A successive quadratic programming algorithm with global and superlinear convergence properties

This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.This work was supported in part by a Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan.     

An efficient solid‐state polycondensation method for synthesizing stereocomplexed poly(lactic acid)s with high molecular weight

Simultaneous solid‐state polycondensation (SSP) of the powdery prepolymers of poly(L ‐lactic acid) (PLLA) and poly(D ‐lactic acid) (PDLA) can produce entire stereocomplexed poly(lactic acid)s (sc‐PLA) with high molecular weight and can be an alternative synthetic route to sc‐PLA. Ordinary melt polycondensations of L ‐ and D ‐lactic acids gave the PLLA and PDLA prepolymers having medium molecular weight which were pulverized for blending in 1:1 ratio. The resultant powder blends were then subjected to SSP at 130–160 °C for 30 h under a reduced pressure of 0.5 Torr. Some of the products thus obtained attained a molecular weight (M_w) as high as 200 kDa, consisting of stereoblock copolymer of PLLA and PDLA. A small amount of the stereocomplex should be formed in the boundaries of the partially melted PLLA and PDLA where the hetero‐chain connection is induced to generate the blocky components. The resultant SSP products showed predominant stereocomplexation after their melt‐processing in the presence of the stereoblock components in spite of containing a small amount of racemic sequences in the homo‐chiral PLLA and PDLA chains. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3714–3722, 2008     

Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints introduced by Birbil et al. (Math Oper Res 31:739–760, 2006). Firstly, by means of a Monte Carlo method, we obtain a nonsmooth discrete approximation of the original problem. Then, we propose a smoothing method together with a penalty technique to get a standard nonlinear programming problem. Some convergence results are established. Moreover, since quasi-Monte Carlo methods are generally faster than Monte Carlo methods, we discuss a quasi-Monte Carlo sampling approach as well. Furthermore, we give an example in economics to illustrate the model and show some numerical results with this example. The first author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science and SRF for ROCS, SEM. The second author’s work was supported in part by the United Kingdom Engineering and Physical Sciences Research Council grant. The third author’s work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.     

Influence of the solvent on nature of gate effect in molecularly imprinted membrane

The solute diffusive permeability in a thin layer of a molecularly imprinted polymer (MIP) is affected by specific binding of the MIP with a template. This phenomenon, termed the "gate effect," would be widely applicable for the development of novel biomimetic sensors. However, the mechanism underlying the gate effect is not totally understood. We present here investigation of the role of specific adsorption of a template and solution content in MIPs on the gate effect. A molecularly imprinted self-supporting membrane was formed by copolymerization of methacrylic acid, 2-vinylpyridine, and triethyleneglycol dimethacrylate in the presence of L- (or D-) phenylalanine as a template. The template adsorbed by membrane with degree of enantio-selectivity in a mixed solvent of methanol and water. The amount of adsorption and binding selectivity showed little sensitivity to the solvent composition. The solution content in the membrane increased with increasing the methanol concentration of the solvent following a sigmoid curve with an inflection point at methanol concentration of 20 wt.%. The content increased in the presence of the template at methanol concentrations higher than the inflection point, and decreased at lower methanol concentrations. The creatinine permeability across the membrane estimated by batchwise dialysis increased in the presence of the template at 50 wt.% methanol in the solvent, and did not change at 20 wt.%. There was no permeability for creatinine in the pure water solvent. Both the solution content and the permeability were not affected by the presence of the enantiomer of the template. The results show that the choice of solvent controls more strongly the nature of the gate effect than the specific binding of the template.     

Effect of sepiolite on the biodegradation of poly(lactic acid) and polycaprolactone

PLA and PCL nanocomposites prepared by adding 5 wt% of a sepiolite (SEPS9) were degraded in compost, leading to effective degradation for all samples.PLA and PLA/SEPS9 seem to be mainly degraded by a bulk mechanism, showing a significant level of polymer degradation, however the presence of SEPS9 particles partially delays the degradation probably due to a preventing effect of these particles on polymer chain mobility and/or PLA/enzymes miscibility. PCL and PCL/SEPS9 showed a preferential surface mechanism of degradation; and in contrast to PLA, sepiolite does not present a considerable barrier effect on the degradation of PCL.     

Dienyl homoallyl alcohols via palladium catalyzed ene-type reaction of aldehydes with 1,3-dienes

The combination of Pd catalyst and Xantphos ligand in the presence of Et(3)B nicely promotes the allylation of aldehydes with conjugated dienes to provide dienyl homoallyl alcohols in excellent yields. The reaction occurs selectively at the C-C double bond bearing higher electron density.