First report on the kinetics of the uncatalyzed esterification of cellulose under homogeneous reaction conditions: a rationale for the effect of carboxylic acid anhydride chain-length on the degree of biopolymer substitution

The kinetics of the homogeneous acylation of microcrystalline cellulose, MCC, with carboxylic acid anhydrides with different acyl chain-length (Nc; ethanoic to hexanoic) in LiCl/N,N-dimethylacetamide have been studied by conductivity measurements from 65 to 85 A degrees C. We have employed cyclohexylmethanol, CHM, and trans-1,2-cyclohexanediol, CHD, as model compounds for the hydroxyl groups of the anhydroglucose unit of cellulose. The ratios of rate constants of acylation of primary (CHM; Prim-OH) and secondary (CHD; Sec-OH) groups have been employed, after correction, in order to split the overall rate constants of the reaction of MCC into contributions from the discrete OH groups. For the model compounds, we have found that k((Prim-OH))/k((Sec-OH)) > 1, akin to reactions of cellulose under heterogeneous conditions; this ratio increases as a function of increasing Nc. The overall, and partial rate constants of the acylation of MCC decrease from ethanoic- to butanoic-anhydride and then increase for pentanoic- and hexanoic anhydride, due to subtle changes in- and compensations of the enthalpy and entropy of activation.

Arbitrage-Free Conditions and Hedging Strategies for Markets with Penalty Costs on Short Positions

We consider a discrete-time financial model in a general sample space with penalty costs on short positions. We consider a friction market closely related to the standard one except that withdrawals from the portfolio value proportional to short positions are made. We provide necessary and sufficient conditions for the nonexistence of arbitrages in this situation and for a self-financing strategy to replicate a contingent claim. For the finite-sample space case, this result leads to an explicit and constructive procedure for obtaining perfect hedging strategies.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.