The preparation of thick-film glass capillary columns

A detailed method for the routine preparation of glass capillary columns is presented. The method consists of coating a glass tube with quartz powder prior to pulling the tube into a capillary. The inner surface of the capillary consists of an even distribution of quartz particles fused to the walls. This surface has been found readily deactivated by standard procedures and ideal for the preparation of thick-film glass capillary columns. The method has been thoroughly tested in two independent laboratories to ensure that the procedures described are reproducible.     

On deformed preprojective algebras

Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.     

分裂的正则Hom-Leibniz-Rinehart代数

作为Hom-Leibniz代数胚的代数类比, 本文引入Hom-Leibniz-Rinehart代数的概念. 证明了分裂的正则Hom-Leibniz-Rinehart代数$L$写成$L=U+\sum_{\gamma}I_\gamma$, 其中$U$为极大交换子代数$H$的子空间和$I_\gamma$为$L$的理想, 若$[\gamma]\neq[d]$, 满足$[I_\gamma, I_d]=0$. 随后分别发展了分裂Hom-Leibniz-Rinehart代数的根和权的连通技术.最后研究了紧致的正则Hom-Leibniz-Rinehart代数的结构.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

Spectroscopic properties of the photoproducts of pyridoxal-5′-P irradiation: Catalytic site recognition of ribonuclease A

Photoproducts of pyridoxal-5-P, i.e., 4-pyridoxic-5-P and bis-pyridoxal-5-P, have been studied by spectroscopic methods. The spectroscopic properties of bis-pyridoxal-5-P (bis-PLP) resemble those of pyridoxal-5-P (PLP) under similar experimental conditions. The coupling of methylen hydrogens to the phosphorus atom has been shown by NMR spectroscopy. The singlet in the³¹P-NMR spectra and the triplet in¹H-undecoupled experiments confirm the presence of the phosphate group in the 5 position of the structure of the vitamin. The effect of pH and solvent composition on the relative distribution of species of bis-pyridoxine-5-P (bis-PNP) has been investigated by absorption and fluorescence spectroscopy. The acid-base dissociation of the phosphate group is easily detected by emission spectroscopy. Bis-PNP and bis-PLP bind to the enzyme RNase A and they behave as competitive inhibitors with respect to the substrate cytidine-2-3-cyclic phosphate. The natural forms of vitamin B₆, pyridoxine, and pyridoxine-5-P have no effect on the catalytic activity of the protein. Experimental evidence derived from fluorescence and inhibition experiments is consistent with the hypothesis that bis-PNP recognizes the catalytic site of RNase A.     

Distinguished extensions of a lattice-ordered group

Any lattice-ordered group (l-group for short) is essentially extended by its lexicographic product with a totally ordered group. That is, anl-homomorphism (i.e., a group and lattice homomorphism) on the extension which is injective on thel-group must be injective on the extension as well. Thus nol-group has a maximal essential extension in the categoryIGp ofl-groups withl-homomorphisms. However, anl-group is a distributive lattice, and so has a maximal essential extension in the categoryD of distributive lattices with lattice homomorphisms. Adistinguished extension of onel-group by another is one which is essential inD. We characterize such extensions, and show that everyl-groupG has a maximal distinguished extensionE(G) which is unique up to anl-isomorphism overG.E(G) contains most other known completions in whichG is order dense, and has mostl-group completeness properties as a result. Finally, we show that ifG is projectable then E(G) is the -completion of the projectable hull ofG.Presented by M. Henriksen.     

Primeness of the enveloping algebra of a Cartan type Lie superalgebra

We show that a primeness criterion for enveloping algebras of Lie superalgebras discovered by Bell is applicable to the Cartan type Lie superalgebras , even. Other algebras are considered but there are no definitive answers in these cases.

     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Effect of ‘Transannular Transmission’ in Dibenzo-18-Crown-6

The effect of the nature of the substituent in the monosubstituted derivatives of dibenzo-18-crown-6 on the reactivity and direction of the electrophilic substitution reaction of the unsubstituted benzene ring has been determined. This transfer is carried out via the macrocycle and therefore is called transannular transmission. The possible mechanism of this transmission is discussed.     

Synthesis of pyridine derivatives by reactions of α,β-unsaturated nitriles with 2-oxo-cycloalkano carbothioic acid anilides

Summary The tandem Michael addition-cyclization of 2-oxo-cycloalkane carbothioic acid anilides1–3 to benzylidenemalononitrile4 yielded spiroannulated pyridines5–7. Reaction of acrylonitrile with2 and3 gave 2,2-disubstituted Michael adducts14,15, whereas with1 led to 2,2,5-tri(2-cyanoethyl)-cyclopentanone11.

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Synthese von Pyridinderivaten durch Reaktionen von ,-ungesättigten Nitrilen mit 2-Oxo-cycloalkano-thiokohlensäure-aniliden

Zusammenfassung Die Michael Tandem-Addition-Cyclisierung von 2-Oxo-cycloalkano-thiokohlensäure-aniliden1–3 mit Benzylidenmalononitril4 ergab die spiroannelierten Pyridine5–7. Reaktion von Acrylnitril mit2 und3 ergab die 2,2-disubstituierten Michael-Addukte14,15, wohingegen mit1 2,2,5-Tri(2-cyanethyl)-cyclopentanon11 erhalten wurde.