Trichlorophenol (TCP) sulfonate esters: a selective alternative to pentafluorophenol (PFP) esters and sulfonyl chlorides for the preparation of sulfonamides

2,4,6-Trichlorophenol (TCP) sulfonate esters undergo effective aminolysis under conventional heating and microwave irradiation; the reactivity of these species is such that chemoselective transformations of PFP sulfonate esters can be achieved.     

Interaction with Brian Garner Wybourne

Quotations from personal letters and other sources are used to give an account of an interaction with Brian Wybourne over the course of a career in theoretcial rare-earth spectroscopy spanning nearly a half-century.     

ICP-MS determination of lead isotope ratios in legal and counterfeit cigarette tobacco samples

A method for the determination of Pb isotope ratios (IR) in cigarette tobacco by quadrupole inductively coupled plasma mass spectrometry (Q-ICP-MS) has been developed and applied to tobacco samples from genuine and counterfeit cigarettes obtained in the USA. The IR 2??Pb/2??Pb, (208)Pb/2??Pb, 2??Pb/2??Pb, 2??Pb/2??Pb and 2??Pb/2??Pb were measured using a Q-ICP-MS instrument. Two certified reference materials, grown in the USA and Bulgaria, were also analysed for comparison with the tobacco samples, as were tobacco samples from cigarettes obtained in Pakistan and China. The precision of the results was sufficient to distinguish between the counterfeit and genuine USA cigarettes. All of the genuine cigarettes and both reference materials, grown in different regions, were statistically distinct based on the measured ratios. The counterfeit cigarettes were indistinguishable from the reference material grown in Bulgaria. The technique shows promise as a method for identifying counterfeit cigarettes, possibly determining the source region.     

A guide to using shadowing filters for forecasting and state estimation

Most traditional, and many modern, methods of state estimation have a number a failings when applied to high-dimensional and nonlinear systems. A promising new alternative that avoids many of these failings is a shadowing filter. An additional advantage of shadowing filters is that when combined with indistinguishable states they provide a consistent generalisation to the imperfect model scenario. This paper is a practical guide to implementing shadowing filters in nonlinear systems. It provides a detailed account of various tests and procedures to ensure successful implementation of a shadowing filter using gradient descent of indeterminism.     

Exploiting dynamical coherence: A geometric approach to parameter estimation in nonlinear models

Parameter estimation in nonlinear models is a common task, and one for which there is no general solution at present. In the case of linear models, the distribution of forecast errors provides a reliable guide to parameter estimation, but in nonlinear models the facts that predictability may vary with location in state space, and that the distribution of forecast errors is expected not to be Normal, means that parameter estimation based on least squares methods will result in systematic errors. A new approach to parameter estimation is presented which focuses on the geometry of trajectories of the model rather than the distribution of distances between model forecast and the observation at a given lead time. Specifically, we test a number of candidate trajectories to determine the duration for which they can shadow the observations, rather than evaluating a forecast error statistic at any specific lead time(s). This yields insights into both the parameters of the dynamical model and those of the observational noise model. The advances reported here are made possible by extracting more information from the dynamical equations, and thus improving the balance between information gleaned from the structural form of the equations and that from the observations. The technique is illustrated for both flows and maps, applied in 2-, 3-, and 8-dimensional dynamical systems, and shown to be effective in a case of incomplete observation where some components of the state are not observed at all. While the demonstration of effectiveness is strong, there remain fundamental challenges in the problem of estimating model parameters when the system that generated the observations is not a member of the model class. Parameter estimation appears ill defined in this case.     

Shape-preserving dynamic programming

Dynamic programming is the essential tool in dynamic economic analysis. Problems such as portfolio allocation for individuals and optimal growth of national economies are typical examples. Numerical methods typically approximate the value function and use value function iteration to compute the value function for the optimal policy. Polynomial approximations are natural choices for approximating value functions when we know that the true value function is smooth. However, numerical value function iteration with polynomial approximations is unstable because standard methods such as interpolation and least squares fitting do not preserve shape. We introduce shape-preserving approximation methods that stabilize value function iteration, and are generally faster than previous stable methods such as piecewise linear interpolation.     

Algebraic forms for the leading factor of the two-electron coefficients of fractional parentage for the atomic l shell

The part of a one-electron coefficient of fractional parentage (cfp) depending, for the atomic l shell, on the spin S, seniority υ, and electron number n of the daughter state, is factored into two parts, the first with dependence on n and υ, and the second with dependence on υ and S. Various techniques are used to extend these results to the two-electron cfp. These entail deriving analogues of the 6-j symbols for the symplectic group Sp(4l + 2) and the special orthogonal group SO(2l + 1). Explicit algebraic expressions are provided, and the choice of multiplicity indices and their circumvention are discussed.     

Bi(OTf)3-catalysed prenylation of electron-rich aryl ethers and phenols with isoprene: a direct route to prenylated derivatives

Electron-rich aryl ethers and phenols react with isoprene (2-methylbuta-1,3-diene) in the presence of catalytic Bi(OTf)(3) at 40 °C to afford the corresponding prenylated or 2,2-dimethylchroman products, respectively, in moderate to good yields. This transformation offers a convenient and expedient entry to prenylated derivatives of electron-rich aromatics that often display enhanced biological activities. The methodology has been employed in the efficient synthesis of a biologically active natural product and related compounds.     

Papieruntersuchung

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