Structure,conformation, and motions of polytetrahydrofuran (PTHF) in the hexagonal form of the PTHF-urea inclusion compound

Combination of differential scanning calorimetry, x-ray diffraction, Fourier transform infrared, and C-13 nuclear magnetic resonance observations made on the crystalline inclusion compound (IC) formed between polytetrahydrofuran (PTHF) and urea (U), together with their comparison to identical observations performed on bulk semicrystalline samples of PTHF, have permitted an analysis of the conformations, motions, and environments available to PTHF chains in both solid-state phases. The isolated PTHF chains occupying the narrow channels of the PTHF-U-IC are highly extended, though small rotational deviations averaging 24° from the nearly all trans, planar zig zag conformation of bulk crystalline PTHF chains produce some significant differences in their behaviors. PTHF chains in PTHF-U-IC possess much greater mobility than bulk crystalline PTHF chains as evidenced by C-13 spin lattice relaxation times, T₁, 50 times shorter (1.5 s) than observed for bulk crystalline PTHF chains (75 s). FTIR observations are consistent with very little specific interaction between guest PTHF chains and host urea matrix molecules and result in similar spectra for bulk and IC PTHF, except for the presence of the CH₂ rocking vibration band at 745 cm^?1 observed for bulk PTHF. The absence of this band in the IC PTHF can be understood by considering the symmetry of the all trans, planar zig zag conformation of bulk crystalline PTHF chains, which prevents the CH₂ rocking mode from coupling with skeletal stretching and bending modes as occurs in the nonplanar, helical PTHF chains in PTHF-U-IC. © 1995 John Wiley & Sons, Inc.     

Optimal trading strategy for European options with transaction costs

The European option with transaction costs is studied. The cost of making a transaction is taken to be proportional by a factor λ to the value (in dollars) of stock traded. When there are no transaction costs (i.e. when λ=0) the well-known Black-Scholes strategy tells how to hedge the option. Since no non-trivial perfect hedging strategy exists when λ>0 (see (Ann. Appl. Probab. 5(2) (1995) 327)), we instead try to maximize the expected utility attainable. We seek to understand the effect transaction costs have on the maximum attainable expected utility over all strategies, when λ is small but non-zero. It turns out that transaction costs diminish the expected utility by an amount which has the order of magnitude λ^2/3. We will compute that correction explicitly modulo an error which is small compared to λ^2/3. We will exhibit an explicit strategy whose expected utility differs from the maximum attainable expected utility by an error small in comparison to λ^2/3.     

A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.     

Electrochemical reduction of pyrethroid insecticides based on esters of α-cyano-3-phenoxybenzyl alcohol at glassy carbon and mercury electrodes in acetonitrile

The electrochemical reduction of eight commercially important pyrethroid insecticides which are esters of either α-cyano-3-phenoxybenzyl alcohol (cycloprothrin, cyphenothrin, cyhalothrin, deltamethrin, esfenvalerate and cypermethrin) or 4-fluro-α-cyano-3-phenoxybenzyl alcohol (cyfluthrin and flumethrin) has been studied under conditions of voltammetry and bulk electrolysis at both glassy carbon and mercury electrodes in acetonitrile. In general, the peak potential of the initial reduction process observed at very negative potentials at both electrode surfaces shifts to a more positive value under conditions of consecutive potential cycling. At the hanging mercury drop electrode the reduction occurs at even more negative potentials than at a glassy carbon electrode because a blocking mechanism appears to be operative. Despite this major difference in the primary reduction step, common voltammetric features are observed at less negative potentials on second and subsequent cycles of the electrode potential at either electrode surface. For example, the initial reduction process always results in the formation of a species which is reversibly reduced at less negative applied potentials. Furthermore, despite the definition of the voltammetric response being highly sensitive to the individual pyrethroid structure, long time-scale bulk electrolysis experiments at glassy carbon or mercury pool electrodes led to the formation of analogous final products. The fact that pyrethroids with a widely varying range of acid moieties exhibit similar voltammetric behaviour suggests that the acid moiety is not directly involved in the initial electron transfer process. Controlled potential electrolysis studies at both electrode surfaces coupled with HPLC and mass spectral identification of products obtained after ethylation with ethyl iodide showed that the reduction mechanism on the longer time-scale involves cleavage of the ester with liberation of free cyanide ion. The major reduction product identified was the anion of either 3-phenoxybenzoic acid or 4-fluoro-3-phenoxybenzoic acid in yields ranging from 31 to 66%.