Distribution of integral points on some hyperboloids of one sheet

Results of B. F. Skubenko (Izv. Akad. Nauk SSSR, Ser. Mat.,26, 721–752 (1962)) are generalized to indefinite ternary quadratic formsf(x)=f ₀(Cx), which are contained in the simplest formf ₀(x)=x ₁ x ₃–x _r ^e We prove that the integral points on the hyperboloid of one sheetf(x)=m,m<0, are uniformly distributed over area (in the sense of hyperbolic metric) and over residue classes for given modulus.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 121, pp. 83–93, 1983.     

Note sur le mécanisme réactionnel de la transposition de Dimroth. Une étude ab initio

An ab initio study of the Dimorth rerarrangement of the -amino-1,2,3,4-tetrazole leads to the conclusion teht in vapour phase the rate determining step is not the ring-chain isomerism, but is either the Z-E iomerism around the C?N double bond or the 1,3-sigmatropic shift of the proton.     

Modification of a Dionex System 12 ion chromatograph for sequential determination of the main components in atmospheric precipitation

A modification of a Dionex System 12 ion chromatograph is described which enables organic anions (acetate and formate), inorganic cations (ammonium, sodium and potassium) and inorganic anions (chloride, nitrate and sulphate) to be determined sequentially in one measuring procedure. The modified instrument consists of a programmable controller unit, a conductimetric meter, two conductimetric detectors of the Dionex System 12 ion chromatograph, the HPIC-AS4A and HPIC-CS3 modern separation units, AMMS-1 and CMMS-1 micro-membrane suppressor columns, a unique system of valves from Dionex and two dual pumps from Biotronik. The limits of detection are between about 1 and 3 micrograms/l for chloride, nitrate and sulphate and between about 2 and 10 micrograms/l for acetate, formate, ammonium, sodium and potassium. The reliability of the method was demonstrated by analysing two NBS simulated rain water Standard Reference Materials. Some examples are given of the application of the method to the sequential determination of the main precipitation components in typical samples from urban and rural regions of the F.R.G. The ion concentrations varied between about 0.02 and 300 mg/l.     

Liquid chromatography of polymer mixtures by a combination of exclusion and full adsorption mechanisms. Three- and four-component polymer blends

Summary Coupling of full adsorption-desorption and size-exclusion chromatography (FAD-SEC) has been applied to the separation and molecular characterization of three- and four-component polymer blends. The method is based on the full adsorption of alln orn−1 components of the polymer blend in a specially designed FAD minicolumn. By appropriate eluent switching the adsorbed polymers are desorbed stepwise from the FAD minicolumn into an on-line SEC column for molecular characterization. It is shown that the desorption isotherms of particular blend components give valuable information about the appropriate displacer composition. The exact position of the desorption isotherms depends, however, both on the amount of polymer adsorbed and in the presence of other, chemically different, polymers within FAD column. The nature and composition of the displacer must, therfore, be adjusted if the intervals between the desorption of particular blend components are to be large enough to prevent displacement overlap. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997.     

Evaluation of a retention model in comprehensive two-dimensional gas chromatography

Modeling the retention in comprehensive two-dimensional gas chromatography (GC x GC) was achieved using retention indices obtained in conventional GC. Predicted results were compared with experimental data obtained in the two-dimensional separation of a synthetic hydrocarbon mixture. This proved to be helpful in optimizing the operating conditions of GC x GC separation of a complex petroleum sample and in identifying chemical families.     

Autoxidation of cyclohexane: conventional views challenged by theory and experiment.

