Efficient Synthesis of Functionalized 2H-Thiopyrans via Hetero-Diels-Alder Reactions of an Enaminothione with Electrophilic Olefins

Summary.  The hetero-Diels-Alder reaction of 3-dimethylamino-1-(2-thienyl)-2-propene-1-thione (diene) with substituted β-nitrostyrenes, as well as maleic and fumaric acids (dienophiles) yielded 3,4-dihydro-2H-thiopyran derivatives. The treatment of some of those cycloadducts with acetic acid caused elimination of dimethylamine, affording stable 2H-thiopyrans. A reaction of the diene with maleic anhydride furnished a cycloadduct which underwent spontaneous rearrangement to form an N,N-dimethylamide derivative. Cycloadditions of the diene to maleimide, N-phenylmaleimide, maleic acid monoanilide, diethyl maleate, fumarate, and butenolide carried out in the presence of acetic anhydride were followed by elimination of dimethylamine under formation of stable 2H-thiopyran derivatives. Received February 19, 2001. Accepted (revised) March 12, 2001     

A ruthenium(II)-trithiacyclononane curcuminate complex: Synthesis,characterization, DNA-interaction,and cytotoxic activity

The coordination of ruthenium(II) complexes to anionic oxygen-based donors are very rare. This study describes a simple, one-pot method for obtaining [ruthenium(II)(trithiacyclononane)(curcumin)(S-DMSO)]Cl (1) in 37% yield. The structural characterization of complex 1 by elemental analysis, FT-IR, 1-D and 2-D NMR, ESI⁺-MS as well as UV–vis and fluorescence spectroscopies are presented. The DNA-melting temperature (T_m) assay shows that salmon sperm DNA (smDNA) in the presence of complex 1 has a higher melting temperature, with ΔT_m = 7.4 °C, while in the presence of curcumin the melting temperature remains unaltered. The in vitro cytotoxic activities of curcumin and complex 1 were investigated using the tumor human prostate cell line, PC-3, and the healthy cell line, PNT-2. Complex 1 is innocuous toward normal prostate epithelial cells and, whereas curcumin is toxic, with inhibition rates of ca. 35 and 65% at 50 and 80 μM, respectively. On the tumor cell line PC-3, complex 1 did not cause viability changes, whereas curcumin exhibited dose-dependent inhibition, with ca. 73% inhibition at the highest concentration tested, i.e. 80 μM. This study suggests that coordination with the trithiacyclononane ruthenium(II) scaffold stabilizes the photochemical properties of curcumin and strongly changes its biologic activity.     

Aza-substitution,benzo-annulation effects and catalytic activity of <Emphasis Type="Italic">β</Emphasis>-octaphenyl-substituted tetrapyrrolic macroheterocyclic cobalt complexes. I. heterogeneous catalysis

The influence of the size of conjugated π-system on catalytic activity of cobalt complex with β-octaphenylporphyrin and its tetraaza-, tetrabenzo and tetrabenzotetraaza derivatives was studied in present work. It is found that catalytic activity for oxidation of sulfur-containing compounds increases under extension of conjugated macrocycle system according to the following series CoP < CoBP ≤ CoPz < CoPPz ? CoPc.     

Hausdorff dimension and conformal measures of Feigenbaum Julia sets

We show that contrary to anticipation suggested by the dictionary between rational maps and Kleinian groups and by the ``hairiness phenomenon', there exist many Feigenbaum Julia sets whose Hausdorff dimension is strictly smaller than two. We also prove that for any Feigenbaum Julia set, the Poincaré critical exponent is equal to the hyperbolic dimension . Moreover, if , then . In the stationary case, the last statement can be reversed: if , then . We also give a new construction of conformal measures on that implies that they exist for any , and analyze their scaling and dissipativity/conservativity properties.

     

Composition operators on Hardy spaces on Lavrentiev domains

For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.

     

A formula with some applications to the theory of Lyapunov exponents

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman’s result. Finally, we give a result about the growth of the spectral radius of products. Financial support from Pronex-Dynamical Systems, CNP_q 001/2000 and from Faperj is gratefully acknowledged.     

Banach envelopes of vector valued H spaces

In the paper we describe the Banach envelopes of Hardy spaces of analytic functions of several variables on polydiscs taking values in quasi-Banach spaces.     

Free vibrations of thin annular plates made from functionally graded material

Subject of the consideration is thin annular plate made of a two-phase functionally graded composte. The plate has periodically inhomogeneous microstructure slowly varying in space: the λ-periodic structure along circular coordinate, but smoothly graded apparent (averaged) properties in the perpendicular, radial direction. The aim of the contribution is to derive and apply a deterministic macroscopic model describing the free vibrations of this plate. Modeling procedure is based on tolerance averaging technique. We received, equations system with smooth coefficients. We made numerical solution of this problem, using finite difference method, and analyze influence of material proportion and microstructure size on first frequency of free vibrations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)