Fourier Analysis of Semistable Distributions

We consider the generalized convolution powers G _α ^*u (x) of an arbitrary semistable distribution function G _α (x) of exponent α∈(0,2), and prove that for all j, k∈{0,1,2,…} and u>0 the derivatives G _α ^(k,j)(x;u)=∂ ^k+j G _α ^*u (x)/∂ x ^k ∂ u ^j , x∈ℝ, are of bounded variation on the whole real line ℝ. The proof, along with an integral recursion in j, is new even in the special case of stable laws, and the result provides a framework for possible asymptotic expansions in merge theorems from the domain of geometric partial attraction of semistable laws. An erratum to this article can be found at     

Organometallic complexes with biological molecues,part 3. in vivo cytotoxicity of diorganotin (IV) chloro and triorganotin (IV) chloro derivatives of penicillin g on chromosomes of aphanius fasciatus (pisces,cyprinodontiformes)

In order to obtain a continuous source of mitotic metaphases, gill tissue of Aphaius fasciatus (Pisces, Cyprinodontiformes) has been successfully employed. Results gathered after exposure of fish to R₂SnClpenG, R₃SnClpenGNa, to the parents R₂SnCl₂, R₃SnCl and to penGNa (penGNa = penicillinGNa; R = methyl, butyl and phenyl) suggest that both the parent organotin (IV) chloride and organotin (IV) chloropenG derivatives are toxic while penGNa exerts no significant toxic activity. Essentially, all of the chromosome abnormalities are classifiable as irregularly staining of chromosomes, breakages, side-arm bridges or pseudochiasmata.     

Synthesis and crystal structure of 1,3,5-tris [4-(phenylethynyl)phenyl]benzene

The crystal structure of 1,3,5-tris[4-(phenylethynyl)phenyl]benzene (1) has been investigated. Compound1 represents a model of the repeating unit of the most typical polyphenylene, which contains 1,3,5-trisubstituted benzene rings (chain centers) and acetylenic groups (complex-forming and cross-linking centers) in the main chain. The acetylene groups of neighboring molecules have a tendency to close mutual arrangement, which is favorable for their topochemical interaction. However, the relative conformational rigidity of molecules1 restricts not only the possibility of the optimal adjustment of the reactive sites of neighboring molecules to one another, but also hampers the close packing of molecules in the crystal, which contains channels filled by the solvent molecules (chloroform).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1986–1992, November, 1994.The work was carried out with the financial support of the International Science Foundation and the American Crystallographic Association.     

Enantioselective separations by capillary GC on derivatized cyclodextrins. Part 2: Determination of enantiomeric excess of some racemic 2,3-isopropylidene-1,2,3-cyclohexanetriol derivatives on permethyl α-, β-, and γ-cyclodextrins

Capillary GC on permethyl α-, β-, and γ-cyclodextrins has been applied to separate and quantify the enantiomers of some 2,3-iso-propylidene-1,2,3-cyclohexanetriol derivatives. Quantitative CGC data are compared to those obtained with chiral shift ¹H NMR.     

19F NMR study of relative polarities and reactivities of N-H,N-Hg,and N-Au bonds in 2-(4-fluorophenyl)benzimidazole and its PhHg and Ph3PAu derivatives in intermolecular exchange

It has been shown by the¹⁹F NMR method that the relative polarities of nitrogenelement bonds in 2-(4-fluorophenyl)benzimidazole and its PhHg and PPh₃Au derivatives increase in the order N-H19F NMR. It has been found that these reactions occur by a bimolecular associative mechanism and that the N-H bond is substantially less reactive than the N-Hg and N-Au bonds, which have identical reactivities within the limits of sensitivity of the method used.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1574–1580, August, 1995.This work was carried out with financial support from the Russian Foundation for Basic Research (Project No. 93-03-5528).     

On accurate boundary conditions for a shape sensitivity equation method

This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd.     

Ein Verfahren zur Synthese enantiomerenreiner Alkanole durch reduktive Entschwefelung von Thiophenalkoholen

Summary Acetals3 and4 of alkylthienylcarbinols1 were prepared using an enantiomerically pure lactol2. In the key step these compounds were desulfurized. After deprotection the target compounds7 andent-7 were obtained.

Herrn Prof. Dr. H. Oelschläger zum 70. Geburtstag gewidmet     

Recent developments in the synthesis of 11β-aryl-estrone derivatives

An industrial synthesis of 11β-aryl-estrone derivatives is described, based on the 1,4-addition of the aryl side-chain, as a cuprate, on to a mixture of allylic 5(10) alpha and beta epoxides, followed by hydrolysis and subsequent aromatization.     

Complex polymer architectures through dimethoxymethyl 1,1‐diphenylethylene derivatives

The reactions of polystyryllithium and potassium on dimethoxymethyl 1,1‐diphenylethylene derivatives were studied in different solvents. In a polar medium, A₃ and A₆ star types were formed according to the stoichiometry, whereas in a nonpolar medium, hyperbranched structures were synthesized. Extensions of an already proposed mechanism in polar and nonpolar media were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3329–3335, 2003     

Ethyl-4,4,4-trifluoroacetoacetate (ETFAA), a powerful building block for enantiopure chirons in trifluoromethyl-β-amino acid series

Herein are studied new transformations of ethyl-4,4,4-trifluoroacetoacetate (ETFAA), giving access to a series of enantiopure chirons bearing both a trifluoromethyl group and an amino moiety. The key intermediate is obtained optically pure by a resolution procedure.