Approximations of Nash equilibria

Inspired by previous works on approximations of optimization problems and recent papers on the approximation of Walrasian and Nash equilibria and on stochastic variational inequalities, the present paper investigates the approximation of Nash equilibria and clarifies the conditions required for the convergence of the approximate equilibria via a direct approach, a variational approach, and an optimization approach. Besides directly addressing the issue of convergence of Nash equilibria via approximation, our investigation leads to a deeper understanding of various notions of functional convergence and their interconnections; more importantly, the investigation yields improved conditions for convergence of the approximate Nash equilibria via the variational approach. An illustrative application of our results to the approximation of a Nash equilibrium in a competitive capacity expansion model under uncertainty is presented.     

Trace determination of dichlorodiphenyltrichloroethane and its main metabolites in environmental water samples with dispersive liquid–liquid microextraction in combination with high performance liquid chromatography and ultraviolet detector

Dichlorodiphenyltrichloroethane,1,1,1-trichloro-2,2-bis(p-chlorophenyl)ethane (DDT) and its main metabolites have been paid much more attention, and present paper describes a new process for the rapid determination of such pollutants in environmental water samples based on dispersive liquid–liquid microextraction (DLLME) and high performance liquid chromatography with ultraviolet detector, which has merits such as high enrichment factor and sensitivity, low cost and easy to operate. Significant parameters such as extraction solvent and dispersive solvent type and volume, pH, extraction time and centrifuging time, which would have important impact on the enrichment of target pollutants, have been investigated in detail. The results exhibited that excellent performance could be achieved with carbon tetrachloride and acetonitrile as the extraction solvent and dispersive solvent, respectively. Under the optimal conditions, excellent linear relationship was gained in the range of 1.0–50 μg L⁻¹, and detection limits were in the range of 0.32–0.51 μg L⁻¹. The precisions of the proposed method were in the range of 2.80–7.50% (RSD). The proposed method was validated with real water samples, and the results indicated the spiked recoveries were in the range of 85.58–119.6% and the established method was very good and competitive in the determination of DDT and its metabolites.     

Pt adsorption on the PbTiO3(110) polar surface: a density functional theory study

The monolayer (ML) and submonolayer Pt on both terminations of PbTiO₃(110) polar surface have been studied by using density functional theory (DFT) with projector‐augmented wave(PAW) potential and a supercell approach. The most favored ML Pt arrangements on PbTiO and O₂ terminations are the hollow site and the short‐bridge site, respectively. By examining the geometries of different ML arrangements, we know that the dominant impetus for stability of the favored adsorption site for PbTiO termination is the Pt–Ti interaction (mainly from covalent bonding), while that for O₂ termination is the Pt–O interaction (mainly from ionic bonding). In addition, the appearance of the gap electronic states in the outermost layers of each termination indicates that a channel for charge transfer between adsorbed layer and substrate is formed. Moreover, the interface hybridization between Pt 5d and O 2p orbitals is also observed, especially for ML Pt on O₂ termination. The stability sequences for various arrangements of 1/2 ML Pt adsorption conform well with those of ML Pt adsorption, and the most stable arrangement is energetically more favorable than the corresponding ML coverage in the view of adsorption energy maximization. The behavior, i.e. the increase in adsorption energy with decrease in coverage, indicates that Pt? Pt interactions weaken those between Pt and the substrate. Copyright © 2009 John Wiley & Sons, Ltd.     

Construction of a universal model for non-invasive identification of cephalosporins for injection using near-infrared diffuse reflectance spectroscopy

A universal classification model has been developed for identification of 26 different products of cephalosporins for injection using near-infrared (NIR) spectroscopy. A total of 324 batches of the 26 products, from 166 manufacturers in China, were used in the study. The classification model was a principle component analysis (PCA)-based method consisting of a primary identification library with four sub-libraries. The accuracy and specificity of the model were tested and were both found to be approximately 95%. The transfer of the classification model between different instruments of the same brand and the same instrument model has been investigated in this study. This study has shown that it is feasible to build a universal classification model to quickly screen for counterfeit drugs in the open market and distribution channels.     

