containing polymers have been grafted via two different techniques are described. Photopolymerization in aqueous dispersion using the functional monomer MAGlc and crosslinked or non-crosslinked PS particles covered with a thin layer of photo-initiator yielded homogeneous glycopolymer brushes attached to spherical PS cores. As an alternative, ATRP was used to graft poly-(N-acetylglucosamine) arms from crosslinked PS cores. Deprotection of the grafted brushes led to water-soluble particles that act as carriers for catalytically active gold nanoparticles. These glycopolymer chains show a high affinity to adsorb WGA whereas no binding to BSA or PNA could be detected.     

Colocalization of connexin 36 and corticotropin-releasing hormone in the mouse brain

Background  

Gap junction proteins, connexins, are expressed in most endocrine and exocrine glands in the body and are at least in some glands crucial for the hormonal secretion. To what extent connexins are expressed in neurons releasing hormones or neuropeptides from or within the central nervous system is, however, unknown. Previous studies provide indirect evidence for gap junction coupling between subsets of neuropeptide-containing neurons in the paraventricular nucleus (PVN) of the hypothalamus. Here we employ double labeling and retrograde tracing methods to investigate to what extent neuroendocrine and neuropeptide-containing neurons of the hypothalamus and brainstem express the neuronal gap junction protein connexin 36.