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.     

Fast computation of incomplete elliptic integral of first kind by half argument transformation

We developed a new method to calculate the incomplete elliptic integral of the first kind, F(j|m){F(\varphi|m)} , by using the half argument formulas of Jacobian elliptic functions. The method reduces the magnitude of j{\varphi} by repeated usage of the formulas while fixing m. The method is sufficiently precise in the sense that the maximum relative error is 3–5 machine epsilons at most. Thanks to the simplicity of the half argument formulas, the new procedure is significantly faster than the existing procedures. For example, it runs 20–60% faster than Bulirsch’ function, el1, and 1.9–2.2 times faster than the method using Carlson’s function, R _F .     

Determination of kynurenic acid levels in rat brain microdialysis samples and changes in kynurenic acid levels induced by N‐acetylaspartic acid

The levels of kynurenic acid, an endogenous antagonist of α₇ nicotinic acetylcholine and N‐methyl‐D ‐aspartate receptors, were measured in microdialysis samples obtained from the prefrontal cortices of rats using column‐switching high‐performance liquid chromatography with fluorescence detection. When the perfusate was constantly infused at a rate of 1.0 μ/min, the in vitro recovery of kynurenic acid through the dialysis membrane was approximately 20.4%, and the precision was within 1.31%. Endogenous kynurenic acid in the microdialysis sample was clearly detected using column‐switching high‐performance liquid chromatography. As an application study, N‐acetyl‐L ‐aspartic acid, an endogenous metabolite and precursor of N‐acetyl‐L ‐aspartyl‐L ‐glutamic acid, which is an agonist of metabotropic glutamate receptors, was infused for 120 min through the microdialysis probe. The kynurenic acid level significantly increased during the infusion of N‐acetyl‐L ‐aspartic acid, suggesting that kynurenic acid might have some association with N‐acetyl‐L ‐aspartic acid in vivo. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Strain‐Promoted Double Azide Addition to Octadehydrodibenzo[12]annulene Derivatives

Octadehydrodibenzo[12]annulenes (DBAs), readily available by the oxidative acetylenic coupling of 1,2‐diethynylbenzene derivatives, were reacted with organic azides. As compared to the well‐known strain‐promoted azide‐alkyne cycloaddition (SpAAC) of 5,6,11,12‐tetradehydrodibenzo[a,e][8]annulene, the reactivity of the DBA alkynes was lower due to the lower strain energy. However, the regioselective double azide addition occurred without any side reactions under mild conditions, yielding bis‐triazole products. The structures of the products were confirmed by an X‐ray crystal structure analysis, and the reaction mechanism was studied by ¹H‐NMR spectroscopy and computational studies. It was also found that the DBAs were hardly fluorescent, while the bis‐triazole products showed a green fluorescence with quantum yields up to 5.1 %. Finally, the new strain‐promoted double azide addition to the DBAs was used for step‐growth polymerization, successfully producing a high molecular weight triazole polymer.