Convergence rates of a global optimization algorithm

Second order conditions for the (pseudo-) convexity of a function restricted to an affine subspace are obtained by extending those already known for functions on ⁿ . These results are then used to analyse the (pseudo-) convexity of potential functions of the type introduced by Karmarkar.This research was completed while the first author was on sabbatical leave at the Département d'Informatiques et de Recherche Opérationelle, Université de Montréal, and supported by NSERC (grant Q015807). This research was also supported by NSERC (grants A8312 and A5408) and la Coopération franco-québécoise (project 20-02-13).     

单A直和子空间

引入单直和子空间的概念,证明了线性空间可唯一分解为单直和子空间的直和,并且给出了计算方法.     

Optimization of Antioxidant Synergy in a Polyherbal Combination by Experimental Design

Culinary herbs and spices are known to be good sources of natural antioxidants. Although the antioxidant effects of individual culinary herbs and spices are widely reported, little is known about their effects when used in combination. The current study was therefore undertaken to compare the antioxidant effects of crude extracts and essential oils of some common culinary herbs and spices in various combinations. The antioxidant interactions of 1:1 combinations of the most active individual extracts and essential oils were investigated as well as the optimization of various ratios using the design of experiments (DoE) approach. The 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2-azinobis (3-ethylbenzothiazoline-6-sulphonic acid) (ABTS), and ferric reducing antioxidant power (FRAP) assays were used to determine the antioxidant activity, and MODDE 9.1^® software (Umetrics AB, Umea, Sweden) was used to determine the DoE. The results revealed synergism for the following combinations: Mentha piperita with Thymus vulgaris methanol extract (ΣFIC = 0.32 and ΣFIC = 0.15 using the DPPH and FRAP assays, respectively); Rosmarinus officinalis with Syzygium aromaticum methanol extract (ΣFIC = 0.47 using the FRAP assay); T. vulgaris with Zingiber officinalis methanol extracts (ΣFIC = 0.19 using the ABTS assay); and R. officinalis with Z. officinalis dichloromethane extract (ΣFIC = 0.22 using the ABTS assay). The DoE produced a statistically significant (R2 = 0.905 and Q2 = 0.710) model that was able to predict extract combinations with high antioxidant activities, as validated experimentally. The antioxidant activities of the crude extracts from a selection of culinary herbs and spices were improved when in combination, hence creating an innovative opportunity for the future development of supplements for optimum health.     

基于无消相干子空间的量子避错码设计

针对量子系统的联合消相干模型,可以找到一些不受消相干错误影响的系统状态,这种状态被称为相干保持态,所有相干保持态构成的空间就称为无消相干子空间(decoherencefreesubspace,缩写为DFS).利用DFS的特性可以实现自动容错的量子避错码.首先提出一种DFS的定义,并且以定理的形式证明其他DFS的定义都是等价的.然后给出了DFS的存在性定理.最后利用群论的方法设计一种构造DFS的简单方法 关键词： 相干保持态 无消相干子空间 量子避错码 容错量子计算     

计及气动和隐身约束结构综合优化的并行子空间优化方法

通过分析基于响应面的并行子空间优化算法的特点指出并行子空间优化算法学科级优化的作用在于向系统级优化响应面提供性能优良的设计点.在此基础上,建立了不要求学科级优化的改进的并行子空间优化算法,进一步降低了设计优化的计算量,解决了分析模块与优化模块间的接口困难.依据该算法建立了结构、气动和隐身一体化设计优化框架,实现了某无人机机翼计及气动和隐身约束的结构综合优化.     

关于量子体系的高效相干能量转移的最优初始化的研究

For an energy transfer network, the irreversible depletion of excited electron energy occurs through either an efficient flow into an outer energy sink or an inefficient decay. With a small decay rate, the energy transfer efficiency is quantitatively reflected by the average life time of excitation energy before being trapped in the sink where the decay process is omitted. In the weak dissipation regime, the trapping time is analyzed within the exciton population subspace based on the secular Redfield equation. The requirement of the noise-enhanced energy transfer is obtained, where the trapping time follows an exact or approximate 1/Γ-scaling of the dissipation strength Γ. On the opposite side, optimal initial system states are conceptually constructed to suppress the 1/Γ-scaling of the trapping time and maximize the coherent transfer efficiency. Our theory is numerically testified in four models, including a biased two-site system, a symmetric three-site branching system, a homogeneous onedimensional chain, and an 8-chromophore FMO protein complex.     

Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional （2D） systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.     

Radical polymerization in the presence of peroxide and reducing agent monomer for branched polymers

In this article, we report the radical polymerization in the presence of peroxide and commercially available or designed reducing agent monomer (RAM) for the preparation of branched poly(methyl methacrylate)s (PMMAs). The reaction behavior of the RAM was studied by NMR. Triple‐detection SEC (TD‐SEC) analysis was used to confirm the branching structure of the prepared PMMAs and to investigate the influence of peroxide concentration and RAM concentration on molecular weight and branched structure. The obtained branched PMMAs exhibited high molecular weights and relatively narrow polydispersities at high conversion of MMA. Interestingly, a significant increase in molecular weight and degree of branching of the obtained polymers are observed in higher BPO concentration, these results are quite different from that reported in the literature. The unique radical polymerization mechanism in the RAM/BPO redox‐initiated radical polymerization system resulted in branched PMMAs with high molecular weights at relatively high RAM and BPO concentrations. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 833–840     

High efficiency of Mn–Ce‐modified TiO2 catalysts for the low‐temperature oxidation of Hg0 under a reducing atmosphere

Manganese‐ and cerium oxide‐modified titania catalysts were prepared by the deposition precipitation for the removal of elemental mercury (Hg⁰) from simulated yellow phosphorus off‐gas at low temperature. In addition, these catalysts were characterized by X‐ray diffraction, Brunauer–Emmett–Teller measurements, X‐ray photoelectron spectroscopy and field‐emission scanning electron microscope to determine the surface morphology of the obtained compounds and explore their formation mechanism. The results revealed that a Mn–Ce loading and reaction temperature of 10% and 150 °C, respectively, as well as a Mn/Ce molar ratio of 2:1, led to an optimal efficiency for the oxidation of elemental mercury. Furthermore, the effects of flue gas components were investigated. The presence of O₂ clearly promoted the oxidation of Hg⁰. A CO atmosphere did not affect the Hg⁰ oxidation, when compared with N₂, whereas the presence of H₂S and water vapor inhibited the oxidation process. Furthermore, the X‐ray photoelectron spectroscopy spectra of Hg 4f revealed that the elemental mercury adsorbed by the catalyst is present as HgO. Finally, the Hg⁰ catalytic oxidation mechanism was discussed on the basis of the experimental results and characterization analysis.