The Synthesis of (±)-α-Vetispirene Via the Dieckmann Condensation of Ethyl 4-(2,6-Dimethyl-1-Carbethoxycyclohex-2-Enyl)-Butyrate

A new process for the synthesis of (±)-α-vetispirene ( 1 ) starting from 2,4-dimethyl-3-carbethaxycyclohexene ( 2 ) is described. The key steps include the stereoselective alkylation of 2 with ethyl 4-bromo-butyrate to yield ethyl 4-(2,6-dimethyl-1-carbethoxycyctohex-2-enyl)-bytyrate ( 3 ) and spiroannulation of 3 by Dieckmann condensation to give 2-carbethoxy-6,10-dimethyl spiro[4,5] deca-6-en-1-one ( 4 ).     

Stability analysis of systems with periodic coefficients: An approximate approach

The paper deals with an approximate method of stability analysis for second order linear systems with periodic coefficients. The periodic functions are approximated during the first period of motion by a constant, a linear or a quadratic function of time such that the resulting approximate equations have known closed form solutions. The approximate equivalent equations are generated through an expansion of periodic coefficients into ultraspherical polynomials. The stability criteria is determined from the solution of approximate equivalent system and the generalized Floquet theory. The technique is quite general and does not require any restriction on the magnitudes of system parameters. In particular, the method has been applied to construct approximate stability chart for the Mathieu equation. A close agreement between the approximate and the exact result is found even for large values of system parameters.     

Graphic rule for non-steady-state enzyme kinetics and protein folding kinetics

When going more deeply into the principles of enzyme action as well as protein folding, one is often confronted with transient process systems. Based on the recent progress in graphic methods of enzyme kinetics, in this article a graphic rule is described, which can be used to deal with transient processes occurring in both enzyme-catalyzed reaction systems and protein folding systems. Introducing the graphic method to nonsteady-state systems can raise the efficiency of the calculations and provide an intuitive picture, helping the analysis of the mechanisms concerned. For instance, using the current graphic rule, one can immediately write out the phase concentrations of enzyme species or protein folding states. Calculation work such as setting up differential equations, making Laplace transformations, and expanding determinants, which is both tedious and liable to error, is completely avoided. The mathematical proof of the non-steady-state graphic rule is given in the appendix.Presented at the Symposium on Applied Graph Theory and Discrete Mathematics in Chemistry held at the University of Saskatchewan, Saskatoon, Canada, September 12-14, 1991, in honor of Professor Frank Harary on the occasion of his 70th birthday.     

NMR and x-ray studies on the morphology of thermoreversible polyacrylonitrile gels

The morphology of thermoreversible polyacrylonitrile–propylene carbonate (PAN-PC) gels was examined using solid-state carbon-13 nuclear magnetic resonance (NMR) spectroscopy and x-ray diffraction. Following complete dissolution of the polymer at elevated temperature and cooling of the concentrated PAN-PC solutions, a gel was formed. The PAN-PC gels consisted of regions of mobile polymer chains, rich in PC, “cross-linked” by regions of rigid polymer. The mobile regions of the gels showed solution-type NMR spectra with resolution of tacticity effects. The rigid component detected by NMR would correspond to the crysttallites detected previously by x-ray diffraction. Wide-angle x-ray diffractograms of the gels showed different peaks when compared with the dry polymer powder. After solvent extraction and drying of the gel, the diffractogram reverted to that of the original dry powder. This new result is the strongest evidence to support the view advanced earlier that the new peaks found in the diffraction pattern of the wet gels arises from solvated polymer crystallites rather than from ordinary polymer crystallites. © 1993 John Wiley & Sons, Inc.     

A convenient chemoenzymatic synthesis of (4aS,5S)-(+)-4,4a,5,6,7,8-hexahydro-5-hydroxy-4a-methylnaphthalen-2(3H)-one.

We have developed a convenient chemoenzymatic method for the preparation of (4aS,5S)-4,4a,5,6,7,8-hexahydro-5-hydroxy-4a-methylnaphthalen-2(3H)-one by taking advantage of the excellent enantioselectivity of alcalase. Four different esters were compared, and the butanoate ester was found to be the best substrate. The stereochemistry of the product is the same as the one predicted from the binding model of alcalase. A simple extraction/partition procedure was used to separate the hydroxyenone product from the remaining ester. This practical procedure would be very useful in a gram-scale operation for securing the title compound in high optical purity.     

Palladium-Catalyzed Synthesis of Tetrahydrocarbazoles

The synthesis of tetrahydrocarbazoles from bromoenaminones derived from β-diketones is described. The reaction proceeds by intramolecular cyclization of bromoenaminones involving arylpalladium complexes.     

Fragmentation of α-Acetoximino Ketoesters in Polyphosphoric Acid

Fragmentations of various α-acetoximino ketoesters in neat polyphosphoric acid medium to form acylium ions were studied. The resulting acylium ions were trapped by benzene rings either intermolecularly or intramolecularly.     

Iron-57, tin-119, and antimony-121 mössbauer spectroscopic investigations of metal atom incorporation into the oxide NbTiP3O12

Tin-119 and iron-57 Mössbauer spectroscopy show that the incorporation of tin and iron into the white oxide NbTiP₃O₁₂ to form black compounds of composition Sn_0.5NTiP₃O₁₂ and Fe_0.33NbTiP₃O₁₂ involves the accomodation of Sn²⁺ and Fe²⁺ in two types of sites in the NbTiP₃O₁₂ host lattice. The change in colour is associated which charge transfer arising from the transfer of electrons from the incorporated metal to the host lattice and the partial reduction of Nb⁵⁺ to a lower oxidation state.The compound SbTiP₃O₁₂ has been synthesised and shown by antimony-121 Mössbauer spectroscopy to contain Sb⁵⁺. The resistance of the SbTiP₃O₁₂ structure to the incorporation of tin and iron is associated with the reluctance of Sb³⁺ to adopt octahedral coordination.     

A note on superprocesses

Summary Subject to a mild restriction onA, generator of the one-particle motion, we show theA-Fleming-Viot superprocess can be obtained from theA-Dawson-Watanabe superprocess by conditioning the latter to have constant total mass.Research conducted while a Sir Christopher Cox Junior Research FellowResearch supported in part by the National Science Foundation grant NSF-DMS-89-3474