Two-level primal–dual proximal decomposition technique to solve large scale optimization problems

We describe a primal–dual application of the proximal point algorithm to nonconvex minimization problems. Motivated by the work of Spingarn and more recently by the work of Hamdi et al. about the primal resource-directive decomposition scheme to solve nonlinear separable problems. This paper discusses some local results of a primal–dual regularization approach that leads to a decomposition algorithm.     

Generalized nonlinear Schrödinger equation with time-dependent dissipation

The generalized nonlinear Schrödinger equation with time-dependent dissipation [1] is considered using decomposition [2].     

A variable-penalty alternating directions method for convex optimization

We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems. This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF Grants CCR-8907671, CDA-9024618 and CCR-9306807.     

可列集合套

[1]中给出模糊集的分解定理与表现定理，指出可利用集合套H＝{H（λ）|λ∈[0,1]}刻化模糊集。本文定义可列集合套H＝{H（a）|a∈Q}，Q是（0，1）的可列稠密子集。相应地给出新的分解定理与表现定理。指出可利用可列集合套刻化的模糊集。     

基于连续小波变换下的土壤有害元素砷含量估测

与传统检测方法相比,利用高光谱技术进行土壤有害元素砷含量的估算,具有快速、准确,成本低的特点,可对干旱区绿洲土壤有害元素砷污染进行动态监测。基于新疆渭干河-库车河三角洲绿洲耕层土壤样品的采集,获取土壤光谱数据和有害元素砷含量。通过bior1.3,db4,gaus4和mexh这4种小波基函数对土壤原始光谱反射率进行连续小波变换,并将变换后光谱数据与有害元素砷进行相关分析,以筛选出的敏感小波系数为自变量,采用偏最小二乘回归、支持向量机回归、BP神经网络和随机森林回归方法对有害元素砷含量进行高光谱反演。研究结果显示：（1）4种小波基函数在3~8尺度的光谱分解效果明显优于其他尺度,特别是4~6尺度的连续小波变换有效提升了光谱反射率与土壤有害元素砷之间的相关性,通过显著性检验的小波系数数量有了明显增多（p<0.01）,在可见光的400~700 nm以及近红外的1 100~1 700和2 200~2 400 nm附近具有较强的相关性;（2）通过比较4种小波基函数对光谱数据中有效信息的辨识能力,认为小波基函数bior1.3和mexh要优于db4和gaus4,其中bior1.3的光谱分解效果最好,gaus4相对最弱;通过bior1.3第5尺度的光谱变换,与土壤有害元素砷显著相关的波段数量最多,为507个（p<0.01）;（3）比较4种建模方法的反演结果发现,SVMR,BPNN和RFR模型相较于PLSR模型具有更强的估测能力,模型的估测精度更高。综合分析各模型的稳定性及估测精度后,认为bior1.3-25-RFR模型可作为研究区土壤有害元素砷的最佳估测模型。该模型的训练集和验证集的R2分别为0.893和0.639,RMSE为1.075和1.651 mg·kg-1,RPD分别为2.89和1.64,表明模型估测效果较好,稳定性较强。采用合适的小波基函数进行连续小波变换可减少土壤高光谱数据中的白噪声,挖掘出土壤光谱数据中的有效信息,对土壤有害元素砷含量的准确估测提供有力的技术保障。     

Synthesis of Nitrogen Doped Multilayered Graphene Flakes: Selective Non‐enzymatic Electrochemical Determination of Dopamine and Uric Acid in presence of Ascorbic Acid.

Nitrogen doped multilayered graphene (NDMLG) is synthesized by annealing the black fluffy mass obtained by decomposing the complex prepared from Zn(OAc)₂, diethanolamine and triethanolamine. The NDMLG has been characterized by HRTEM, FESEM, XRD, XPS, Raman spectroscopy, BET which indicate formation of nitrogen doped multilayer graphene flakes with high surface area. NDMLG shows better electrochemical oxidation property towards Dopamine, Uric acid and Ascorbic acid. The linear response ranges for determination of DA, UA and AA are 0.5–150 µM, 3–60 µM and 80–2000 µM respectively and the detection limits (S/N=3) are 15 nM, 15 nM, 580 nM, respectively in the mixture.     

Analysis of volatile organic compounds released from the decay of surrogate human models simulating victims of collapsed buildings by thermal desorption–comprehensive two-dimensional gas chromatography–time of flight mass spectrometry

Field experiments were devised to mimic the entrapment conditions under the rubble of collapsed buildings aiming to investigate the evolution of volatile organic compounds (VOCs) during the early dead body decomposition stage. Three pig carcasses were placed inside concrete tunnels of a search and rescue (SAR) operational field terrain for simulating the entrapment environment after a building collapse. The experimental campaign employed both laboratory and on-site analytical methods running in parallel. The current work focuses only on the results of the laboratory method using thermal desorption coupled to comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (TD-GC × GC-TOF MS). The flow-modulated TD-GC × GC-TOF MS provided enhanced separation of the VOC profile and served as a reference method for the evaluation of the on-site analytical methods in the current experimental campaign. Bespoke software was used to deconvolve the VOC profile to extract as much information as possible into peak lists. In total, 288 unique VOCs were identified (i.e., not found in blank samples). The majority were aliphatics (172), aromatics (25) and nitrogen compounds (19), followed by ketones (17), esters (13), alcohols (12), aldehydes (11), sulfur (9), miscellaneous (8) and acid compounds (2). The TD-GC × GC-TOF MS proved to be a sensitive and powerful system for resolving the chemical puzzle of above-ground “scent of death”.     

New POCOP-type pincer complexes of Nickel(II)

The pincer complex [(POCOP)Ni(NCMe)][OSO₂CF₃] (1: POCOP = {2,6-(i-Pr₂PO)₂C₆H₃}) undergoes an acetonitrile substitution reaction in the presence of CN(t-Bu), KCN, and KOCN to give the new complexes [(POCOP)Ni{CN(t-Bu)}][O₃SCF₃] and (POCOP)Ni(X) (X = CN and NCO). The Ni-CN derivative is also obtained from a gradual decomposition of the Ni-CN(t-Bu) derivative, while the aquo derivative [(POCOP)Ni(OH₂)][O₃SCF₃] was obtained from slow hydrolysis of (POCOP)Ni(OSO₂CF₃). All new complexes have been characterized spectroscopically and by X-ray crystallography. IR and solid state structural data indicate that Ni-L/X interactions are dominated by ligand-to-metal σ-donation; presence of little or no π-backbonding is consistent with the electrophilicity of the cationic fragment [(POCOP)Ni]⁺.     

超级铝热剂Al/CuO前驱体的制备、表征、热分解机理及非等温分解反应动力学

以硝酸铜、无水乙醇、1,2-环氧丙烷和纳米铝粉为原料, 在超声振荡条件下, 采用溶胶-凝胶法制备了纳米复合含能材料——超级铝热剂Al/CuO的前驱体. 利用热重-差示扫描量热-傅里叶变换红外-质谱(TG- DSC-FTIR-MS)联用技术, 研究了纳米Al/CuO溶胶-凝胶前驱体的热行为和分解过程及机理. 利用不同升温速率下的TG-DTG分析, 研究了纳米超级铝热剂Al/CuO的溶胶-凝胶前驱体的热分解反应机理, 采用了6种动力学分析方法进行动力学参数计算, 得到前驱体分解反应的表观活化能、反应级数、频率因子等动力学参数, 纳米Al/CuO前驱体分解反应的动力学方程为: dα/dt=10^14.0×4α^3/4exp(-2.0×10⁴/T).     

A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces.