Refinement of the crystal structure of (RS)-carnitine hydrochloride

A single crystal of (RS)-carnitine hydrochloride has been obtained, and its crystal structure has been refined by an x-ray structural experiment.Tashkent Pharmaceutical Institute. Translated from Khimiya Prirodnykh Soedinenii, No. 6, pp. 842–844, November–December, 1991.     

Carbon-carbon bond formation from azaallyl and imine couplings about metal-metal bonds

Typical C-C bond-forming processes feature oxidative addition, insertion, and reductive elimination reactions. An alternative strategy toward C-C bond formation involves the generation of transient radicals that can couple at or around one or more metal centers. Generation of transient azaallyl ligands that reductively couple at CH positions possessing radical character is described. Two C-C bonds form, and the redox non-innocence of the resulting pyridine-imines may be critical to formation of a third C-C bond via dinuclear di-imine oxidative coupling. Unique metal-metal bonds are a consequence of the chelation.     

Refinement of the crystal structure of (RS)-carnitine hydrochloride

A single crystal of (RS)-carnitine hydrochloride has been obtained, and its crystal structure has been refined by an x-ray structural experiment.     

Olefin substitution in (silox)3M(olefin) (silox = (t)Bu3SiO; M = Nb, Ta): the role of density of states in second vs third row transition metal reactivity

The substitution chemistry of olefin complexes (silox)3M(ole) (silox = (t)Bu3SiO; M = Nb (1-ole), Ta (2-ole); ole = C2H4 (as 13C2H4 or C2D4), C2H3Me, C2H3Et, cis-2-C4H8, iso-C4H8, C2H3Ph, cC5H8, cC6H10, cC7H10 (norbornene)) was investigated. For 1-ole, substitution was dissociative (deltaG(double dagger)(diss)), and in combination with calculated olefin binding free energies (deltaG(o)(bind)), activation free energies for olefin association (deltaG(double dagger)(assoc)) to (silox)3Nb (1) were estimated. For 2-ole, substitution was not observed prior to rearrangement to alkylidenes. Instead, activation free energies for olefin association to (silox)3Ta (2) were measured, and when combined with deltaG(o)(bind) (calcd), estimates of olefin dissociation rates from 2-ole were obtained. Despite stronger binding energies for 1-ole vs 2-ole, the dissociation of olefins from 1-ole is much faster than that from 2-ole. The association of olefins to 1 is also much faster than that to 2. Linear free energy relationships (with respect to deltaG(o)(bind)) characterize olefin dissociation from 1-ole, but not olefin dissociation from 2-ole, and olefin association to 2, but not olefin association to 1. Calculated transition states for olefin dissociation from (HO)3M(C2H4) (M = Nb, 1'-C2H4; Ta, 2'-C2H4) are asymmetric and have orbitals consistent with either singlet or triplet states. The rearrangement of (silox)3Nb(trans-Vy,Ph-cPr) (1-VyPhcPr) to (silox)3Nb=CHCH=CHCH2CH2Ph (3) is consistent with a diradical intermediate akin to the transition state for substitution. The disparity between Nb and Ta in olefin substitution chemistry is rationalized on the basis of a greater density of states (DOS) for the products (i.e., (silox)3M + ole) where M = Nb, leading to intersystem crossing events that facilitate dissociation. At the crux of the DOS difference is the greater 5dz2/6s mixing for Ta vs the 4dz2/5s mixing of Nb. This rationalization is generalized to explain the nominally swifter reactivities of 4d vs 5d elements.     

The steady-state evaluation of small anechoic chambers

An historical survey of the techniques of measurement and assessment of anechoic chambers is given with a view to deciding the optimum method of evaluating the new anechoic chamber at Bradford University. Experimental results taken on the chamber, using the inverse distance and frequency response tests, are presented. An attempt is made to correlate the results of these tests with predicted results obtained from steady-state measurements taken, in an interference tube, on the novel type of absorber used in the chamber. In conclusion, guidelines for the design of small anechoic chambers are given.     

A path probability approach to the solute transport problem

An alternative solute transport algorithm, termed the path probability approach, is presented. The method may be more effective than typical finite methods in some numerical solution problems. The method differs from predominant numerical techniques in that the conventional conservation differential is replaced by a series of equations defining solute migration in terms of a finite number of representative particle position histories and corresponding probabilities. The governing physical assumptions applied in model development are conditionally consistent with those of conventional Lagrangian and Eulerian conceptualizations, but mathematical expression and development of the problem differ from traditional approaches. The method represents dispersion orthogonal to the primary axis of advective transport explicitly, according to arbitrary user-defined probability functions; longitudinal dispersion effects result from the existence of velocity shear effects along the primary axis of movement. It is possible to incorporate Fickian dispersive processes, and thereby reproduce results obtainable with traditional stream tube models; but non-Fickian alternatives can also be explored. Simulation results of the path probability model are compared to analogous results from a representative finite difference model for a hypothetical test flow channel. The comparison demonstrated the ability of the new model to effectively generate simulation results with a computational effeciency considerably higher than conventional techniques under the conditions tested.     

Hedging for the long run

In the years following the publication of Black and Scholes (J Political Econ, 81(3), 637?C654, 1973), numerous alternative models have been proposed for pricing and hedging equity derivatives. Prominent examples include stochastic volatility models, jump-diffusion models, and models based on Lévy processes. These all have their own shortcomings, and evidence suggests that none is up to the task of satisfactorily pricing and hedging extremely long-dated claims. Since they all fall within the ambit of risk-neutral valuation, it is natural to speculate that the deficiencies of these models are (at least in part) attributable to the constraints imposed by the risk-neutral approach itself. To investigate this idea, we present a simple two-parameter model for a diversified equity accumulation index. Although our model does not admit an equivalent risk-neutral probability measure, it nevertheless fulfils a minimal no-arbitrage condition for an economically viable financial market. Furthermore, we demonstrate that contingent claims can be priced and hedged, without the need for an equivalent change of probability measure. Convenient formulae for the prices and hedge ratios of a number of standard European claims are derived, and a series of hedge experiments for extremely long-dated claims on the S&P 500 total return index are conducted. Our model serves also as a convenient medium for illustrating and clarifying several points on asset price bubbles and the economics of arbitrage.