Conformationally controlled intramolecular heterocyclization of 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3

Perfluoro-2-methyl-2-pentene-thiocyanate-3 reacts with ammonia to give 2,4-diaminoperfluoro-4-methyl-2-pentenethiocyanate-3 ( 4 ) and 2-aminoperfluoro-4, 4-dimethyl-4,5-dihydro-5-ethylidene-1,3-thiazole ( 5 ). Compound 4 is kinetically stable and at 150°C under-goes rotational isomerization to afford the cyclic isomer 2-amino-4,4-bis(trifluoromethyl)-4,5-dihydro-5-(1-aminoperfluoroethylidene) -1,3-thiazole ( 6 ). Intramolecular cyclizations, resulting in the thiazolines 5 and 6 , proceed likewise via the Thorpe reaction. For compounds 4–6 , X-ray diffraction analyses were undertaken and IR spectra in solution and in solid state were investigated. It is supposed that a high kinetic preference for formation of 4 and the fact that it does not undergo spontaneous cyclization in ammonolysis stem from the NH …︁ N intramolecular hydrogen bonding between two amino groups.     

Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions

We suggest here a least-change correction to available finite element (FE) solution. This postprocessing procedure is aimed at recovering the monotonicity and some other important properties that may not be exhibited by the FE solution. Although our approach is presented for FEs, it admits natural extension to other numerical schemes, such as finite differences and finite volumes. For the postprocessing, a priori information about the monotonicity is assumed to be available, either for the whole domain or for a subdomain where the lost monotonicity is to be recovered. The obvious requirement is that such information is to be obtained without involving the exact solution, e.g. from expected symmetries of this solution.The postprocessing is based on solving a monotonic regression problem with some extra constraints. One of them is a linear equality-type constraint that models the conservativity requirement. The other ones are box-type constraints, and they originate from the discrete maximum principle. The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessed FE solution preserves the accuracy of the discrete FE approximation.We introduce an algorithm for solving the postprocessing problem. It can be viewed as a dual ascent method based on the Lagrangian relaxation of the equality constraint. We justify theoretically its correctness. Its efficiency is demonstrated by the presented results of numerical experiments.     

Periodic wavelets on the <Emphasis Type="Italic">p</Emphasis>-adic Vilenkin group

Using the Walsh-Dirichlet type kernel, we construct periodic wavelets on the p-adic Vilenkin group. These wavelets are similar to the trigonometric wavelets which were introduced by C. K. Chui and H. N. Mhaskar [1]. Results on the corresponding fast algorithms for decomposition and reconstruction are also discussed.     

q-Moduli of Continuity in H( ), p>0, and an Inequality of Hardy and Littlewood

Some aspects of the interplay between approximation properties of analytic functions and the smoothness of its boundary values are discussed. One main result describes the equivalence of a special q-modulus of continuity and an intrinsic K-functional. Further, a generalization of a theorem due to G. H. Hardy and J. E. Littlewood (1932, Math. Z.34, 403–439) on the growth of fractional derivatives is deduced with the help of this K-functional.     

One-sided invertibility of binomial functional operators with a shift on rearrangement-invariant spaces

Let be an oriented Jordan smooth curve and a diffeomorphism of onto itself which has an arbitrary nonempty set of periodic points. We prove criteria for one-sided invertibility of the binomial functional operator