Mechanistic Insights into the Reversible Formation of Iodosylarene–Iron Porphyrin Complexes in the Reactions of Oxoiron(IV) Porphyrin π‐Cation Radicals and Iodoarenes: Equilibrium,Epoxidizing Intermediate,and Oxygen Exchange

We have shown previously that iodosylbenzene–iron(III ) porphyrin intermediates ( 2 ) are generated in the reactions of oxoiron(IV ) porphyrin π‐cation radicals ( 1 ) and iodobenzene (PhI), that 1 and 2 are at equilibrium in the presence of PhI, and that the epoxidation of olefins by 2 affords high yields of epoxide products. In the present work, we report detailed mechanistic studies on the nature of the equilibrium between 1 and 2 in the presence of iodoarenes (ArI), the determination of reactive species responsible for olefin epoxidation when two intermediates (i.e., 1 and 2 ) are present in a reaction solution, and the fast oxygen exchange between 1 and H₂¹⁸O in the presence of ArI. In the first part, we have provided strong evidence that 1 and 2 are indeed at equilibrium and that the equilibrium is controlled by factors such as the electronic nature of iron porphyrins, the electron richness of ArI, and the concentration of ArI. Secondly, we have demonstrated that 1 is the sole active oxidant in olefin epoxidation when 1 and 2 are present concurrently in a reaction solution. Finally, we have shown that the presence of ArI in a reaction solution containing 1 and H₂¹⁸O facilitates the oxygen exchange between the oxo group of 1 and H₂¹⁸O and that the oxygen exchange is markedly influenced by factors such as ArI incubation time, the amounts of ArI and H₂¹⁸O used, and the electronic nature of ArI. The latter results are rationalized by the formation of an undetectable amount of 2 from the reaction of 1 and ArI through equilibrium that leads to a fast oxygen exchange between 2 and H₂¹⁸O.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

A cellular automaton technique for modelling of a binary dendritic growth with convection

A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs–Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909–1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen–Ivanstov solution for the concentration-driven growth in a forced flow.     

Ekeland’s principle for vector equilibrium problems

In this paper, the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones. The aim is to provide a vector version of Ekeland’s theorem related to equilibrium problems. To prove this principle, a weak notion of continuity of a vector-valued function is considered, and some of its properties are presented. Via the vector Ekeland’s principle, existence results for vector equilibria are proved in both compact and noncompact domains.     

一类二元相关威布尔分布的可靠性问题

本文考虑生存函数为${\ol{F}(x_{1},x_{2})}=\exp\{-[(x_{1}^{1/\alpha}/\theta_{1})^{1/\delta}+(x_{2}^{1/\alpha}/\theta_{2})^{1/\delta}]^{\delta}\},\;x_{i}>0,\;\alpha>0$, $1\geq\delta>0,\;\theta_{i}>0\;(i=1,2)$的二元威布尔分布的两种可靠性问题, 提出可靠度$\pr$的估计并讨论了它们的渐近性, 最后还作了模拟计算.     

Crystal dissolution kinetics and Gibbs free energy

The dependence of dissolution rates on the difference of Gibbs free energy is of critical importance for our understanding of crystal dissolution, reactive flow models and their applications to a variety of environmentally related problems. Here, we review experimental data generated with mineral powders and single crystals to develop a better understanding of apparent inconsistencies between otherwise internally consistent data sets. Additional information from direct surface observations and measurements with vertical scanning interferometry (VSI) and atomic force microscopy (AFM) of albite dissolution at 25, 150 and 185 °C may shed new light on this old but unsolved question. Our discussion is based on the importance of etch pit development, its ΔG dependence, and the pits’ role as a source for steps and step movement in the dissolution process. Results indicate that reaction history may be of critical importance in determining the overall reaction mechanism and its rate. Different rates are observed for systems having otherwise identical ΔG_r acquired from increasing versus decreasing disequilibrium positions.

In this context, we finally discuss the validity of the common application of transition state theory (TST) to elementary and overall reactions governing the dissolution process. In this discussion of crystal dissolution, we contrast TST applications with a stochastic, many-body treatment that has led to the development of a stepwave model. This discussion also focuses on the controversy caused by the rivalry between surface adsorption models and a probabilistic model that seeks to incorporate the full three-dimensional crystal structure.     

A Bayesian analysis for the seismic data on Taiwan

A Bayesian approach is used to analyze the seismic events with magnitudes at least 4.7 on Taiwan. Following the idea proposed by Ogata (1988,Journal of the American Statistical Association,83, 9–27), an epidemic model for the process of occurrence times given the observed magnitude values is considered, incorporated with gamma prior distributions for the parameters in the model, while the hyper-parameters of the prior are essentially determined by the seismic data in an earlier period. Bayesian inference is made on the conditional intensity function via Markov chain Monte Carlo method. The results yield acceptable accuracies in predicting large earthquake events within short time periods.     

森林发展系统的一个非线性半离散模型

本文建立了森林发展系统的一类非线性林龄面积结构的半离散模型 ,并讨论了半离散系统解的存在唯一性 ,给出了线性半离散系统稳定的一些充分条件     

Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.     

病毒感染群体动力学模型分析

本文构建并讨论了一类病毒感染的群体动力学模型,得到了模型存在轨道稳定周 期解的充分条件,较好地解释了在病毒持续感染者体内观察到的病毒载量波动现象.