Facile preparation and synergy study of DMC/ZnGA composite catalyst for the synthesis of oligo (propylene‐carbonate) diols

To overcome the weak carbon dioxide (CO₂) conversion ability of Zn‐Co double metal cyanide (DMC) catalyst, zinc glutarate (ZnGA) catalyst was introduced into the DMC catalytic system and applied for the synthesis of oligo (propylene‐carbonate) diols. The DMC/ZnGA composite catalyst (mass ratio = 10:1) exhibited an excellent synergistic effect which had enhanced CO₂ activation ability, high yield and good selectivity. In copolymerization process, ZnGA catalyst not only provided activated CO₂ for DMC catalyst, but also transferred the propagating chain with more alternating structures to DMC catalyst. Both of the two effects increased the carbonate content in the final products. Overall, DMC catalyst dedicated to the polymer chain growth, while the increased CO₂ conversion mainly attributed to ZnGA catalyst. Oligo (propylene‐carbonate) diols with carbonate unit content of 45.1 mol%, Mn of 1228 g/mol, W_PC of 4.3 wt% and high yield of 1689 g/g _cat was obtained.     

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.     

Influence of imide functionalized organo‐modified Mg‐Al layered double hydroxide on the thermal and mechanical properties of new aliphatic‐aromatic poly (amide‐imide)

A new dicarboxylic acid modified Mg‐Al LDH (DLDH) containing imide groups was prepared and its effects on the thermal and mechanical properties of the new synthesized aliphatic‐aromatic poly (amide‐imide) (PAI) were investigated via preparation of PAI/nanocomposite films by solution casting method. The results of X‐ray diffraction (XRD), field emission‐scanning electron microscopy (FE‐SEM) and transmission electron microscopy (TEM) showed a uniform dispersion for LDH layers into the PAI matrix. For comparison, the effects of polyacrylic acid‐co‐poly‐2‐acrylamido‐ 2‐methylpropanesulfonic acid (PAMPS‐co‐PAA) modified Mg‐Al LDH (ALDH) on the PAI properties were also studied. The thermogravimetric analysis (TGA) results exhibited that the temperature at 5 mass% loss (T₅) increased from 277 °C to 310 °C for nanocomposite containing 2 mass% of DLDH, while T₅ for nanocomposite containing 2 mass% of ALDH increased to 320 °C, along with the more enhancement of char residue compared to the neat PAI. According to the tensile test results, with 5 mass% DLDH loading in the PAI matrix, the tensile strength increased from 51.6 to 70.8 MPa along with an increase in Young's modulus. Also the Young's modulus of PAI nanocomposite containing 5 mass% ALDH reduced from 1.95 to 0.81 GPa.     

Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

Jordan operator algebras revisited

Jordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particular, surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras.     

A note on uniqueness of the ground state for nonlinear Schrödinger equations

We are concerned with the following nonlinear Schrödinger equation $-{\epsilon }^2\Delta u+V\left(x\right)u={\left|u\right|}^{p-2}u,u\in H^1\left({\mathbb{R}}^N\right),$where $N\ge 3$, $2<p<\frac{2N}{N-2}$. For $\epsilon$ small enough and a class of $V\left(x\right)$, we show the uniqueness of the positive ground state under certain assumptions on asymptotic behavior of $V\left(x\right)$ and its first derivatives. Here our results are suitable for a kind of $V\left(x\right)$ which has different increasing rates at different directions.     

面向远海岛礁群的双向物流网络规划

针对若干远海岛礁群系统封闭性的分布特点,将中心岛礁选址、各岛礁建设泊位数量和规模、仓库储存量、运输船型和数量以及航线设置、班期组织等作为规划内容,以整个运输网络系统总成本最低为原则,综合考虑了仓库存储理论,建立了兼顾“选址-库存-路径”的规划模型。结合所建模型特点,提出了双层并行搜索遗传算法,构建了以海上运输为基本交通方式的双向物流系统。最后,以我国南海为例进行建模并求解,采用不同算法并通过多组不同规模的算例进行演算比较,验证了所建模型和算法的有效性与合理性。     

Change points in heavy‐tailed multivariate time series: Methods using precision matrices

We propose two robust data‐driven techniques for detecting network structure change points between heavy‐tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false‐positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t‐distributed (heavy‐tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.