Recovering a frame from its sheaves of algebras

Let

be a frame, α an element of

and T a finitary algebraic theory. In this paper we compare the category

of sheaves of T-algebras on

with the category Sh(α↓,T) of sheaves of T-algebras on α↓ (where α↓ is the initial segment {β|β<α}). This comparison suggests the definition of formal initial segments of the category

. For a large class of theories to be called ‘integral’ (examples of which are sets, monoids, groups, rings, modules on a integral domain, boolean algebras,hellip;) the formal initial segments of

coincide with the usual initial segments of

: this means that we are able to recover

axiomatically from

.When

is the initial frame {0, 1}, the frame of formal initial segments of

is the frame of open subsets of a compact space Spec T, called the spectrum of the theory T. When T is the theory of modules on some ring R, we recover in this way various well known notions of spectra and their corresponding sheaf-representation of the ring.     

Structure determination of [C3H3N2]+ ions,formed from monosubstituted pyrazoles C3H3N2R,by collision-induced dissociation mass spectrometry

[C₃H₃N₂]⁺ ions have been generated under electron impact conditions from some monosubstituted pyrazoles C₃H₃N₂R. Collision-induced dissociation (CID) mass spectra of deuterium-labelled precursors suggest that the majority of the [C₃H₃N₂]⁺ ions formed from 1-nitro- and 4-bromo-pyrazole retain their cyclic structure, whereas the ions from 3(5)-bromopyrazole are mainly linear. This is confirmed by the relative values observed for the overall cross-sections for CID and for ion loss. An isotope effect of the order of 1.5–1.9 has been found for the collision-induced loss of H^˙ from [C₃H₃N₂]⁺, generated from 3(5)- and 4-bromopyrazole.     

Two-photon induced fluorescence and resonance-enhanced ionization of sulfur atoms

Two-photon induced fluorescence and resonance-enhanced photoionization have been observed in atomic sulfur originating from both the ³P_2,1,0 and the ¹D₂ states. Sulfur atoms are generated by the sequential multiphoton dissociation of CS₂ at probing wavelengths. The two-photon absorption process involves the 3 ³P_2,1,0 → 4 ³P_2,0,1 or the 3 ¹D₂ → 4 ¹F₃ transitions with resolution of the individual J″ → J′ transitions in most cases. Intensities of the 3³P_J″ → 4 ³P_J′ transitions have been compared with Hartree-Fock calculated transition probabilities from the analogous transitions in atomic oxygen. Photoionization is observed in a three-photon (two to resonance) ionization originating from the ³P_2,1,0 and the ¹D₂ states. Induced fluorescence is observed at 167 and 180 nm which is dipole-allowed radiation from the intermediate ³S⁰₁ and ¹D⁰₂ states, respectively.     

The reaction of 4-(p-nitrobenzyl)pyridine with some electrophiles

The nucleophile 4-(p-nitrobenzyl)pyridine was allowed to react with four carcinogenic alkylating agents, chloromethyl methyl ether, bis(chloromethyl) ether, glycol sulfate and propane sultone, one carcinogenic acylating agent, N,N-dimethylcarbamyl chloride, and one noncarcinogenic electrophile, perchlorocyclobutenone. The structures of the major products formed, which are substituted pyridinium salts or 1,4-dihydropyridines, were determined.     

α-Diimines as monodentate or bridging ligands; synthesis and characterization of palladium(II) and rhodium(I) di(t-butyl)diimine complexes

Complexes of di(t-butyl)diimine with PdCl₂(PhCN)₂ and with (CO)₂RhCl dimer have been synthesized and characterized. The diimine ligand is monodentate bonded in PdCl₂(t-butyldiimine)₂, while in (t-butyldiimine)-[Rh(CO)₂Cl]₂ it bridges two Cl(CO)₂Rh units.     

