Equivalence of the generalized complementarity problem to differentiable unconstrained minimization

We consider an unconstrained minimization reformulation of the generalized complementarity problem (GCP). The merit function introduced here is differentiable and has the property that its global minimizers coincide with the solutions of GCP. Conditions for its stationary points to be global minimizers are given. Moreover, it is shown that the level sets of the merit function are bounded under suitable assumptions. We also show that the merit function provides global error bounds for GCP. These results are based on a condition which reduces to the condition of the uniform P-function when GCP is specialized to the nonlinear complementarity problem. This condition also turns out to be useful in proving the existence and uniqueness of a solution for GCP itself. Finally, we obtain as a byproduct an error bound result with the natural residual for GCP.We thank Jong-Shi Pang for his valuable comments on error bound results with the natural residual for the nonlinear complementarity problem. We are also grateful to the anonymous referees for some helpful comments. The research of the second author was supported in part by the Science Research Grant-in-Aid from the Ministry of Education, Science, and Culture, Japan.     

New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

A Small One-Fiber WDM Optical Ethernet PC Card for FTTD

A new generation of network interface card for fiber-to-the-desktop has been fabricated. The fabricated card is PC-card size and suitable for notebook PCs. It could become the key element in the coming optical Ethernet age.     

Novel fluorescent asparaginyl-N-acetyl-d-glucosamines (Asn-GlcNAc) for the resolution of oligosaccharides in glycopeptides, based on enzyme transglycosylation reaction

Several fluorescent asparaginyl-N-acetyl-d-glucosamines (Asn-GlcNAcs), i.e., DBD-Asn-GlcNAc, NBD-Asn-GlcNAc, NDA-Asn-GlcNAc, PS-Asn-GlcNAc, FITC-Asn-GlcNAc, DMEQ-Asn-GlcNAc and DBD-PZ-Boc-Asn-GlcNAc, were synthesized as the acceptors for the resolution of oligosaccharides in glycopeptides. The resolution of oligosaccharides is based on the transglycosylation reaction with end-β-N-acetylglucosaminidase (Endo-M), isolated from Mucor hiemalis. The synthesis of each fluorescent acceptor was carried out in a one-pot reaction of Asn-GlcNAc and the corresponding fluorescent tagging reagent. The transglycosylation reaction using Endo-M proceeds at RT in neutral phosphate buffer (pH 6.0) and reached maxima at around 30 min. When Fmoc-Asn-GlcNAc (acceptor) was enzymatically reacted with Disialo-Asn (donor) in the presence of Endo-M, the ratio of Disialo-Asn-Fmoc (transglycosylation product) was almost comparable with the decreasing ratio of Fmoc-Asn-GlcNAc. Therefore, the transglycosylation activity of Endo-M from Disialo-Asn (donor) and fluorescent-Asn-GlcNAc (acceptor) was calculated from the decreasing ratio of fluorescent-Asn-GlcNAc. The order was NDA-Asn-GlcNAc > DBD-Asn-GlcNAc Fmoc-Asn-GlcNAc > NBD-Asn-GlcNAc DMEQ-Asn-GlcNAc > DNS-Asn-GlcNAc > PS-Asn-GlcNAc > FITC-Asn-GlcNAc. On the other hand, the activity with a fluorescent acceptor (DBD-PZ-Boc-Asn-GlcNAc), labeled to a carboxylic acid group in the Asn residue, was the strongest among the synthesized acceptors.     

Influence of RNA Strand Rigidity on Polyion Complex Formation with Block Catiomers

Polyion complexes (b‐PICs) are prepared by mixing single‐ or double‐stranded oligo RNA (aniomer) with poly(ethylene glycol)‐b‐poly(l ‐lysine) (PEG‐PLL) (block catiomer) to clarify the effect of aniomer chain rigidity on association behaviors at varying concentrations. Here, a 21‐mer single‐stranded RNA (ssRNA) (persistence length: 1.0 nm) and a 21‐mer double‐stranded RNA (small interfering RNA, siRNA) (persistence length: 62 nm) are compared. Both oligo RNAs form a minimal charge‐neutralized ionomer pair with a single PEG‐PLL chain, termed unit b‐PIC (uPIC), at low concentrations (<≈0.01 mg mL⁻¹). Above the critical association concentration (≈0.01 mg mL⁻¹), ssRNA b‐PICs form secondary associates, PIC micelles, with sizes up to 30–70 nm, while no such multimolecular assembly is observed for siRNA b‐PICs. The entropy gain associated with the formation of a segregated PIC phase in the multimolecular PIC micelles may not be large enough for rigid siRNA strands to compensate with appreciably high steric repulsion derived from PEG chains. Chain rigidity appears to be a critical parameter in polyion complex association.

     

Controlled-release system mediated by a retro Diels-Alder reaction induced by the photothermal effect of gold nanorods

Controlled-release systems that respond to external stimuli have received great interest for use in medical treatments such as for drug delivery to specific sites. Gold nanorods have an absorption band at the near-infrared region and convert the absorbed light energy into heat, which is known as a "photothermal effect". Therefore, gold nanorods are expected to act not only as an on-demand thermal converter for photothermal therapy but also as a controller of a drug-release system capable of responding to the near-infrared light irradiation. In this study, to construct a controlled-release system that responds to near-infrared light irradiation, we modified gold nanorods with polyethylene glycol (PEG) through Diels-Alder cycloadducts. When the modified gold nanorods were irradiated by near-infrared light, the PEG chains were released from the gold nanorods because of the retro Diels-Alder reaction induced by the photothermal effect. As a result of the PEG release, the gold nanorods formed aggregates. This type of controlled-release system coupled with the aggregate formation of the gold nanorods triggered by near-infrared light could be expanded to applications of gold nanorods in medical fields such as drug and photothermal therapy.     

Variational Inequality Formulation of a Class of Multi-Leader-Follower Games

The multi-leader-follower game can be looked on as a generalization of the Nash equilibrium problem and the Stackelberg game, which contains several leaders and a number of followers. Recently, the multi-leader-follower game has been drawing more and more attention, for example, in electricity power markets. However, when we formulate a general multi-leader-follower game as a single-level game, it will give rise to a lot of problems, such as the lack of convexity and the failure of constraint qualifications. In this paper, to get rid of these difficulties, we focus on a class of multi-leader-follower games that satisfy some particular, but still reasonable assumptions, and show that these games can be formulated as ordinary Nash equilibrium problems, and then as variational inequalities. We establish some results on the existence and uniqueness of a leader-follower Nash equilibrium. We also present illustrative numerical examples from an electricity power market model.     

Preparation, characterization and biodegradation of biopolymer nanocomposites based on fumed silica

PLA and PCL based nanocomposites prepared by adding three different types of fumed silica were obtained by melt blending. Materials were characterized by means of Scanning Electron Microscopy (SEM), Differential Scanning Calorimetry (DSC), Thermogravimetric Analysis (TGA) and Dynamic–Mechanical Thermal Analysis (DMTA).A good distribution of the fumed silica into both polymer matrices was observed. The highest thermo-mechanical improvements were reached by addition of the fumed silica with higher surface area. PLA and its nanocomposites were degraded in compost at 58 °C; at this temperature all samples presented a significant level of polymer degradation, but a certain protection action of silica towards PLA degradation was observed, whereas the addition of fumed silica did not show considerable influence on the degradation trend of PCL. These dissimilarities were attributed to the different degradation mechanism of the two polymers.