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.     

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.     

Fresnel filtering of Gaussian beams in microcavities

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory.     

On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

Restricted generalized Nash equilibria and controlled penalty algorithm

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem, in which each player’s strategy set may depend on the rival players’ strategies. The GNEP has recently drawn much attention because of its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. However, a GNEP usually has multiple or even infinitely many solutions, and it is not a trivial matter to choose a meaningful solution from those equilibria. The purpose of this paper is two-fold. First we present an incremental penalty method for the broad class of GNEPs and show that it can find a GNE under suitable conditions. Next, we formally define the restricted GNE for the GNEPs with shared constraints and propose a controlled penalty method, which includes the incremental penalty method as a subprocedure, to compute a restricted GNE. Numerical examples are provided to illustrate the proposed approach.     

Analysis of oxidation process of cholecystokinin octapeptide with reactive oxygen species by high‐performance liquid chromatography and subsequent electrospray ionization mass spectrometry

The C‐terminal octapeptide of cholecystokinin (CCK8) includes some easily oxidizable amino acids. The oxidation of CCK8 by reactive oxygen species (ROS) such as hydrogen peroxide (H₂O₂) and hydroxyl radicals (OH^?) was investigated using reversed‐phase high performance liquid chromatography (RP‐HPLC) and subsequent electrospray ionization mass spectrometry. The mechanism of oxidation of CCK8 in the H₂O₂ system differed from that of CCK8 in the Fenton system, in which OH^? are produced. In the H₂O₂ system, ²⁸Met and ³¹Met were oxidized to methionine sulfoxide, and no further oxidation or degradation/hydrolysis occurred. On the other hand, in the Fenton system, ²⁸Met and ³¹Met residues were oxidized to methionine sulfone via the formation of methionine sulfoxide. In addition, the oxidized product was observed at the Trp residue but not at the Tyr residue, and small peptide fragments from CCK8 were observed in the Fenton system. From these results, it was concluded that ²⁸Met and ³¹Met residues of CCK8 are susceptible to oxidation by ROS. Copyright © 2009 John Wiley & Sons, Ltd.