Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line

In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd.     

Global stability of a multi‐group model with distributed delay and vaccination

A delayed multi‐group SVEIR epidemic model with vaccination and a general incidence function has been formulated and studied in this paper. Mathematical analysis shows that the basic reproduction number plays a key role in the dynamics of the model: the disease‐free equilibrium is globally asymptotically stable when , while the endemic equilibrium exists uniquely and is globally asymptotically stable when . For the proofs, we exploit a graph‐theoretical approach to the method of Lyapunov functionals. Our results show that distributed delay has no impact on the global stability of equilibria, and the results improve and generalize some known results. Copyright © 2016 John Wiley & Sons, Ltd.     

A Near-Infrared Dye That Undergoes Multiple Interconversions through Acid–Base Equilibrium and Reversible Redox Processes

A near-infrared (NIR) polymethine dye ( 1 ), consisting of a cyclohepta[1,2-b;4,3-b′]dithiophene and two phenol moieties, was synthesized. This dye exhibited pH-responsive changes in its photophysical properties due to a two-step acid–base equilibrium that produced a protonated cation ( 1H⁺ ) and an anion ( 1⁻ ). While 1H⁺ showed an intense fluorescence in the red region of the visible spectrum, 1⁻ exhibited a strong absorption in the NIR region. The tropylium ion character in 1H⁺ induces high pK_a1 and pK_a2 values for 1 . Moreover, a stable radical ( 1^. ) was prepared, which showed a NIR absorption band with a maximum at circa 1600 nm. The cyclic voltammogram of 1^. revealed a two-step reversible redox process that produced 1⁻ and the cation 1⁺ , which is different from 1H⁺ . These redox processes accompany drastic electrochromic changes in the vis–NIR region. Overall, 1 is susceptible to multiple interconversions between five forms, due to the multifaceted character of the cycloheptadithiophene skeleton.     

Equality of the homogeneous and the Gabor wave front set

We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition, we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.