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.     

Fully-developed pipe and planar flows of multimode viscoelastic fluids

Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end.     

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.     

Phase Transformation of Nanosized Zirconia

1 INTRODUCTION Without introduction of any stabilizing reagent, mesoporous zirconia was prepared via solid state re- action-structure directed method, which broke through the traditional preparation route (liquid reaction)[1]. Using this novel method, the samples possess not only mesoporous structure, but also nano-size. Normal size zirconia has three kinds of crys- talline phases: monoclinic phase existing at room tem- perature, tetragonal phase stabilizing between 1170～2370 ℃ and cubi…     

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].     

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.     

Theoretical Study of Ethanethiol Adsorption on HZSM-5 Zeolite

The density functional theory and the cluster model methods have been employed to investigate the interactions between ethanethiol and HZSM-5 zeolites. Molecular complexes formed by the adsorption of ethanethiol on silanol H3SiOH with two coordination forms, model Bronsted acid sites of zeolite cluster H3Si(OH)Al(OH)2SiH3 interaction with ethanethiol, aluminum species adsorbed ethanethiol have been comparatively studied. Full optimization and frequency analysis of all cluster models have been carried out using B3LYP hybrid method at 3-21G basis level for hydrogen atoms and 6-31G(d) basis set level for silicon, aluminum, oxygen, carbon, and sulfur atoms. The structures and energy changes of different coordination forms of H3Si(OH)Al(OH)2SiH3-ethanethiol, silanol-ethanethiol and Al(OH)3-ethanethiol have been studied. The calculated results showed the nature of interactions was van der Waals force as exhibited by not much change in geometric structures and properties. The preference order of ethanethiol adsorbed on HZSM-5 zeolite may be residual aluminum species, bridging hydroxyl groups and silanol OH groups from the adsorption heat. The adsorbed models of protonized ethanethiol on bridging hydroxyl OH groups and linear hydrogen bonded ethanethiol on bridging OH groups suggested in literature might not exist as revealed by this theoretical calculation. Possible adsorption models were obtained for the first time.