Approximate necessary conditions for locally weak Pareto optimality

Necessary conditions for a given pointx ⁰ to be a locally weak solution to the Pareto minimization problem of a vector-valued functionF=(f ₁,...,f _m ),F:XR ^m,XR ^m, are presented. As noted in Ref. 1, the classical necessary condition-conv {Df ₁(x ⁰)|i=1,...,m}T ^*(X, x ⁰) need not hold when the contingent coneT is used. We have proven, however, that a properly adjusted approximate version of this classical condition always holds. Strangely enough, the approximation form>2 must be weaker than form=2.The authors would like to thank the anonymous referee for the suggestions which led to an improved presentation of the paper.     

Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

High-rate Decoupled Water Electrolysis System Integrated with α-MoO3 as a Redox Mediator with Fast Anhydrous Proton Kinetics

Hydrogen is a promising alternative to fossil fuels that can reduce greenhouse gas emissions. Decoupled water electrolysis system using a reversible proton storage redox mediator, where the oxygen evolution reaction and hydrogen evolution reaction are separated in time and space, is an effective approach to producing hydrogen gas with high purity, high flexibility, and low cost. To realize fast hydrogen production in such a system, a redox mediator capable of releasing protons rapidly is required. Herein, α-MoO₃, with an ultrafast proton transfer property that can be explained by a dense hydrogen bond network in the lattice oxygen arrays of HxMoO₃, is examined as a high-rate redox mediator for fast hydrogen production in acidic electrolytes. The α-MoO₃ redox mediator shows both a large capacity of 204 mAh g⁻¹ and fast hydrogen production at a current rate of 10 A cm⁻²(≈153 A g⁻¹), outperforming most of the previously reported solid-state redox mediators.     

Photothermal Heating-Assisted Superior Antibacterial and Antibiofilm Activity of High-Entropy-Alloy Nanoparticles

Antibacterial elements and non-contact heating abilities have been proven effective for antibacterial and antibiofilm activities, but it remains a challenge to integrate both within one material. Herein, assisted by the high-entropy effect, FeNiTiCrMnCu_x high-entropy alloy nanoparticles (HEA-NPs) with excellent photothermal heating properties for boosting antibacterial and antibiofilm performances are synthesized. Benefitting from the synergetic effect of copper ions released and thermal damage by the HEA-NPs, more reactive oxygen species (ROS) are generated, leading to the rupture of the cell membranes and the eradication of the biofilms. As a result, the antibiofilm efficiency (400 µg mL⁻¹) of the mostly optimized FeNiTiCrMnCu_1.0 HEA-NPs in the marine nutrient medium, which is the worst-case scenario for the antimicrobial material, can be improved from 81% to 97.4% under 30 min solar irradiation (1 sun). The present study demonstrates a new strategy for effectively treating marine microorganisms that cause biofouling and microbial corrosion using HEA-NPs with photothermal heating characteristics as an antibacterial auxiliary.     

封装器件多应力叠加失效仿真分析与验证

针对某双列直插式(DIP)封装器件在整机温循试验中出现的失效现象,分析在器件与电路板焊接环节、电路板与整机装配环节和整机温循试验环节3个工况下可能的失效原因,对原因分别进行单工况和多工况的失效仿真分析。针对不同仿真模型在不同工况下的叠加仿真难题,提出基于ANSYS Workbench有限元软件的多应力叠加仿真方法,对比单一工况和多种工况下的仿真结果。结果表明,DIP封装器件失效是器件在焊接尺寸不匹配、过定位装配和温循试验三种工况下,机械应力和热应力的叠加使玻璃绝缘子产生裂纹导致的,有限元仿真结果与实验结果基本吻合,为DIP封装器件在多工况下应力叠加失效的故障机理研究提供一种可参考的仿真方法。     

The determination of starting conditions for modifier optimization in reversed-phase HPLC

Summary After a brief introduction of the subject, the paper focusses on the first step in any optimization procedure: the delineation of the parameter space, wherein the global optimum is to be found. For organic modifier optimization in reversed-phase liquid chromatography it is shown that the necessary information can be derived from a single water-methanol gradient. It first yields an estimate of the total number of solutes in the sample, which is vital to define the peak capacity needed to achieve separation at a certain confidence level. Next, the gradient allows the prediction of suitable isocratic methanol binary solvents, and transfer rules formulate the iso-eluotropic composition of the common binary solvents (tetrahydrofuran and acetonitrile). Because all predictions are based on a statistical analysis of a limited data base, attention is given to the practical situation where an actual sample deviates from the average solute behaviour. Such deviations are revealed in the first isocratic run and can be used to arrive at a better estimate of solute retention.     

On guaranteed stability of uncertain linear systems via linear control

This paper addresses the problem of stabilizing an uncertain linear system. The uncertaintyq(·) which enters the dynamics is nonstistical in nature. That is, noa priori statistics forq(·) are assumed; only boundsQ on the admissible variations ofq(·) are taken as given. The results given here applied to so-called matched systems differ from previous results in two ways. Firstly, the stabilizing control in this paper is linear; for this same class of problems, many of the existing results would require a nonlinear control. Furthermore, those results which do in fact yield linear controls are only valid when a certain matrix (q) (formed using the given data) is negative definite for allq Q. In contrast, the theory given here only requires compactness of the bounding setQ. Secondly, we show that the so-called matching conditions (used in earlier work) can be generalized so as to encompass a larger class of dynamical systems.This research was supported by the US Department of Energy under Contract No. ET-78-S-01-3390.     

Synthesis of α, ω perfluoropolyether iodides

Perfluoropolyether (PFPE) diacyl halides of formula XCOCF₂O[(CF₂O)_n(CF₂CF₂O)_m]_pCF₂COX, with X = Cl, F and molecular weight (MW) 400-4000 g mol⁻¹ are smoothly converted in high yields to the corresponding α, ω diiodides in the absence of solvent, employing KI or LiI at 210 °C with extrusion of CO. During the reactions, β-elimination of COF₂ from the terminal difluoromethylene oxide units (CF₂O, C₁ unit) occurs to some extent until a tetrafluoroethylene oxide unit (OCF₂CF₂, C₂ unit) is encountered yielding a OCF₂CF₂I terminus. This considerably alters the MW distribution of the final diiodide especially for low MW PFPEs. Operating in supercritical conditions of CO (scCO) or both scCO and CO₂ (scCO₂) on low (<600 g mol⁻¹) MW diacyl halides, lowers β-elimination from 95 to 52 mol% if KI is used or from 43 to 30 mol% if LiI is used. With higher MW (>600 g mol⁻¹) β-elimination is lowered from 15 to <1 mol% in scCO conditions employing KI.     

An open optimization problem in statistical quality control

We ask the experts in global optimization if there is an efficient solution to an optimization problem in acceptance sampling: Here, one often has incomplete prior information about the quality of incoming lots. Given a cost model, a decision rule for the inspection of a lot may then be designed that minimizes the maximum loss compatible with the available information. The resulting minimax problem is sometimes hard to solve, as the loss functions may have several local maxima which vary in an unpredictable way with the parameters of the decision rule.