Structure of extreme correlated equilibria: a zero-sum example and its implications

We exhibit the rich structure of the set of correlated equilibria by analyzing the simplest of polynomial games: the mixed extension of matching pennies. We show that while the correlated equilibrium set is convex and compact, the structure of its extreme points can be quite complicated. In finite games the ratio of extreme correlated to extreme Nash equilibria can be greater than exponential in the size of the strategy spaces. In polynomial games there can exist extreme correlated equilibria which are not finitely supported; we construct a large family of examples using techniques from ergodic theory. We show that in general the set of correlated equilibrium distributions of a polynomial game cannot be described by conditions on finitely many moments (means, covariances, etc.), in marked contrast to the set of Nash equilibria which is always expressible in terms of finitely many moments.     

Convergence rate for consensus with delays

We study the problem of reaching a consensus in the values of a distributed system of agents with time-varying connectivity in the presence of delays. We consider a widely studied consensus algorithm, in which at each time step, every agent forms a weighted average of its own value with values received from the neighboring agents. We study an asynchronous operation of this algorithm using delayed agent values. Our focus is on establishing convergence rate results for this algorithm. In particular, we first show convergence to consensus under a bounded delay condition and some connectivity and intercommunication conditions imposed on the multi-agent system. We then provide a bound on the time required to reach the consensus. Our bound is given as an explicit function of the system parameters including the delay bound and the bound on agents’ intercommunication intervals.     

Electronic structure of two coupled Si δ-doped GaAs as dependent on the donor thickness

For the uniform distribution we have theoretically investigated the influence of donor thickness on two coupled Si -doped GaAs structure, at T=0 K. Electronic structure have been calculated by solving the Schrödinger and Poisson equations self-consistently. We thus find the confining potential, the electronic density, the subband energies and their eigen envelope functions, the subband occupations and Fermi energy. From the self-consistent calculation, we have seen that the effective potential profile and the electronic density of two coupled Si -doped GaAs structure are sensitive to the donor thickness while the subband energies and the subband occupations are not sensitive to the donor thickness . PACS 73.20.Dx; 73.20.At; 73.90.+f     

Effects of hydrogen bonding on the monolayer properties of amphiphilic double-decker-shaped polyhedral silsesquioxanes

"Core-corona" type amphiphiles, which comprise double-decker-shaped POSSs (DDSQs) as the core and two or four di(ethylene glycol) (DEG) units as the coronae, have recently been reported to form a stable monolayer at the air-water interface. In this paper, another core-corona amphiphile, 2DEGNH-DDSQ, which has a urethane group at the end of the coronae, was synthesized to elucidate the effects of hydrogen bonding on monolayer properties. The surface pressure-area isotherm and Brewster angle microscopy revealed that 2DEGNH-DDSQ initially formed rodlike assemblies. They subsequently coalescence to form a uniform monolayer with compression. Actually, 2DEGNH-DDSQs are well ordered in the rodlike assembly because of the strong hydrogen bonds among the urethane groups, as confirmed by FT-IR spectra. Although the monolayer was not transferred onto a solid substrate, mixing of 2DEGNH-DDSQ with 2DEG-DDSQ, which has already been reported to form a liquidlike monolayer, overcame this problem. The 1:1 molar mixture of 2DEGNH-DDSQ and 2DEG-DDSQ forms a uniform liquidlike monolayer. The mixed monolayer was transferred onto a solid substrate as a Z-type Langmuir-Blodgett film. Atomic force microscopic (AFM) images of the mixed-bilayer film showed a uniform surface with root-mean-square surface roughness of 0.21 nm. The intermolecular hydrogen bonds between the urethane groups in 2DEGNH-DDSQ and the hydroxyl groups in 2DEG-DDSQ improve the monolayer properties, which enable successful transfer of the LB film.     

