Global stability and periodic solution of the viral dynamics

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.     

Synthesis and characterization of white‐light‐emitting polyfluorenes containing orange phosphorescent moieties in the side chain

Two orange phosphorescent iridium complex monomers, 9‐hexyl‐9‐(iridium (III)bis(2‐(4′‐fluorophenyl)‐4‐phenylquinoline‐N,C^2′)(tetradecanedionate‐11,13))‐2,7‐dibromofluorene (Br‐PIr) and 9‐hexyl‐9‐(iridium(III)bis(2‐(4′‐fluorophenyl)‐4‐methylquinoline‐N,C^2′)(tetradecanedionate‐11,13))‐2,7‐dibromofluorene (Br‐MIr), were successfully synthesized. The Suzuki polycondensation of 2,7‐bis(trimethylene boronate)‐9,9‐dioctylfluorene with 2,7‐dibromo‐9,9‐dioctylfluorene and Br‐PIr or Br‐MIr afforded two series of copolymers, PIrPFs and MIrPFs, in good yields, in which the concentrations of the phosphorescent moieties were kept small (0.5–3 mol % feed ratio) to realize incomplete energy transfer. The photoluminescence (PL) of the copolymers showed blue‐ and orange‐emission peaks. A white‐light‐emitting diode with a configuration of indium tin oxide/poly(3,4‐ethylenedioxythiophene):poly(styrenesulfonate)/PIr05PF (0.5 mol % feed ratio of Br‐PIr)/Ca/Al exhibited a luminous efficiency of 4.49 cd/A and a power efficiency of 2.35 lm/W at 6.0 V with Commission Internationale de L'Eclairage (CIE) coordinates of (0.46, 0.33). The CIE coordinates were improved to (0.34, 0.33) when copolymer MIr10PF (1.0 mol % feed ratio of Br‐MIr) was employed as the white‐emissive layer. The strong orange emission in the electroluminescence spectra in comparison with PL for these kinds of polymers was attributed to the additional contribution of charge trapping in the phosphorescent dopants. © 2007 Wiley Periodicals, Inc. JPolym Sci Part A: Polym Chem 45: 1746–1757, 2007     

Exponential averaging for traveling wave solutions in rapidly varying periodic media

Reaction diffusion systems on cylindrical domains with terms that vary rapidly and periodically in the unbounded direction can be analyzed by averaging techniques. Here, using iterated normal form transformations and Gevrey regularity of bounded solutions, we prove a result on exponential averaging for such systems, i.e., we show that traveling wave solutions can be described by a spatially homogenous equation and exponentially small remainders. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Digital volume gratings

An optical element constructed by stacking a set of binary-phase grating sheets can simulate the functions of optically recorded volume gratings. Our electromagnetic numerical study also shows that if one of the grating sheets is replaced by another one with different grating period, power spectrum of the diffracted wave changes completely with extra diffraction orders. This property will claim strong advantage in security document applications. Analysis of alignment error reveals interesting phenomena concerning to how misalignment affects diffraction efficiency.     

Two classes of piecewise-linear difference equations with eventual periodicity three

In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all nontrivial solutions of one equation are eventually periodic with prime period three. We will show this result for one case of the second equation.     

Organometallic chemistry related to applications for microelectronics in Japan

This is meant to be a brief overview of the developments of research activities in Japan on organometallic compounds related to their use in electronic and optoelectronic devices. The importance of organometallic compounds in the deposition of metal and semiconductor films for the fabrication of many electronic and opto-electronic devices cannot be exaggerated. Their scope has now extended to thin-film electronic ceramics and high-temperature oxide superconductors. A variety of organometallic compounds have been used as source materials in many types of processing procedures, such as metal–organic chemical vapor deposition (MOCVD), metalorganic vapor-phase epitaxy (MOVPE), metal–organic molecular-beam epitaxy (MOMBE), etc. Deposited materials include silicon, Group III–V and II–VI compound semiconductors, metals, superconducting oxides and other inorganic materials. Organometallic compounds are utilized as such in many electronic and optoelectronic devices; examples are conducting and semiconducting materials, photovoltaic, photochromic, electrochromic and nonlinear optical materials. This review consists of two parts: (I) research related to the fabrication of semiconductor, metal and inorganic materials; and (II) research related to the direct use of organometallic materials and basic fundamental research.     

高维系统周期解的共振分支

本文利用Liapunov－Schmidt方法获得了高维自治系统在共振情况下决定周期解个数的分支函数，并通过计算分支函数的主项，分析分支函数的零点，研究了具两对共轭特征根的四维系统多个周期解的共振分支问题．     

A proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards

We prove a recent theorem by C. Culter every polygonal outer billiard in the affine plane has a periodic trajectory.