Probing the pyrolysis of methyl formate in the dilute gas phase by synchrotron radiation and theory

The thermal dissociation of the atmospheric constituent methyl formate was probed by coupling pyrolysis with imaging photoelectron photoion coincidence spectroscopy (iPEPICO) using synchrotron VUV radiation at the Swiss Light Source (SLS). iPEPICO allows threshold photoelectron spectra to be obtained for pyrolysis products, distinguishing isomers and separating ionic and neutral dissociation pathways. In this work, the pyrolysis products of dilute methyl formate, CH₃OC(O)H, were elucidated to be CH₃OH + CO, 2 CH₂O and CH₄ + CO₂ as in part distinct from the dissociation of the radical cation (CH₃OH^+• + CO and CH₂OH⁺ + HCO). Density functional theory, CCSD(T), and CBS-QB3 calculations were used to describe the experimentally observed reaction mechanisms, and the thermal decomposition kinetics and the competition between the reaction channels are addressed in a statistical model. One result of the theoretical model is that CH₂O formation was predicted to come directly from methyl formate at temperatures below 1200 K, while above 1800 K, it is formed primarily from the thermal decomposition of methanol.     

Existence of positive periodic solution of a hepatitis B virus infection model

In this paper, a periodic model for hepatitis B virus infection is proposed. The model describes the breeding of the infected cells and the periodic variation of the environment. On the basis of the continuation theorem of coincidence degree theory, a condition for the existence of a positive periodic solution to the model is established. The result can be used to explain the wave phenomenon on the density of the pathogens in patients blood and the occurrence of superinfection in hepatitis B virus infections. Copyright © 2014 John Wiley & Sons, Ltd.     

A prey–predator interaction under fluctuating level water

We consider three species system, namely prey (roach), predator (pike) and plankton. We derive persistence and extinction conditions of the populations. Using coincidence degree theory, we determine conditions for which the system has a periodic solution. Copyright © 2014 John Wiley & Sons, Ltd.     

捕食模型正周期解存在性的一个注记

利用重合度理论中的延拓定理讨论了多滞量捕食模型(dN_1(t))/dt=N_1(t)[r_1(t)-a_(11)(t)N_1(t-τ_1(t))-a_(12)(t)N_2(t-τ_2(t))] (dN_2(t))/dt=N_2(t)[-r_2(t)+a_(21)(t)N_1(t-τ_3(t))]的正周期解的存在性,得到了保证上述系统周期解存在的一组时滞依赖的充分条件,补充和完善了已有学者的工作.     

一类具有时滞的比率依赖型捕食者-食饵系统周期正解的存在性

考虑一类具有时滞的比率依赖型捕食者-食饵系统,利用重合度理论中的延拓定理,得到系统存在正周期解的充分条件.     

具偏差变元高阶Lienard方程周期解存在性

利用重合度理论,研究了一类具偏差变元高阶L ienard型方程周期解的存在性,获得了该方程至少存在一个周期解的充分条件.     

SOLUTIONS TO A SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

This article deals with the following second-order multi-point boundary value problem x′′(t) = f(t,x(t),x′(t))+e(t),t ∈(0,1),x′(0)=(α_ix′(ξ_i) from i=1 to m,x(1)=(β_jx(ηj) from j=1 to n .Under the resonance conditions α_i from i=1 to m =1,β_j from j=1 to n=1,β_jηj from j=1 to n =1,by applying the coincidence degree theory,some existence results of the problem are established.The emphasis here is that the dimension of the linear operator is two.In this paper,we extend and improve some previously known results like the ones in the references.     

类W-KKM(X,Y,Z),几乎不动点定理和不动点定理

引进了相对弱$R$-子集和类($W$-)KKM$(X,Y,Z)$的概念,给出了相对KKM映射与相对弱$R$-子集之间的等价关系以及$W$-KKM$(X,Y,Z)$的一个性质,然后给出了两个连续选择定理并得到不动点定理和重合点定理, 最后,在一致拓扑空间上得到具有弱-KKM性质的映射的几乎不动点,不动点和重合点的存在定理.     

一类具有HollingⅢ型食饵—捕食系统的周期解存在性

利用重合度理论中的延拓定理研究非自治周期食饵—捕食系统的非平凡周期解存在性,给出了周期解存在的充分条件.     

一类高阶中立型泛函微分方程周期解的存在性

研究了一类高阶非线性中立型泛函微分方程x~((2n))(t)+cx~((2n))(t-τ)+f(x)x′+bx(t)+g(x(t-σ))=p(t)周期解的存在性,利用分析技巧结合重合度理论给出了该方程存在周期解的充分性定理.