等热流密度加热垂直下降液膜的研究

利用等热流密度加热条件下降膜流动的三维模型方程进行线性稳定性分析和数值模拟。线性稳定性分析表明，模型方程在小到中等Reynolds数下都适用，并且流向不稳定性增长率随着Reynolds数和Marangoni数增加而增加，展向不稳定性增长率则随着Marangoni数增加而增加，随着Reynolds数增加而减小，流向和展向对扰动波数都存在一个不稳定区间。三维数值模拟表明，在等热流密度加热条件下，液膜在随机扰动的情况下最终会形成带孤立波的三维溪流状结构，液膜与气体的换热也因溪流状结构的出现而加强；在随机扰动的基础上引入占优势地位的展向最不稳定扰动会使得换热增强，液膜会提前破裂；在随机扰动的基础上引入占优势地位的流向最不稳定扰动时，液膜的换热会增强，但不会提前破裂；在随机扰动的基础上同时引入占优势地位的流向和展向最不稳定扰动时，换热会加强且液膜会提前破裂。     

Highly alkaline stable anion exchange membranes from nonplanar polybenzimidazole with steric hindrance backbone

The anion exchange membranes (AEMs) with both high ionic conductivity and alkali stability are always the research focus of the AEM fuel cells. Here, a novel nonplanar polymer for AEMs manufacture, mPBI‐TP‐x‐R, with excellent hydroxide stability and satisfactory processability is reported for the first time. The serial mPBI‐TP‐x resins with steric hindrance were prepared by copolymerization among 3,3′,4,4′‐tetraaminobiphenyl, isophthalic acid and tetraphenyl‐terephthalic acid (TP) in different ratios under microwave condensation. The copolymers mPBI‐TP‐x were quaternized at N1/N3‐sites of benzimidazole unit in backbone with alkyl groups (R?CH₃, C₂H₅, n‐C₃H₇, or n‐C₄H₉) to prepare soluble ionomers, and the corresponding membranes in hydroxyl ion form were prepared by a solution casting method and subsequent ion‐exchange process. The chemical structure of all membranes was characterized using FTIR and ¹H NMR spectroscopy. The properties of ion exchange capacity, water uptake, swelling ratio, tensile strength, ionic conductivity, and alkaline stability were measured. Among the prepared membranes, the mPBI‐TP‐15%‐(n‐Bu) exhibited the excellent alkaline stability (only degradation ca. 5% under 1M NaOH aqueous solution at 60 °C for 800 h) and satisfactory OH^? conductivity (46.66 mS/cm at 80 °C). The current research provides a useful exploration to commercial application of alkaline fuel cell. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1087–1096     

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.     

A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.     

Improving the approximation of the probability density function of random nonautonomous logistic‐type differential equations

In this paper, we address the problem of approximating the probability density function of the following random logistic differential equation: P^′(t,ω)=A(t,ω)(1?P(t,ω))P(t,ω), t∈[t₀,T], P(t₀,ω)=P₀(ω), where ω is any outcome in the sample space Ω. In the recent contribution [Cortés, JC, et al. Commun Nonlinear Sci Numer Simulat 2019; 72: 121–138], the authors imposed conditions on the diffusion coefficient A(t) and on the initial condition P₀ to approximate the density function f₁(p,t) of P(t): A(t) is expressed as a Karhunen–Loève expansion with absolutely continuous random coefficients that have certain growth and are independent of the absolutely continuous random variable P₀, and the density of P₀, , is Lipschitz on (0,1). In this article, we tackle the problem in a different manner, by using probability tools that allow the hypotheses to be less restrictive. We only suppose that A(t) is expanded on L²([t₀,T]×Ω), so that we include other expansions such as random power series. We only require absolute continuity for P₀, so that A(t) may be discrete or singular, due to a modified version of the random variable transformation technique. For , only almost everywhere continuity and boundedness on (0,1) are needed. We construct an approximating sequence of density functions in terms of expectations that tends to f₁(p,t) pointwise. Numerical examples illustrate our theoretical results.     

三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Comparative in vivo constituents and pharmacokinetic study in rats after oral administration of ultrafine granular powder and traditional decoction slices of Chinese Salvia

Salvia miltiorrhiza, one of the most well‐known herbal medicines, is commonly used for the treatment of coronary heart diseases in China. Besides traditional decoction slices (TDS), another relatively new product of S. miltiorrhiza, ultrafine granular powder (UGP; D90 < 45 μm), is also increasingly being used. In this paper, a UHPLC‐LTQ‐Orbitrap MS technique was developed for a metabolite profile study after oral administration of UGP and TDS of S. miltiorrhiza. The results showed that the number of in vivo absorbed compounds from UGP was much greater than that from TDS, and different types of products from S. miltiorrhiza will have different metabolic processes in vivo. Furthermore, a UHPLC‐Q‐Trap MS/MS method for simultaneously determining four tanshinones (tanshinone IIA, dihydrotanshinone I, tanshinone I and cryptotanshinone) was established and applied to assess the pharmacokinetics of the two types of products. All of the analytes displayed significant higher area under the concentration–time curve and peak concentration after oral administration of UGP than after TDS, indicating that ultrafine powder product could improve the bioavailability and absorption of cryptotanshinon,tanshinone II A,dihydrotanshinonE I and tanshinone I in vivo. The present study provides scientific information for further exploration of the pharmacology of these two types of S. miltiorrhiza and offers a reference for clinical administration of S. miltiorrhiza.     

Terpolymerization of Triisopropylsilyl Acrylate,Methyl Methacrylate,and Butyl Acrylate: Reactivity Ratio Estimation

Ternary monomer reactivity ratios of triisopropylsilyl acrylate (SiA), methyl methacrylate (MMA), and n‐butyl acrylate (BA), as common monomers in self‐polishing coatings (SPCs) binders are obtained using experimental data collected from free radical bulk polymerization at 70 °C. Different terpolymerizations at low and medium‐high conversions are performed at optimized feed compositions. Estimations are made using the error‐in‐variables model (EVM) framework, applying the recast form of the Alfrey–Goldfinger (AG) model and a direct numerical integration (DNI) approach to the collected data. Estimations from individual low and medium‐high conversion data are compared to those found with the combined data (full conversion range data). The highest certainty in point estimates are obtained with analysis of the full conversion range data. Furthermore, the reactivity ratios determined from the combined data fall between those found with analysis of individual low and medium‐high conversion data, another corroboration of reliable data collection. Reactivity ratios determined from analysis of the combined data (r_SiA/MMA = 0.4185, r_MMA/SiA = 1.3754, r_SiA/BA = 0.8739, r_BA/SiA = 0.5736, r_BA/MMA = 0.3692, r_MMA/BA = 1.7919) are used in the recast AG model to predict cumulative terpolymer composition as a function of conversion. The experimental data and model prediction show satisfactory agreement.     

On Applications of Quasi-Monotone Sequences and Quasi Power Increasing Sequences

In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results.