On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Identifying assembly maps in K- and L-theory

In this paper we prove the equivalence of various algebraically or geometrically defined assembly maps used in formulating the main conjectures in K- and L-theory, and C^*-theory.Partially supported by NSERC grant A4000 and NSF grant DMS 9104026. The authors also wish to thank the SFB für Geometrie und Analysis, Münster, and the Max Planck Institut für Mathematik, Bonn, for their hospitality and support.Received: 7 May 2001     

A facile synthesis of oxazines by indium-induced reduction-rearrangement of the nitro β-lactams

An indium-induced reduction-rearrangement reaction of nitro-substituted β-lactams has been used for facile synthesis of oxazines in aqueous ethanol.     

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.     

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.     

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.