The Angle Defect for Odd-Dimensional Simplicial Manifolds

In a 1967 paper, Banchoff stated that a certain type of polyhedral curvature, that applies to all finite polyhedra, was zero at all vertices of an odd-dimensional polyhedral manifold; one then obtains an elementary proof that odd-dimensional manifolds have zero Euler characteristic. In a previous paper, the author defined a different approach to curvature for arbitrary simplicial complexes, based upon a direct generalization of the angle defect. The generalized angle defect is not zero at the simplices of every odd-dimensional manifold. In this paper we use a sequence based upon the Bernoulli numbers to define a variant of the angle defect for finite simplicial complexes that still satisfies a Gauss-Bonnet-type theorem, but is also zero at any simplex of an odd-dimensional simplicial complex K (of dimension at least 3), such that χ(link(ηⁱ, K)) = 2 for all i-simplices ηⁱ of K, where i is an even integer such that 0 ≤ i ≤ n – 1. As a corollary, an elementary proof is given that any such simplicial complex has Euler characteristic zero.     

The crystal and molecular structure of 12,13-dibromopseurotin.

The crystal structure of 12,13-dibromopseurotin has been determined by single crystal X-ray analysis. The crystals belong to space group P2₁ with a = 16.75, b = 9.63, c = 7.42 Å, β 95.9°, Z = 2. The structure was solved by the heavy atom technique and refined to R = 0.062 with 819 significant reflexions for 299 parameters.     

Porous metal–organic alloys based on soluble coordination cages

Diverse strategies for the preparation of mixed-metal three-dimensional porous solids abound, although many of them lend themselves only moderate levels of tunability. Herein, we report the design and synthesis of surface functionalized permanently microporous coordination cages and their use in the isolation of mixed metal solids. Judicious alkoxide-based ligand functionalization was utilized to tune the solubility of starting copper(ii)-based cages and their resulting compatibility with the mixed-cage approach described here. We further prepared a family of isostructural molybdenum(ii) cages for a subset of the ligands. The preparation of mixed-metal cage solids proceeds under facile conditions where solutions of parent cages are mixed and product phases isolated. A suite of spectroscopic and characterization tools confirm the starting cages are intact in the amorphous product. Finally, we show that utilization of precise ligand functional groups can be used to prepare mixed cage solids that can be easily and cleanly separated into their constituent components through simple solvent washing or solvent extraction techniques.

Surface-functionalized porous coordination cages can be used to create homogeneous mixed-cage alloys with high levels of tunability and processability.     

An electron microscopic and enzymic study of rat liver peroxisomal nucleoid core and its association with urate oxidase

The appearance of the characteristic crystalloid core of rat liver peroxisomes is emulated by the electron microscopic (EM) appearance of highly purified urate oxidase prepared from the same tissue. The purity of the enzyme preparation was established by gel electrophoresis under various conditions and the specific enzyme activity was at least as high as any previously reported. The amino acid composition of urate oxidase was determined. As additional evidence for close association of the peroxisomal core with urate oxidase, it was demonstrated that the biphasic changes in rat liver urate oxidase activity in response to prolonged starvation were paralleled by changes in the EM appearance of peroxisomes. Under comparable conditions catalase, another peroxisomal enzyme, did not show the same changes in activity as did urate oxidase. Evidence for the possible identity of urate oxidase with the peroxisomal crystalloid of rat liver has been presented, all materials having been obtained from, and experiments performed with, the rat.     

Radiative lifetimes of ions measured with the photoelectron spectrometer

Using a modified photoelectron spectrometer the radiative lifetimes of some electronically excited diatomic and triatomic molecular ions have been determined. The method is based on measuring the time delay between the ejection of a photoelectron from a molecule and the emission of a photon from the resulting ion.     

Electrospray ionization quadrupole time-of-flight and matrix-assisted laser desorption/ionization tandem time-of-flight mass spectrometric analyses to solve micro-heterogeneity in post-translationally modified peptides from Phoneutria nigriventer (Aranea, Ctenidae) venom

Previous studies of the fractionated venom of the Brazilian armed spider Phoneutria nigriventer, obtained by gel filtration, have demonstrated the presence of a fraction PhM, a pool of small peptides (up to 2000 Da) that provoke contractions in smooth muscle of guinea pig ileum. Initial attempts to sequence these peptides were largely unsuccessful because of the low purification yield and the fact that the majority seemed to be blocked at their N-termini. In the present work, analysis of this venom fraction by mass spectrometry has revealed the existence of a highly complex mixture of peptides with molecular weights corresponding to those observed for the muscle-active peptides previously described (800-1800 Da). These peptides appear to be a family of isoforms with some particular features. The amino acid sequences of 15 isoforms have been determined by tandem mass spectrometry (MS/MS) using both electrospray ionization quadrupole time-of-flight mass spectrometry (ESI-Q/ToFMS) and matrix-assisted laser desorption/ionization tandem time-of-flight mass spectrometry (MALDI-ToF/ToFMS). These molecules contain post-translational modifications such as proteolysis and C-terminal amidation, which combine to generate additional isoforms. All the isoforms sequenced in this study possess an N-terminal pyroglutamic acid residue. A search for sequence similarities with other peptides in databanks revealed that these peptides are structurally related to the tachykinins, a family of neuro-hormone peptides. The data obtained in this study will be essential for the subsequent steps of this research, the synthesis of these peptides and pharmacological characterization of their biological activity.     

(2S,3S,4R)-2-正戊基-3,4-二叠氮基四氢噻吩的合成

以（＋）－4，10－二氧杂三环[5.2.1.O^2,6]－癸－8－烯－3－醇为原料。经8步反应，对映选择性地合成出去氧维生素H的重要中间体：（2S，3S，4R）－2－正戊基－3，4－二叠氮基四氢噻吩。为对映选择性合成手性四氢噻吩类化合物提供了新的方法。