Wintersweet Branch‐Like C/C@SnO2/MoS2 Nanofibers as High‐Performance Li and Na‐Ion Battery Anodes

Structure and morphology of molybdenum disulfide (MoS₂) play an important role in improving its reversible lithium storage and sodium storage as anodes. In this study, a facile method is developed to prepare C/C@SnO₂/MoS₂ nanofibers with MoS₂ nanoflakes anchoring on the core–shell C/C@SnO₂ nanofibers through hydrothermal reaction. By adjusting the concentration of MoS₂ precursors, the synthesized MoS₂ with different slabs dimensions, size, and morphologies are obtained, constituting budding and blooming wintersweet branch‐like composite structure, respectively. Owing to scattered MoS₂ nanoparticles and sporadic MoS₂ nanoflakes, the budding wintersweet branch‐like composite nanofibers processes less slabs of staking in number and large specific surface area. Benefiting from the exposed C@SnO₂ shell layer, the synergistic effect among SnO₂, carbon, and MoS₂ is strengthened, which maximizes the advantage of each material to exhibit stable specific capacities of 650 and 230 mAh g^?1 for Li‐ion batteries and Na‐ion batteries after 200 cycles.     

KDP晶体微纳米加工表层缺陷对其激光损伤阈值的影响

使用有限元方法分析了在激光辐照条件下,KDP晶体已加工表面存在的残余内应力、微裂纹及微孔等多种微纳米加工表层缺陷对晶体激光损伤阈值的影响。通过分析发现:KDP晶体微纳米加工表层缺陷的存在,会影响晶体表面的温度场及热应力场的分布,使入射激光的能量积聚在缺陷附近的很小范围内,造成晶体缺陷处产生局部熔融现象,从而使KDP晶体产生损伤,降低KDP晶体的激光损伤阈值。针对微纳米表层的微裂纹进行了损伤阈值测试实验,结果表明微裂纹的存在会降低KDP晶体的激光损伤阈值(约降低3J/cm2),实验结果与仿真结果符合得很好。     

氨水降膜吸收传热传质强化的研究进展

综述了近年来应用于氨水降膜吸收性能强化的研究成果,总结了氨水降膜吸收的强化方法,分析了氨水降膜吸收过程中的影响因素,指出研究中的一些不足,并对该领域未来的研究方向进行了讨论,指出采用物理处理、化学处理和纳米技术三种强化手段相结合的方法是未来强化吸收可能的发展趋势。     

漫透射成像法激光强度时空分布测量装置

 提出用CCD漫透射成像法测量激光强度时空分布和激光功率,给出了测量原理, 简要叙述了装置总体结构,介绍了测量装置各部分,给出了散射屏的散射特性,重点分析了光路布局、镜头焦距、光圈、景深、滤光片的参数选择,介绍了数据处理软件,给出了激光强度分布测量实验结果。结果表明：漫透射成像法测量激光强度时空分布是可行的,该装置测量强度分布分辨力高达5 mm;测量功率准确、可靠,测量不确定度小于6%,使用方便,实现了在小空间内对大光斑进行功率和强度分布的同时准确测量。     

Optical out-of-plane spin polarization and charge conductivities in spin-orbit-coupled systems in the presence of an in-plane magnetic field

Out-of-plane spin and charge responses to the terahertz field for a clean two-dimensional electron gas with a Rashba spin-orbit interaction in the presence of an in-plane magnetic field are studied. We show that the characteristic optical spectral behavior is remarkably different from that of the system in the absence of in-plane magnetic fields. It is found that the optical spin polarization normal to the plane is nonzero even for this clean system, in sharp contrast to the static case. Due to the combined effect of spin-orbit coupling and in-plane magnetic field, both diagonal and off-diagonal components of optical charge conductivity tensor are nonvanishing. It is indicated that one can control the spin polarization and the optical current by adjusting the optical frequency. In addition, the out-of-plane spin polarization and conductivities strongly rely on the direction of the external magnetic field. Nevertheless, they meet different angle-dependent relations. This dynamical out-of-plane spin polarization could be measured by the time-resolved Kerr rotation technique.