Thioether‐Bearing Hyperbranched Polyether Polyols with Methionine‐Like Side‐Chains: A Versatile Platform for Orthogonal Functionalization

The synthesis of thioether‐bearing hyperbranched polyether polyols based on an AB/AB₂ type copolymerization (cyclic latent monomers) is introduced. The polymers are prepared by anionic ring‐opening multibranching copolymerization of glycidol and 2‐(methylthio)ethyl glycidyl ether (MTEGE), which is conveniently accessible in a single etherification step. Slow monomer addition provides control over molecular weights. Moderate dispersities (Đ = 1.48–1.85) are obtained, given the hyperbranched structure. In situ ¹H NMR copolymerization kinetics reveal reactivity ratios of r _G = 3.7 and r _MTEGE = 0.27. Using slow monomer addition, copolymer composition can be systematically varied, allowing for the adjustment of the hydroxyl/thioether ratio, the degree of branching (DB = 0.36–0.48), thermal properties, and cloud point temperatures in aqueous solution in the range of 29–75 °C. Thioether oxidation to sulfoxides enables to tailor the copolymers' solubility profile. Use of these copolymers as a versatile, multifunctional platform for orthogonal modification is highlighted. The methyl sulfide groups can be selectively alkoxylated, using propylene oxide, allyl glycidyl ether, or furfuryl glycidyl ether, resulting in functional hyperbranched polyelectrolytes. Reaction of the alcohol groups with benzyl isocyanate demonstrates successful orthogonal functionalization.

     

协效剂对膨胀阻燃聚丙烯基木塑复合材料的阻燃增效研究

赋予木塑复合材料(WPC)的阻燃性能成为近年来该领域国内外的研究热点之一。本文通过两轮正交试验,研究8种常见的协效剂对膨胀型阻燃剂(IFRs,m(聚磷酸铵,APP)∶m(季戊四醇,PER)=2∶1)的阻燃增效作用,筛选出具有显著协效作用的协效剂组MgO/EG(可膨胀石墨)/SiO_2,其组成为m(MgO)∶m(EG)∶m(SiO_2)=1∶5∶5,其与IFRs的最佳配比为m(IFRs)∶m(MgO/EG/SiO_2)=1∶0.18,得到性能良好的阻燃型聚丙烯基木塑复合材料。通过热重分析(TGA)和锥形量热分析(CONE)评价IFRs及协效剂组对聚丙烯(PP)基木塑复合材料(WPC)热稳定性能和阻燃性能的影响。结果表明,IFRs及MgO/EG/SiO_2的加入可以有效提高WPC的热稳定性,WPC/IFRs/MgO/EG/SiO_2600℃的残炭率达到22.42%。WPC/IFRs的热释放速率峰(PHRR)、总热释放量(THR)和总烟释放量(TSP)相比于WPC分别降低了21.9%、8.7%和22%。MgO/EG/SiO_2的加入可以进一步提高IFRs的阻燃效率,WPC/IFRs/MgO/EG/SiO_2的PHRR和THR相比于WPC分别降低了33.0%和13.8%。     

On stationary Markov processes with polynomial conditional moments

We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say m is a polynomial of degree at most m. We show that then under some additional, natural technical assumption there exists a family of orthogonal polynomial martingales. More precisely we show that such a family of processes is completely characterized by the sequence {(α_n, p_n)}_{n ? 0} where α′_ns are some positive reals while p′_ns are some monic orthogonal polynomials. Bakry and Mazet (Séminaire de Probabilit?s, vol. 37, 2003) showed that under some additional mild technical conditions each such sequence generates some stationary Markov process with polynomial regression.

We single out two important subclasses of the considered class of Markov processes. The class of harnesses that we characterize completely. The second one constitutes of the processes that have independent regression property and are stationary. Processes with independent regression property so to say generalize ordinary Ornstein–Uhlenbeck (OU) processes or can also be understood as time scale transformations of Lévy processes. We list several properties of these processes. In particular we show that if these process are time scale transforms of Lévy processes then they are not stationary unless we deal with classical OU process. Conversely, time scale transformations of stationary processes with independent regression property are not Lévy unless we deal with classical OU process.     

Speciation of Arsenic in Drinking Water by Dispersive Liquid–Liquid Microextraction,Graphite Furnace Atomic Absorption Spectrometry,and Orthogonal Array Design

Orthogonal array design was used to optimize arsenic speciation in drinking water in contact with materials by dispersive liquid–liquid microextraction followed by graphite furnace atomic absorption spectrometry. Arsenic speciation was achieved by the formation of an arsenic(III) hydrophobic complex with a new chelating agent, 1,2,6-hexanetriol trithioglycolate, at neutral pH. The complex was extracted into the organic phase, while arsenic(V) remained in aqueous solution. The concentration of As(V) was determined by subtracting As(III) from the total arsenic following the reduction of As(V) to As(III) by L-cysteine. Orthogonal array design with OA₁₆ (44) and OA₉ (33) matrices was used to optimize the efficiency of dispersive liquid–liquid microextraction and the reduction of As(V) to As(III), respectively. Under the optimal conditions, the detection limit was 0.03?µg?L^?1 for As(III) and the relative standard deviation was 5.9% with an enhancement factor of 87. The calibration curve was linear from 0.19 to 3.0?µg?L^?1 with a correlation coefficient of 0.9996. The developed method was used for arsenic speciation in solutions of drinking water that contacted materials. The recoveries of fortified samples were in an acceptable range from 92.0 to 113.3%.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

“蓝瓶子”实验再探究*

利用SPSS 25.0统计软件对“蓝瓶子”实验进行正交实验设计,通过统计学分析得出最佳实验条件。利用氧化还原传感器(ORP)对“蓝瓶子”振荡体系的电极电势变化曲线进行分析,并针对蓝色的产生和消失过程设计3组对比实验深入探究,阐明其反应原理,意在引导学生深刻理解趣味实验现象背后的微观反应本质。     

Confidence intervals and ellipsoids for estimable functions and estimable vectors in models with orthogonal block structure

Sub-models of mixed linear models are considered. The independence of these sub-models leads to sufficient statistics for the parameters relevant for their densities. Using pivot variables, confidence regions are obtained as well hypothesis testing for variance components, estimable functions, and estimable vectors. In addition, to compare the estimators and the models, we present the histograms with the empirical joint densities for positive and negative parts of the estimators. The figures, for the two-dimensional charts, contain the corresponding UMVUE and are all unimodal with the UMVUE near the mode. The nearness of the estimators and the modes validates the presented methodology and allows the safe use of induced densities. A numerical example applied to real data is presented.     

Simulation of the interaction of light with 3-D metallic nanostructures using a proper orthogonal decomposition-Galerkin reduced-order discontinuous Galerkin time-domain method

In this artice, we report on a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) technique for the system of 3-D time-domain Maxwell's equations coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. By using the singular value decomposition (SVD) method, the POD basis vectors are extracted offline from the snapshots produced by a high order discontinuous Galerkin time-domain (DGTD) solver. With a Galerkin projection and a second order leap-frog (LF₂) time discretization, a discrete ROM is constructed. The stability condition of the ROM is then analyzed. In particular, when the boundary is a perfect electric conductor condition, the global energy of the ROM is bounded, which is consistent with the characteristics of global energy in the DGTD method. It is shown that the ROM based on Galerkin projection can maintain the stability characteristics of the original high dimensional model. Numerical experiments are presented to verify the accuracy, demonstrate the capabilities of the POD-based ROM and assess its efficiency for 3-D nanophotonic problems.