Trifluoromethyl Derivatives of Benzooxatellurole

Replacement of the iodine atom in an iodine (III) CF₃‐transfer reagent with a Te‐aryl moiety was accomplished in a three‐step synthetic sequence. Three compounds of this type have been prepared, two of which were characterized by X‐ray diffraction. Single crystal structures were also obtained for three related Te(IV) compounds unreported so far ( 4a , 4b , 6b ). Comparison with the iodine (III) analogues indicate a large degree of structural similarity, however these species display an interesting decomposition pathway under thermal conditions. In addition to the expected Te?CF₃ bond cleavage, C?F bond cleavage is also observed, unlike in the case of iodine (III) compounds.     

Novel sydnone derivatives carrying azidomethyl-1,2, 4-oxadiazole unit and their 1,3-dipolar cycloadditions

A series of 1,2,4-oxadiazolymethyl sydnones carrying azido group were synthesized and subjected to react with a variety of alkenic and acetylenic dipolarophilic reagents; N-phenyl maleimide, phenyl vinyl sulfone, and phenyl propiolic acid. All the new products are identified by spectral/physical data including high-resolution mass measurements and X-ray diffraction data.     

On Vertical Diffusion of Gases in a Horizontal Reservoir

Exact and approximate solutions to vertical diffusion in gravity-stable, ideal gas mixtures in gas reservoirs, depleted oil reservoirs, or drained aquifers are presented, and characteristic times of diffusion are obtained. Our solutions also can be used to test numerical simulators that model diffusion after gas injection. First, we consider isothermal, countercurrent vertical diffusion of carbon dioxide and methane in a horizontally homogeneous reservoir. Initially, the bottom part of the reservoir, with no flow boundaries at the top and bottom, is filled with CO₂ and the upper part with CH₄. At time equal zero, the two gases begin to diffuse. We obtain the exact solution to the initial and boundary-value problem using Fourier series method. For the same problem, we also obtain an approximate solution using the integrated mass balance method. The latter solution has a particularly simple structure, provides a good approximation and retains the important features of the exact solution. Its simplicity allows one to perform calculations that are difficult and non-transparent with the Fourier series method. It also can be used to test numerical algorithms. Furthermore, we consider diffusion of CO₂ with partitioning into connate water. We show that at reservoir pressures the CO₂ retardation by water cannot be neglected. The diffusion-retardation problem is modelled by a non-linear diffusion equation whose self-similar solution is obtained. Finally, we obtain a self-similar solution to a nonlinear diffusion problem. This solution is a good approximation at early times, before the diffusing gases reach considerable concentrations at the top and bottom boundaries of the reservoir.     

[1,3]-Dipolar cycloaddition of N-aryl sydnones to benzothiophene 1,1-dioxide, 1-cyclopropylprop-2-yn-1-ol and 1-(prop-2-ynyl)-1H-indole

[1,3]-Dipolar cycloadditions of N-aryl sydnones to benzothiophene 1,1-dioxide, 1-cyclopropylprop-2-yn-1-ol and 1-(prop-2-ynyl)indole gave fused pyrazole derivatives when carried out in refluxing toluene. While the first two dipolarophiles gave single regioisomers, this indolic derivative gave mixtures, the ratios of which appeared to be controlled by the phenyl substituents. Their structures were identified in the usual manner, supported by single crystal X-ray diffraction measurements.     

Group homomorphisms inducing isomorphisms in cohomology

In this article, we call a ring R right generalized semiregular if for any a ∈ R there exist two left ideals P, L of R such that lr(a) = P⊕ L, where P ? Ra and Ra ∩ L is small in R. The class of generalized semiregular rings contains all semiregular rings and all AP-injective rings. Some properties of these rings are studied and some results about semiregular rings and AP-injective rings are extended. In addition, we call a ring R semi-π-regular if for any a ∈ R there exist a positive integer n and e ² = e ∈ a ⁿ R such that (1 ? e)a ⁿ  ∈ J(R), the Jacobson radical of R. It is shown that a ring R is semi-π-regular if and only if R/J(R) is π-regular and idempotents can be lifted modulo J(R).