Separability and distance

Translated from Matematicheskie Zametki, Vol. 50, No. 5, pp. 18–22, November, 1991.     

Algebraic properties of the 1 + 1-dimensional Heisenberg spin field model

The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system is generated.     

An adaptive filter for gravitational-wave antennas

Summary We report on the development of an adaptive optimum filter for processing the data of a resonant bar gravitational-wave detector. This filter, based on the matched-filter theory, is adaptive in the sense that the function it realizes is derived from the actual noise spectrum of the data being analysed (instead from an idealized model of the noise). Its implementation is mostly based on frequency domain techniques. We also report on the application of the new filter to the data of the cryogenic antenna Explorer of the Rome group, with particular reference to the comparison between its performance and that of an otpimum filter with fixed values of the parameters.     

The complete set of symmetry operators of the schrödinger equation

The complete set of symmetry operators of an arbitrary order associated with the Schrödinger equation is found. It is shown that this equation is invariant with respect to a 28-dimensional Lie algebra, realized in the class of differential operators of the second order. Higher-order symmetries of the Levi-Leblond equation are investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1521–1526, November, 1991.     

Reactions of the nitrate radical with a series of reduced organic sulphur compounds in air

A 480 L evacuable reaction chamber, equipped with FT-IR spectroscopy on-line and ion chromatography off-line, has been used to study the gas phase reaction between the nitrate radical, NO₃, and the reduced organic sulphur compounds CH₃CH₂SH, (CH₃CH₂)₂S, (CH₃CH₂)₂S₂, and CH₃CH₂SCH₃ in air. The products CH₃CH₂SO₃H, SO₂, H₂SO₄, CH₃CHO, and CH₃CH₂ONO₂ were identified and quantified in the reactions of the first three compounds, CH₃CH₂SH, (CH₃CH₂)₂S, and (CH₃CH₂)₂S₂. The reaction products were CH₃CH₂SO₃H, CH₃SO₃H, SO₂, H₂SO₄, CH₃CHO, and CH₂O in the reaction of CH₃CH₂SCH₃. On the basis of identified reaction products and intermediates observed in the infrared spectra, mechanisms are proposed for the reactions between the NO₃ radical and the four reduced organic sulphur compounds. The results of this study, together with those from previous experiments performed in this laboratory on CH₃SCH₃, CH₃SH, and CH₃SSCH₃ lead to the conclusion that all these species, in the reaction with the NO₃ radical, follow a similar degradation mechanism producing SO₂, H₂SO₄, R? SO₃H, R? CHO, and R? CH₂ONO₂, as the main reaction products. The inital step of the reaction of NO₃ with R? S? R and R? S? H type (R = CH₃, CH₂CH₃) reduced organic sulphur compounds was found to be H-atom abstraction, probably after the formation of an initial adduct. For the reaction between NO₃ and R? S? S? R type compounds, evidence for an addition-decomposition reaction, as the initial steps, was obtained. R? S·, R? S(O)·, and R? S(O)₂· appear to be formed as intermediates in all the reactions. © John Wiley & Sons, Inc.     

Solubility diagrams of the potassium iodide-water-N,N-dimethylformamide and iodine-iodide-water-N,N-dimethylformamide systems at 25°C

The solubility diagrams of the potassium iodide-water-N,N-dimethylformamide (DMFA) and iodine-iodide-water-N,N-dimethylformamide systems were studied at 25°C by the method of sections. The systems are characterized by three-phase equilibria of the peritonic and eutonic types, respectively. Potassium iodide in the I₂-KI-/H₂O-DMFA (95: 5 wt %)/ system was found to salt in crystalline iodine. The selected composition of the H₂O-DMFA mixed solvent possessed a higher iodine-solving ability compared with pure mixture components.     

X-ray photoelectron spectroscopy characterization of composite TiO2–poly(vinylidenefluoride) films synthesised for applications in pesticide photocatalytic degradation

X-ray photoelectron spectroscopy (XPS) was adopted for the analytical characterization of composite titanium dioxide–poly(vinylidenefluoride) (TiO₂–PVDF) films developed for applications in the photocatalytic degradation of pollutants.

The composites were deposited on glass substrates by casting or spin coating from TiO₂–PVDF suspensions in dimethylformamide (DMF). XPS data on the TiO₂–PVDF surface composition were used to optimize preparation conditions (composition of the TiO₂/PVDF suspension, deposition technique) in terms of titanium dioxide surface amount and film stability.

The use of spin-coating deposition and the increase of TiO₂ amount in the DMF suspensions were found to improve the titanium surface content, although high TiO₂/PVDF ratios led to film instability. PVDF–TiO₂ films were also used in preliminary photocatalytic degradation tests on isoproturon, a phenylurea herbicide, under solar UV irradiation; the results were compared to direct photolysis to evaluate the catalytic efficiency of immobilized TiO₂ and the role played by the PVDF film during the degradation process.