Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Definable sets and expansions of models of Peano arithmetic

We consider expansions of models of Peano arithmetic to models ofA ₂ ^s -¦ ₁ ¹ + ₁ ¹ –AC which consist of families of sets definable by nonstandard formulas.     

Investigation of 2-[(<Emphasis Type="Italic">E</Emphasis>)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3H-indolium as a new highly sensitive reagent for the spectrophotometric determination of nitrophenols

A new, simple, rapid, and sensitive spectrophotometric method has been developed for the determination of nitrophenols [picric acid (PA); dinitrophenols (DNP)] in wastewater samples. The method is based on the reaction of nitrophenols with 2-[(E)-2-(4-diethylaminophenyl)-1-ethenyl]-1,3,3-trimethyl-3 H-indolium chloride reagent to form the colored ion associates, which are extracted by organic solvents. The molar absorptivity of the ion associates of PA with the investigated reagent ranges from 8.3×10⁴ to 11.3×10⁴ L mol^–1 cm^–1, depending on the extractant. Because only PA is extracted in an acidic medium with the investigated reagent, but both PA and DNP are extracted in an alkaline medium, it is possible to determine both substances in a mixture. Appropriate reaction conditions have been established. The absorbance of the colored extracts obeys Beers law in the range of 0.04–4.58 mg L^–1 PA, 1.0–18.4 mg L^–1 2,4-DNP and 1.2–14.7 mg L^–1 2,6-DNP, respectively. The limit of detections, calculated from a blank test (n=10; P=0.95), are 0.05 mg L^–1 PA, 0.9 mg L^–1 (2,4-DNP), and 1.1 mg L^–1 (2,6-DNP), respectively.     

Mesoionic compounds with a bridged nitrogen atom. 4. Thiazolo[3, 2-a]quinolinium 1-oxide derivatives

It is shown that diverse 2-substituted thiazolo[3,2-a]quinolinium 1-oxides can be obtained from 2-quinolylmercaptoacetic acids. The structures of the synthesized compounds were confirmed by the PMR and mass spectra.See [1] for communication 3.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 621–626, May, 1980.     

ZrCl4-promoted halogen migration during an electrophilic amination of halogenated phenols

An electrophilic amination of halogenated phenols with diisopropyl diazenedicarboxylate in the presence of ZrCl4 as a Lewis acid, accompanied by a halogen migration, was demonstrated for the first time; the fluorine, chlorine, bromine, or iodine atom migrated during the amination process under mild reaction conditions.     

Synthesis of 5-amino-3a,4-dicyano-2,3,3a,6a-tetrahydrofuro[2,3-b]pyrroles

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, p. 282, February, 1992.