Energy-dispersive x-ray fluorescence analysis for sulphur,chlorine, potassium and calcium in aerosols

Problems in the use of x-ray spectrometry for the fast multi-element analysis of environmental samples such as aerosols collected on filters arise from absorption of the fluorescence intensity in the filter and in the collected matter. A procedure is described for the determination of the elements sulphur to calcium in aerosols collected on Whatman 41 filters. Two methods are compared for deconvolution of the spectra. These are based on counting in fixed energy channels or on non-linear least-squares analysis. Corrections for absorption effects have been calculated. Calibration is done with thin film standard deposits. The accuracy of the method is better than 15%. Difficulties in ascertaining the chlorine content of the filter are discussed. The evaporation of the chlorine fraction from the filter was studied in detail.     

Activation analysis of geological material using ruthenium as a multiisotopic comparator

The isotopes⁹⁷Ru,¹⁰³Ru and¹⁰⁵Ru, produced by reactor irradiation of elemental ruthenium, were applied as triple comparators in the activation analysis of rock FU-41, a basanitoid from Fuerteventura, Canary Island. The concentrations of the following elements were determined: Sm, Sc, Fe, Co, Na, La, Hf, Eu, Th and Cr. The aim of this work was the experimental control of the error theory of the multiple comparator method as well as the experimental check of the accuracy. Presented at the 3rd Symposium on the Recent Developments in Neutron Activation Analysis, Cambridge (U.K.), 2–4 July 1973.     

Sequential injection spectrophotometric determination of phenylephrine hydrochloride in pharmaceutical preparations

A fully automated sequential injection spectrophotometric method for the determination of phenylephrine hydrochloride in pharmaceutical preparations is reported. The method is based on the condensation reaction of the analyte with 4-aminoantipyrine in the presence of potassium ferricyanide. The absorbance of the condensation product was monitored at 503 nm. A linear relationship between the relative peak height and concentration was obtained in the range 0.5-17.5 mg l⁻¹. The detection limit (as 3σ value) was 0.09 mg l⁻¹ and repeatability was 0.8 and 0.6% at 2.5 and 5 mg l⁻¹, respectively. Results obtained by this method agreed very well with those obtained by the AOAC official method.     

Oxidation of polypropylene in benzene solution

The oxidation of both amorphous and crystalline polypropylene in benzene solution was studied at 100–130°C. tert-Butyl peroxide was used as an initiator. The kinetic behavior of the amorphous and crystalline forms differs slightly; the oxidation rate of the amorphous type is slower for a given polymer and initiator concentration. The oxidation rate of solutions of the crystalline form can be simply described by the expression: R₀ = 1.87 × 10¹³ exp {?29,000/RT} [t-Bu₂O₂]^0.58[polypropylene]^0.73, mole/l.-min. Product analyses of the oxidized solutions are incomplete, but the results do show that only ～40% of the absorbed oxygen is present as hydroperoxide. Further, much of the hydroperoxide is present in low molecular weight polar fragments which are acetone-soluble. These results show that oxidized polypropylene cannot be regarded simply as “polypropylene hydroperoxide” with repeating hydroperoxide groups attached to the polymer chain in 1,3,5… (tertiary) positions.     

HPLC–MS determination of the oxidation products of the reaction between α- and β-pinene and OH radicals

Biogenic non-methane hydrocarbons such as isoprene, alpha-pinene, and beta-pinene, are emitted by forests in very large quantities. To evaluate the role of alpha- and beta-pinene and their contribution to the global production of trace gases and especially aerosol precursors, a study of the oxidation mechanism of alpha- and beta-pinene with hydroxyl radicals must be conducted.The degradation products of both monoterpenes with hydroxyl radicals were identified and quantified in a fast-flow reactor. The products were collected on a liquid-nitrogen trap coated with a 2,4-DNPH solution to which two internal standards (benzaldehyde-2,4-DNPH and tolualdehyde-2,4-DNPH) had been added. The collection method was based on the in situ conversion of aldehyde and/or ketone compounds to their 2,4-dinitrophenylhydrazone derivatives. The derivatives were analyzed by HPLC-MS using APCI(-). TIC chromatograms and mass spectral data for the various oxidation products are presented.For alpha-pinene, pinonaldehyde is the most important degradation product, with smaller amounts of acetone, formaldehyde, campholenealdehyde, and acetaldehyde. For beta-pinene, nopinone and formaldehyde are the most abundant products, of almost equal importance, whereas acetone and acetaldehyde are minor compounds.