In spite of its industrial importance, the detailed reaction mechanism of cyclohexane autoxidation by O2 is still insufficiently known. Based on quantum chemical potential energy surfaces, rate coefficients of the primary and secondary chain propagation steps involving the cyclohexylperoxyl (CyOO) radical were evaluated using multiconformer transition-state theory. Including tunneling and hindered-internal-rotation effects, the rate coefficient for hydrogen-atom abstraction from cyclohexane (CyH) by CyOO was calculated to be k(T)= 1.46 x 10(-11) x exp(-17.8 kcal mol(-1)/ RT) cm3s(-1) (300-600K), close to the experimental data. A "Franck-Rabinowitch cage" reaction between the nascent cyclohexylhydroperoxide (CyOOH) and cyclohexyl radical, products from CyOO + CyH, is put forward as an initially important cyclohexanol (CyOH) formation channel. alphaH abstraction by CyOO. from cyclohexanone was calculated to be only about five times faster than that from CyH, too slow to explain all the observed side products. The a-hydrogen (alphaH) abstractions from CyOH and CyOOH by CyOO. are predicted to be about 10 and 40 times faster, respectively, than the CyOO. +CyH reaction. The very fast CyOO.+CyOOH reaction proceeds through the unstable Cy-alphaH .OOH radical that decomposes spontaneously into the ketone (Q=O) plus the OH radical; the "hot" .OH is found to produce the bulk of the alcohol via a second, "activated cage" reaction analogous to that above. It is thus shown how the very reactive CyOOH intermediate is the predominant source of ketone and alcohol, while it also leads to some side products. The alpha-hydroxycyclohexylperoxyl radical formed during the moderately fast oxidation of CyOH is shown to decompose fast into HO2 + cyclohexanone in a rapidly equilibrated reaction, which constitutes a smaller, second ketone source. These two fast cyclohexanone forming routes avoid the need for unfavorable molecular routes hitherto invoked as ketone sources. The theoretical predictions are supported and complemented by experimental findings. The newly proposed scheme is also largely applicable to the oxidation of other hydrocarbons, such as toluene, xylene, and ethylbenzene.     

A novel reactivity of SeO(2) with 1,3-dienes: formation of syn 1,2- and 1,4-diols via a facile C-Se bond oxidation

[reaction: see text] A novel reaction between 1,3-dienes and selenium dioxide to give syn 1,2- and 1,4-diol cyclic selenites was studied in detail. This study indicates that an initial concerted [4 + 2] cycloaddition followed by a stereospecific carbon-selenium bond oxidation is involved in this unprecedented syn dihydroxy addition reaction mediated by selenium dioxide.     

Solid-phase extraction of fluoxetine and norfluoxetine from serum with gas chromatography-electron-capture detection

A rapid, selective, and sensitive method is described for the purification and analysis of fluoxetine and norfluoxetine using a solid-phase extraction column and gas chromatography-electron-capture detection. Linear quantitative response curves for fluoxetine and norfluoxetine are generated over a concentration range of 20-200 ng/ml. Overall extraction efficiency of the extraction procedure is found to be greater than 90% and greater than 75% with correlation coefficients of 0.997 and 0.993 for fluoxetine and norfluoxetine, respectively.     

Zeta-potentials of self-assembled surface micelles of ionic surfactants adsorbed at hydrophobic graphite surfaces

The zeta-potentials of the self-assembled surface ionic surfactants (sodium dodecyl sulfate—SDS and hexadecyltrimethyl ammonium bromide—CTAB) on graphite surfaces were determined both from streaming potential and electrophoretic mobility measurements. The adsorption of the surfactants at graphite–liquid interfaces has been studied using atomic force microscopy (AFM) soft-contact imaging which shows the formation of linear, parallel hemicylinders with headgroups oriented towards the solution. The magnitude of the zeta-potential increased with an increase in surfactant concentration, reaching a constant value at a concentration corresponding to the point of surface micelle formation as confirmed from AFM imaging. The streaming potential and electrophoretic mobility measurements showed that the zeta-potentials of SDS and CTAB surface micelles adsorbed at the graphite surface were about −75 and +70 mV, respectively, well in agreement with the values reported for bulk phase micelles in the literature.     

Oxygen-17 nuclear magnetic resonance: The effects of remote unsaturation on 17o-chemical shifts in polycyclic ethers

Natural-abundance ¹⁷O-NMR spectra of 7-oxanorbornane exo-3-oxatricyclo [3.2.1.0^2.4]octane and their unsaturated derivatives (endo cyclic and exocyclic double bonds) have been measured. Linear correlation laws were observed for $\text{δ}{}_{\mathrm{o}}\text{δ}{}_{\mathrm{c}}$ of these ethers/corresponding hydrocarbons. The “cyclization shifts” for δ_o in ethers were not correlated by the “cyclization shifts” for δ_c of the corresponding hydrocarbons.