Convergence of numerical solutions to stochastic age-dependent population equations

In this paper, stochastic age-dependent population equations, one of the important classes of hybrid systems, are studied. In general, most of stochastic age-dependent population equations do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical scheme and show the convergence of the numerical approximation solution to the true solution.     

A new stochastic method of reconstructing porous media

We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program. We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability. The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than 0.2 to ensure its connectivity and conductivity.     

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.     

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1     

Synthesis, Characterization and Thermal Decomposition Mechanism of Cetyltrimethyl Ammonium Tetrathiotungstate

The synthesis, characterization and thermal decomposition mechanism of cetyltrimethyl ammonium tetrathiotungstate （CTriMATT） were studied herein. The as-synthesized CTriMATT was characterized by Elemental analysis, X-ray diffraction （XRD）, Fourier transform infrared （FT-IR）, Ultraviolet visible （UV-Vis） spectra. The results showed that the as-synthesized CTriMATT had high purity and good crystallinity. The introduction of alkyl groups induced a shift of the stretching vibration band of W-S bond to lower wavenumber, while it had no influence on the position of WS4^2-. Thermogravimetric analysis （TG）, differential thermal analysis （DTA） and in situ XRD characterizations revealed that CTriMATT began to decompose at 423 K in nitrogen and was converted to WS2 eventually. In addition, the decomposition product of CTriMATT at 673 K in nitrogen was characterized by N2 adsorption （BET） and scanning electron microscopy （SEM）. The results demonstrated that WS2 with higher specific surface area, and pore volume could be obtained from the thermal decomposition of CTriMATT in nitrogen.     

Theoretical investigation of the decarbonylation of acetaldehyde by Fe+ and Cr+.

We report a comprehensive theoretical study on the decarbonylation of acetaldehyde by Fe+ and Cr+. Various intermediates, transition states, and products involved in the decarbonylation reactions are fully optimized at the B3LYP/6-311+G(2df,2pd) level of theory. The potential energy surfaces (PESs) corresponding to [M,O,C2,H4]+(M=Cr and Fe) are examined in detail using B3LYP and CCSD(T) methods, respectively. The validity of these theoretical methods is calibrated with respect to the available thermochemical data. Calculations suggest that the Cr+ mediated decarbonylation of acetaldehyde takes place in four steps on the sextet surface: encounter complexation, C-C activation, aldehyde H-shift, and nonreactive dissociation, in good accordance with the Co+ mediated decarbonylation of acetaldehyde [Zhao, Zhang, Guo, Wu, Lu, Chem. Phys. Lett. 2005, 414, 28], while for the Fe+/acetaldehyde system decarbonylation can occur on both the quartet and the sextet PESs. The quartet pathway, which experiences spin-orbit coupling between the two surfaces, is energetically more favorable; whereas along the sextet decarbonylation coordinate several high-energy barriers are revealed. The theoretical results are compared with the experimental product kinetic energy and angular distributions of decarbonylation of acetaldehyde by Fe+ and Cr+ measured using a crossed-beam technique [Sonnenfroh, Farrar, J. Am. Chem. Soc. 1986, 108, 3521].     

Preparation and swelling properties of hydrolysis-resistant superabsorbent composite based on acrylic acid and sodium bentonite

Abstract

A novel hydrolysis-resistant superabsorbent composite was prepared via the solution polymerization based on acrylic acid (AA) and sodium bentonite (SBT) as monomers, tetraallylammonium bromine (TAAB) as crosslinker and ammonium persulfate (APS) as initiator. The mechanism of polymerization and the structure of the superabsorbent polymer (SAP) were studied by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (X-ray), and scanning electron microscopy (SEM). The reaction conditions such as different mass ratios of APS to AA, TAAB to AA, SBT to AA, neutralization degree of AA were optimized by orthogonal experiment, and the influence of each reaction condition on the capacity of water absorption at 150?°C was investigated via single-factor controlled experiment. The hydrolysis resistance and swelling kinetics of the SAP were studied in different solutions at 150?°C. Compared to traditional SAPs, the SAP synthesized with TAAB as crosslinker performed a more excellent hydrolysis resistance and water absorbency capacity at high temperatures. The water absorbency in distilled water or 0.1?mol L^?1 NaCl solution could reach 392.6 and 145.2?g g^?1at 150?°C, respectively. The SAP maintaining high swelling capacity in the pH range of 5–9 indicated its wide application values in the acidic or alkaline environment at high temperature. In addition, the SAP exhibited good reusability which could still retain about 73% of its initial water absorbency after reswelling six times at 150?°C.     

流变学法研究部分水解聚丙烯酰胺/Cr(III)交联反应I.浓度的影响

采用流变学法系统地考察了部分水解聚丙烯酰胺（HPAM）/Cr(III)交联体系的 反应动力学。HPAM溶液的粘性模量G”大于弹性模量G’,且其数值随时间不发生变 化,体系为粘性溶液。而HPAM/Cr(III)体系的G’和G”的数值都随时间变化,G” 在反应开始阶段大于G’,当反应进行一段时间后,G’超过G”占据主要地位,体 系成为弹性体系。交联过程可分为三个阶段：第一上升阶段,平缓上升阶段和第二 上升阶段。利用G’～ t曲线可以推测反应机理。实验发现成胶速率随反应物HPAM 和Cr(III)的浓度的增加而增加,而成胶时间缩短。在羧基浓度过量的情况下,交 联反应对Cr(III)浓度的反应级数是1。凝胶的有效弹性交联密度随聚合物浓度的增 加而增,且随凝胶反应的进行而增加。凝胶的交联点间的平均分子量随Cr(III)浓 度的增加和交联反应的进行而下降。     

纳米二氧化锆在甲醇合成催化剂Cu/Ga2O3/ZrO2中的作用

The introduction of mesoporous nanosize zirconia to the catalyst for methanol synthesis dedicates the nanosized catalyst and mesoporous duplicated properties. The catalyst bears the larger surface area, larger mesoporous volume and more uniform diameter, more surface metal atoms and oxygen vacancies than the catalyst prepared with the conventional coprecipitation method. The modification of microstructure and electronic effect could result in the change of the reduced chemical state and decrease of reducuction temperature of copper, donating the higher activity and methanol selectivity to the catalyst. The results of methanol synthesis demonstrate that the Cu^＋ is the optimum active site. Also, the interaction between the copper and zirconia shows the synergistic effect to fulfil the methanol synthesis.     

微孔分子筛纳米晶的控制合成及其催化应用

纳米分子筛因具有高的外表面积和短的孔道结构而显示了独特的催化活性和选择性, 近年来已成为催化界的研究热点.本文就分子筛纳米晶的控制合成、催化基础研究,特别是当前分子筛纳米晶在自组装分级多孔材料和分子筛基纳米复合材料方面的新方向进行了系统的综述,分析了纳米分子筛研究中的机会和应用前景.