Microwave-accelerated conjugate addition of aldehydes to α,β-unsaturated ketones

Aldehydes undergo smooth conjugate addition to α,β-unsaturated ketones in the presence of 5-(2-hydroxyethyl)-1,3-thiazolium halides and DBU adsorbed onto the surface of basic alumina under microwave irradiation and solvent-free conditions to afford 1,4-diketones in enhanced yields and reduced reaction times compared to conventional methods.     

Addition of Bromotrichloromethane and Tetrachloromethane to cis-Cyclooctene,Cyclohexene, and Norbornadiene in the Presence of Palladium(II) Complexes

Addition of bromotrichloromethane and tetrachloromethane to alkenes in the presence of palladium(II) complexes begins with single-electron transfer from the palladium atom to polyhalomethane molecule, followed by fragmentation of the radical anion thus formed and generation of trichloromethyl radical. Halogen transfer to a carbon-centered radical arising from addition of trichloromethyl radical at the double bond occurs both from the polyhalomethane molecule and from halide palladium complex.     

Synthesis and Structure of Mixed Phosphonium-iodonium Ylide

A mixed phosphonium-iodonium ylide, phenyliodoniumethoxycarbonylmethylenetriphenylphosphorane borofluoride, was synthesized. Its structure was established by means of X-ray diffraction analysis. Temperature dependence of ¹H, ¹³C, and ³¹P spectra of the ylide synthesized was investigated. A dynamic equilibrium between Z and E-isomers was observed.     

Two-row nilpotent orbits of cyclic quivers

We prove that the local intersection cohomology of nilpotent orbit closures of cyclic quivers is trivial when the two orbits involved correspond to partitions with at most two rows. This gives a geometric proof of a result of Graham and Lehrer, which states that standard modules of the affine Hecke algebra of GL_d corresponding to nilpotents with at most two Jordan blocks are multiplicity-free. Received: 7 February 2002 / Published online: 8 November 2002     

Two-Frequency Autowave Processes in the Complex Ginzburg–Landau Equation

We study the complex Ginzburg–Landau equation with zero Neumann boundary conditions on a finite interval and establish that this boundary problem (with suitably chosen parameters) has countably many stable two-dimensional self-similar tori. The case of periodic boundary conditions is also investigated.     

On Weak Solutions of an Integral Equation Driven by a p-Semimartingale of Special Type

We consider the integral equation driven by a standard Brownian motion and by a fractional Brownian motion. Sufficient conditions under which the equation has a weak solution are obtained.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

Structure and properties of potassium titanyl phosphate single crystals with 7 and 11 at. % Nb

This study is a continuation of research into the atomic structure and physical properties of niobium-doped potassium titanyl phosphate crystals, KTiOPO₄ (KTP: Nb). Crystals containing 7 and 11 at. % of niobium were grown and studied. With an increase in niobium content, the number of vacancies and additional potassium positions in the structure also increase. This fact accounts for an increase in both the intensities of relaxation peaks and the conductivity of KTP: Nb crystals.