Polyethylene Glycol as String for the Simultaneous Complexation of α-Cyclodextrin and Cucurbit[6]uril

α-Cyclodextrin and cucurbit[6]uril are macrocyclic ligands with nearly identical molecular properties. Both ligands possess nonpolar cavities with similar dimensions. They are able to include nonpolar molecules within their cavities. The main difference between both ligands is their solubility in water. An acceptable solubility for cucurbit[6]uril is only given in the presence of acids or salts. Due to the similarity of both ligands, the formation of mixed polyrotaxanes seems to be possible. The synthesis of statistically threaded α-cyclodextrin and cucurbit[6]uril on polyethylene glycol 2000 is verified using elemental analysis, ¹H-NMR spectroscopy and differential scanning calorimetry. Under the experimental conditions used the number of threaded α-cyclodextrin molecules is higher compared with cucurbit[6]uril. However it is shown that the formation of mixed complexes is possible.     

A dynamical characterization of evolutionarily stable states

Evolutionary stability, the central solution concept in evolutionary game theory, is closely related to local asymptotic stability in a certain nonlinear dynamical system operating on the state space, the so-called "replicator dynamics". However, a purely dynamical characterization of evolutionary stability is not available in an elementary manner. This characterization can be achieved by investigating so-called "derived games" which consist of mixed strategies corresponding to successful states in the original game. Using well-known facts, several characterization results are obtained within this context. These also may shed light on the extremality properties of evolutionary stability.     

SPOC模式下无机与分析化学课程教学实践

以无机与分析化学课程教学为例,探讨了SPOC混合教学模式下提高学生知识与能力的有效途径。在该课程教学中的应用和考核评价中,采用课堂教学与在线自主学习相结合的教学方式,实现了以能力培养为目标的本科教育模式的"三个转变":(1)以教为主向以学为主的转变;(2)以课堂教学为主向课内课外结合为主的转变;(3)以结果评价为主向以结果与过程评价相结合为主的转变。有效地提高了教学质量,突出地解决了目前高等院校本科教育模式面临的学生学习主动性差、参与度少的问题。     

Preparation of mixed matrix membranes based on polyimide and aminated graphene oxide for CO2 separation

The aminated graphene oxide (GO) was prepared by the functionalization of pristine GO with ethylenediamine and then dispersed into the poly(amic acid) (the precursor of polyimide [PI]) solution followed by the chemical imidization to successfully fabricate the PI/amine‐functionalized GO mixed matrix membranes (MMMs) using in‐situ polymerization method. Chemical structure and morphology of the GO before and after amine modification were characterized by scanning electron microscopy, Raman spectrum, Fourier transform infrared, and X‐ray photoelectron spectroscopy. Scanning electron microscopy indicated that fine dispersion of GO throughout PI matrix was achieved, which indicates that the in‐situ polymerization approach can enhance the interfacial interaction between the GO and the PI matrix, and then improve the dispersion of carbon material in the polymer matrix. Compared with the conventional solution mixture method, the MMMs prepared with in‐situ polymerization method showed excellent CO₂ permeability and CO₂/N₂ selectivity. The MMMs doped with 3 wt.% aminated GO exhibited maximum gas separation performance with a CO₂ permeability of 12.34 Barrer and a CO₂/N₂ selectivity of 38.56. These results suggest that the amino groups on GO have strong interaction with the CO₂ molecules, which can significantly increase the solubility of polar gas. Our results provide an easy and efficient way to prepare MMMs with good mechanical behavior and excellent gas separation performance.     

Polyurethane‐mesoporous silica gas separation membranes

The concept of mixed matrix membrane comprising dispersed inorganic fillers into a polymer media has revealed appealing to tune the gas separation performance. In this work, the membranes were prepared by incorporation of mesoporous silica into polyurethane (PU). Mesoporous silica particles with different pore size and structures, MCM‐41, cubic MCM‐48 and SBA‐16, were synthesized by templating method and functionalized with 3‐aminopropyltriethoxysilane (APTES). High porosity and aminated surface of the mesoporous silica enhance the adhesion of the particles to the PU matrix. The SEM and FTIR results showed strong interactions between the particles and the PU chains. Moreover, the thermal stability of the hybrid PUs improved compared to the pure polymer. Gas transport properties of the membranes were measured for pure CO₂, CH₄, O₂, and N₂ gases at 10 bar and 25°C. The results showed that the gas permeabilities enhanced with increasing in the loading of modified mesoporous silica particles. High porosity and amine‐functionalized particles render opportunities to enhance the gas diffusivity and solubility through the membranes. The enhanced gas transport properties of the mixed matrix membranes reveal the advantages of mesoporous silica to improve the gas permeability (CO₂ permeability up to ~70) without scarifying the gas selectivity (α(CO₂/N₂)~ 30 for 5 wt% SBA‐16 content).     

Two-Grid Algorithm of $H^{1}$-Galerkin Mixed Finite Element Methods for Semilinear Parabolic Integro-Differential Equations

In this paper, we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by $H^{1}$-Galerkin mixed finite element methods. We use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization, and backward Euler scheme for temporal discretization. Firstly, a priori error estimates and some superclose properties are derived. Secondly, a two-grid scheme is presented and its convergence is discussed. In the proposed two-grid scheme, the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal accuracy. Finally, a numerical experiment is implemented to verify theoretical results of the proposed scheme. The theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice $h=H^2$.     

斜对角2×2分块算子矩阵的二次数值半径不等式

本文研究了Hilbert空间上斜对角2×2分块有界算子矩阵■的二次数值半径不等式,应用非负实数的经典凸性不等式推广了A的二次数值半径不等式.     

因子上非线性混合三重积保持映射

设$\mathcal{A}$, $\mathcal{B}$是两个因子且$\dim\mathcal{A}>4$.本文证明了双射$\phi:\mathcal{A}\rightarrow\mathcal{B}$ 满足对所有的$A,B,C\in\mathcal A$有$\phi([A,B]\bullet C)=[\phi(A),\phi(B)]\bullet\phi(C)$当且仅当$\phi$是线性*-同构, 共轭线性*- 同构,负的线性*-同构, 负的共轭线性*-同构.     

A general class of inequalities with mixed means

Suppose (T, Σ, μ) is a space with positive measure,f: ? → ? is a strictly monotone continuous function, and &;(T) is the set of real μ-measurable functions onT. Letx(·) ∈ &;(T) andf ○x)(·) ∈L ₁(T,μ). Comparison theorems are proved for the means $\mathfrak{M}_{(T,{\mathbf{ }}\mu ,{\mathbf{ }}f)} (x( \cdot ))$ and the mixed means $\mathfrak{M}_{(T_1 ,{\mathbf{ }}\mu _1 ,{\mathbf{ }}f_1 )} (\mathfrak{M}_{(T_2 ,{\mathbf{ }}\mu _2 ,{\mathbf{ }}f_2 )} (x( \cdot )))$ these inequalities imply analogs and generalizations of some classical inequalities, namely those of Hölder, Minkowski, Bellman, Pearson, Godunova and Levin, Steffensen, Marshall and Olkin, and others. These results are a continuation of the author's studies.