Liouville theorem for higher-order elliptic systems of cordes type

We study a quasilinear elliptic system in a Euclidean space with a Douglis-Nirenberg structure. We introduce a cordesicity condition for a system which guarantees that Liouville theorem holds: if the rate of growth of the generalized solution of a system at infinity is les than the limit rate which depends on cordesicity indices, then this solution is a polynomial of a specific degree.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 199–205, February, 1991.     

Alkenyl derivatives of 5-nitro-2-pyridone: Synthesis and halocyclization

Alkylation of 5-nitro-2-pyridone by alkenyl halides in acetone in the presence of K₂СО₃ proceeds with generation of a mixture of N- and О-derivatives with N-isomer prevailing. 1-Allyl- and 1-methylallyl-5-nitro-2-pyridone react with halogens with the formation of 2-halomethyl-6-nitro-2,3-dihydrooxazolo[3,2-a]-pyridinium halides. 1-Prenyl-5-nitro-2-pyridone reacts with bromine with the formation of 3-bromine-2,2-dimethyl-7-nitro-3,4-dihydro-2Н-pyrido[2,1-b][1,3]oxazinium bromide, and with iodine giving 2,2-dimethyl-7-nitro-3,4-dihydro-2Н-pyrido[2,1-b][1,3]oxazinium triiodide.     

Reduction of copper(II) complexes of tridentate ligands by nitric oxide and fluorescent detection of NO in methanol and water media

Two copper complexes, 1 and 2, with tridentate N-donor ligands, L(1) and L(2) [L(1)= (1-methyl-1H-imidazol-2-ylmethyl)-(2-pyridin-2-yl-ethyl)amine, L(2) = (2-pyridin-2-yl-ethyl)-pyridin-2 yl-methylamine] respectively, have been synthesized and characterized. On exposure to nitric oxide, the copper(II) centers in complexes 1 and 2 were found to undergo reduction in various solvents. In acetonitrile solvent the reduction was accompanied by a simultaneous N-nitrosation on the secondary amine center on the ligand frameworks. Complexes 3 and 4 were prepared with ligands L(3) and L(4), respectively. L(3) and L(4) [L(3) = 5-dimethylamino-naphthalene-1-sulfonic acid (1-methyl-1H-imidazol-2-ylmethyl)-(2-pyridin-2-yl-ethyl)-amide; L(4) = 5-dimethylamino-naphthalene-1-sulfonic acid(2-pyridin-2-yl-ethyl)-pyridin-2-ylmethyl-amide] are the dansyl derivatives of L(1) and L(2), respectively. Complex 4, due to paramagnetic quenching, does not display any fluorescence; however, on addition of nitric oxide to a methanol or water solution of complex 4, the fluorescence intensity of the fluorophore has been found to be restored. This is attributed to the reduction of the Cu(II) center by nitric oxide to diamagnetic Cu(I). The turn-on of quenched fluorescence intensity has been observed both in methanol and water media.     

Effect on thermoluminescence parameters of biotite mineral due to thermal quenching

The Thermally Stimulated Luminescence (TSL) at room temperature X-ray irradiated natural biotite in form of micro-grain powder was studied under various heating rates. TSL peaks showed at temperatures 393 K, 399.6 K, 403.5 K, 404.5 K, 406.9 K at their respective heating rates 2 K/s, 4 K/s, 6 K/s, 8 K/s and 10 K/s. The effect of thermal quenching on thermoluminescence parameters such as peak maximum temperature, peak area, FWHM, geometrical symmetry factor, the activation energy were investigated. From the symmetry factor it is clear that the TL glow curve follows the first order kinetics for the lowest heating rate, but as the heating rate increases it defers from the first order. The activation energies for each heating rates were calculated by using Chen peak shape methods for general order kinetics and found to be decreased for higher heating rates. When activation energy is calculated by variable heating rate method it is observed that the method overestimated the value of activation energy and pre-exponential frequency factor significantly due to thermal quenching.