Langmuir-Blodgett films composed of amphiphilic double-decker shaped polyhedral oligomeric silsesquioxanes

New amphiphilic polyhedral oligomeric silsesquioxanes (POSSs) were synthesized, and their monolayer behavior on a water surface and Langmuir-Blodgett (LB) film formation were studied. Two kinds of amphiphilic POSS molecules, which have two or four di(ethylene glycol) units (2OH-DDSQ and 4OH-DDSQ, respectively), were synthesized by direct hydrosilylation of di(ethylene glycol) vinyl ether with double-decker shaped polyhedral oligomeric silsesquioxanes (DDSQs). Surface pressure (π)-area (A) isotherms and Brewster angle microscope (BAM) measurements indicated that both amphiphilic DDSQs form a stable monolayer at the air-water interface. In addition, 4OH-DDSQ can be deposited on a solid substrate by the LB technique. Atomic force microscope (AFM) images of a one-layer 4OH-DDSQ film showed a homogenous uniform surface on a hydrophilic silicon substrate, whereas nanometer scale dots were formed on a hydrophobic silicon substrate. Multilayer deposition on a hydrophobic substrate resulted in an increase of dot size with increasing deposition number of layers. Moreover, homogenous multilayer films with a few voids were obtained on a hydrophilic substrate. The results indicate that 4OH-DDSQ is a good candidate for preparing hybrid nanoassemblies.     

Synthesis and magnetic properties of a porphine-based photosynthesizer with magnetic nano-carriers

The coupling of benzyl protected dopamine with meso-tetra(4-carboxyphenyl)porphine (m-TCPP) and a simple deprotection by hydrogenation under catalyst (Pd/C) to remove the benzyl groups afforded the meso-tetra(4-carboxyphenyl)porphine-dopamine conjugate, m-TCPPD (1). Previously prepared superparamagnetic iron oxide nanoparticles (SPIONs) were coated with m-TCPPD by sonication in methanol, and then the m-TCPPD coated SPIONs (2) were separated with a permanent magnet. The microstructure and magnetic properties of the m-TCPPD coated SPIONs were characterized by UV, ¹H NMR, MALDI MS, XRD, TEM, FT-IR, TGA and VSM. The crystallite size obtained from X-ray line profile fitting is comparable with the particle size obtained from TEM. Magnetization measurements reveal that m-TCPPD coated SPIONs do not reach saturation even at high fields. The absence of remanance and weak magnetization, which are characteristic features of superparamagnetics, has been observed. The average particle size has been determined, by fitting the Langevin function to the experimental M−H hysteresis curves, as approximately 8 nm.     

A simple microfluidic probe of nanoparticle suspension stability

We describe a simple experimental tool that enables stability of multicomponent nanoparticle suspensions to be readily assessed by establishing a confinement-imposed chemical discontinuity at the interface between co-flowing laminar streams in a microchannel. When applied to examine Al(2)O(3) nanoparticle suspensions, this method readily reveals compositions that are susceptible to aggregation even when conventional bulk measurements (zeta potential, dynamic light scattering, bulk viscosity) suggest only subtle differences between formulations. This microfluidic stability test enables simple and rapid assessment of quality and variability in complex multicomponent mixtures for which few, if any, comparable data exist. The paradoxical ease at which localized aggregation can be triggered in suspensions that would otherwise appear stable also serves as a caution to researchers undertaking tracer-based studies of nanomaterial suspensions.     

Combining Step-Growth and Chain-Growth Polymerizations in One Pot: Light-Induced Fabrication of Conductive Nanoporous PEDOT-PCL Scaffold

A novel method based on light-induced fabrication of a poly (3,4-ethylenedioxythiophene)-polycaprolactone (PEDOT-PCL) scaffold using phenacyl bromide (PAB) as a single-component photoinitiator is presented. HBr released from the step-growth polymerization of EDOT is utilized as an in situ catalyst for the chain-growth polymerization of ε-caprolactone. Detailed investigations disclose the formation of a self-assembled nanoporous electroconductive scaffold (1.2 mS cm⁻¹). Fluorescence emission spectra of the fabricated scaffold exhibit a mixed solvatochromic behavior, indicating specific interactions between the self-assembled scaffold and solvents with varying polarities, as evidenced by transmission electron microscopy (TEM). Moreover, the same light-induced technique can also be applied for bulk photopolymerization showcasing the versatility and wide-ranging scope of the originated method. In brief, this study introduces a novel approach for light-induced polymerization reactions that is merging step-growth and chain-growth mechanisms. This innovative approach is promising to facilitate in situ polymerization of monomers possessing diverse functionalities.