Synthesis of (-)-2s,3s, 11s,12r-2,3,11,12-tetraphenyl[18]crown-6

The synthesis of ( - ) 2S,3S,11S,12R-2, 3,11,12-tetraphenyl [18]-crown-6 from (-)-1S,2S-hydrobenzoin and meso-hydrobenzoin is described. Chemical shifts and vicinal coupling constants of the benzylic protons in the 2 S, 3 S and 11 S,12 R substructures in the free ligands and in complexes with KSCN and 1-phenylethylammonium bromides and a brief discussion of the related conformational changes are also presented. A detailed procedure for the resolution of racemic hydrobenzoin is given.     

β-Lactam Derivatives as Enzyme Inhibitors: Peptidic Derivatives of ( RS )-2-Oxo-4-phenylazetidine-1-alkanoic Acids

4-Phenylazetidine-2-one was transformed into 4-phenylazetidine-1-alkanoic acids, which were reacted in the presence of diphenylphosphoroazidate with amino acid esters and dipeptide esters yielding β-lactam peptides with different spacers between the lactam ring and the peptide moiety. All structures were established by elementary analyses, HPLC, optical rotation, and spectroscopic data and all new compounds were tested as inhibitors of PPE using standard procedures. Four compounds exhibited a weak activity compared with the standard inhibitor trifluoroacetyl-l-val-l-tyr-l-val.     

A convenient synthesis of 1,3-oxazolidin-4-ones and 1,3-oxazin-4-ones

1,3-Oxazolidin-4-ones and 1,3-oxazin-4-ones were synthesized by formal cyclocondensation of imines with α- or β-hydroxy acids.     

Determination of physiological noble metals in human urine using liquid-liquid extraction and Zeeman electrothermal atomic absorption spectrometry

An extremely sensitive, reliable and simple procedure is described for the determination of physiological palladium, platinum and gold in human urine. The urine samples were adjusted to pH 4 (Pd, Au) or pH 5 (Pt), followed by conversion of the analytes to their pyrrolidinedithiocarbamate complexes. These complexes were separated from the matrix by liquid-liquid extraction into 4-methyl-2-pentanone resulting in a 25-fold enrichment. Determination was by electrothermal atomic absorption spectrometry (ET-AAS) using longitudinal inverse alternating current Zeeman-effect background correction. The limits of detection calculated from three standard deviations of the blank values were 20 ng l⁻¹ for Pd and Au and 70 ng l⁻¹ Pt. Within-day precision (n = 10, 5 μg l⁻¹) ranged 5.2%–7.7%. The procedure is successfully applied to determine urinary palladium, platinum and gold in nine unexposed persons. Palladium levels in urine ranged < 20–80 ng l⁻¹ (arithmetical MEAN=38.7 ng l⁻¹), while gold levels ranged < 20–130 ng l⁻¹ (36.0 ng l⁻¹). Physiological platinum levels in urine were all < 70 ng l⁻¹. The accuracy of the procedure was checked by analyzing a series of urine samples by a second independent method (magnetic sector field inductively-coupled plasma-mass spectrometry) in combination with UV photolysis.     

Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation

We consider the dynamics of a nonlinear partial differential equation perturbed by additive noise. Assuming that the underlying deterministic equation has an unstable equilibrium, we show that the nonlinear stochastic partial differential equation exhibits essentially linear dynamics far from equilibrium. More precisely, we show that most trajectories starting at the unstable equilibrium are driven away in two stages. After passing through a cylindrical region, most trajectories diverge from the deterministic equilibrium through a cone-shaped region which is centered around a finite-dimensional subspace corresponding to strongly unstable eigenfunctions of the linearized equation, and on which the influence of the nonlinearity is surprisingly small.

This abstract result is then applied to explain spinodal decomposition in the stochastic Cahn-Hilliard-Cook equation on a domain . This equation depends on a small interaction parameter  , and one is generally interested in asymptotic results as  . Specifically, we show that linear behavior dominates the dynamics up to distances from the deterministic equilibrium which can reach  with respect to the -norm.

     

A mathematical model for the first-pass dynamics of antibiotics acting on the cardiovascular system

We present a preliminary first-pass dynamic model for delivery of drug compounds to the lungs and heart. We use a compartmental mass-balance approach to develop a system of nonlinear differential equations for mass accumulated in the heart as a result of intravenous injection. We discuss sensitivity analysis as well as methodology for minimizing mass in the heart while maximizing mass delivered to the lungs on a first circulatory pass.     

The real-pole sandwich for rational approximations and oscillation equations

Rational approximations to the exponential function with real poles only are studied with respect to stability at infinity and maximal order. Along each half line in the parameter space it is shown that these two properties occur in an alternating way (or do not occur at all). As an application of the general results the special approximations withq-fold poles at ± ^–1 only, real, are studied. A short proof of the superconvergence for collocation methods is also given.Dedicated to W. Gröbner on the occasion of his 80th birthday.     

Maximum norms of random sums and transient pattern formation

Many interesting and complicated patterns in the applied sciences are formed through transient pattern formation processes. In this paper we concentrate on the phenomenon of spinodal decomposition in metal alloys as described by the Cahn-Hilliard equation. This model depends on a small parameter, and one is generally interested in establishing sharp lower bounds on the amplitudes of the patterns as the parameter approaches zero. Recent results on spinodal decomposition have produced such lower bounds. Unfortunately, for higher-dimensional base domains these bounds are orders of magnitude smaller than what one would expect from simulations and experiments. The bounds exhibit a dependence on the dimension of the domain, which from a theoretical point of view seemed unavoidable, but which could not be observed in practice.

In this paper we resolve this apparent paradox. By employing probabilistic methods, we can improve the lower bounds for certain domains and remove the dimension dependence. We thereby obtain optimal results which close the gap between analytical methods and numerical observations, and provide more insight into the nature of the decomposition process. We also indicate how our results can be adapted to other situations.

     

Improving biorefinery planning: Integration of spatial data using exact optimization nested in an evolutionary strategy

Biorefineries can provide a product portfolio from renewable biomass similar to that of crude oil refineries. To operate biorefineries of any kind, however, the availability of biomass inputs is crucial and must be considered during planning. Here, we develop a planning approach that uses Geographic Information Systems (GIS) to account for spatially scattered biomass when optimizing a biorefinery’s location, capacity, and configuration. To deal with the challenges of a non-smooth objective function arising from the geographic data, higher dimensionality, and strict constraints, the planning problem is repeatedly decomposed by nesting an exact nonlinear program (NLP) inside an evolutionary strategy (ES) heuristic, which handles the spatial data from the GIS. We demonstrate the functionality of the algorithm and show how including spatial data improves the planning process by optimizing a synthesis gas biorefinery using this new planning approach.