The necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional differential equations

In this paper, using Fourier series, we study the problem of the existence of periodic solutions of a type of periodic neutral differential difference system. Some necessary and sufficient conditions for the existence of periodic solutions of a type of neutral functional equation system are obtained, and at the same time, we present a method with formula shows how to find the periodic solutions.     

Synthesis of grafted poly(p‐phenyleneethynylene) with energy donor–acceptor architecture via atom transfer radical polymerization: Towards nonaggregating and hole‐facilitating light‐emitting material

In this contribution, we demonstrate a new effective methodology for constructing highly efficient and durable poly(p‐phenyleneethynylene) (PPE) containing emissive material with nonaggregating and hole‐facilitating properties through the introduction of hole‐transporting blocks into the PPE system as the grafting coils as well as building the energy donor–acceptor architecture between the grafting coils and the PPE backbone. Poly(2‐(carbazol‐9‐yl)ethyl methacrylate) (PCzEMA), herein, is chosen as the hole‐transporting blocks, and incorporated into the PPE system as the grafting coils via atom transfer radical polymerization. The chemical structure of the resultant copolymer, PPE‐g‐PCzEMA, was characterized by NMR and gel permeation chromatography, showing that the desirable copolymer was obtained with the narrow polydispersity. The increased thermal stability of PPE‐g‐PCzEMA was confirmed by thermogravimetric analysis and differential scanning calorimetry along with its macroinitiator. The optoelectronic properties of this copolymer were studied in detail by ultraviolet‐visible absorption, photoluminescence emission and excitation spectra, and cyclic voltammogram (CV). The results indicate that PPE‐g‐PCzEMA exhibits the solid‐state luminescent property dominated by individual lumophores, and also the energy transfer process from the PCzEMA blocks to the PPE backbone with a relatively higher energy transfer efficiency in the solid‐state compared to that of the solution state. Additionally, the hole‐injection property is greatly facilitated due to the presence of PCzEMA, as confirmed by CV profiles. All these data indicate that PPE‐g‐PCzEMA is a good candidate for use in optoelectronic devices. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3776–3787, 2007     

狭义相对论效应──运动时钟变慢的计算机模拟演示实验

利用精炼的C语言进行程序设计，定量模拟狭义相结论的运动时钟变慢，并对处于两种不同时空观的时钟运行进行对比，使得时间膨胀效应变得直观。     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Study of interactions of various ionic species with solvents toward the design of receptors

In earlier studies, the interactions of isolated ionic species with various solvents were investigated using ab initio calculations. The ionic species investigated included cations (proton, hydronium, ammonium, and metal cations) and anions (single electron, hydroxide, and halide anions). However in the present study, we investigate the interactions of these ionic species with the solvent in the presence of other competing ionic species. We also elaborate on how the information obtained from these extensive studies have been employed in designing and synthesizing various kinds of novel ionophores and receptors.     

Smaller Output Beam Divergence in the Slowly Opened Q-Switch Operation

The mechanism of the slowly opened Q-switch operation was investigated thoroughly. Maximum energy extraction from the resonator could be optimized, and the smallest output beam divergence could be achieved. In this article, we present a detailed analysis that has numerically verified the mode-selection mechanism in the slowly opened Q-switch operation, and the degree of the smaller output laser beam divergence that has been achieved. The mechanism of the slowly opened Q-switch operation is the inherent advantage of the passive saturable absorber in this operation. We can use the maximum energy extraction and the smallest output beam divergence results of the slowly opened Q-switch operation to design and optimize various passive saturable absorbers: plastic dye sheets, LiF:F₂⁻ color center crystals, Cr4⁺: YAG crystals, RG1000 color glass filters, and the single crystal semiconductor saturable absorber wafers that are in developed in our microchip laser systems.     

Synthesis and properties of noncoplanar rigid‐rod aromatic polyhydrazides and poly(1,3,4‐oxadiazole)s containing phenyl or naphthyl substituents

Two new phenyl‐ and naphthyl‐substituted rigid‐rod aromatic dicarboxylic acid monomers, 2,2′‐diphenylbiphenyl‐4,4′‐dicarboxylic acid ( 4 ) and 2,2′‐di(1‐naphthyl)biphenyl‐4,4′‐dicarboxylic acid ( 5 ), were synthesized by the Suzuki coupling reaction of 2,2′‐diiodobiphenyl‐4,4′‐dicarboxylic acid dimethyl ester with benzeneboronic acid and naphthaleneboronic acid, respectively, followed by alkaline hydrolysis of the ester groups. Four new polyhydrazides were prepared from the dicarboxylic acids 4 and 5 with terephthalic dihydrazide (TPH) and isophthalic dihydrazide (IPH), respectively, via the Yamazaki phosphorylation reaction. These polyhydrazides were amorphous and readily soluble in many organic solvents. Differential scanning calorimetry (DSC) indicated that these hydrazide polymers had glass transition temperatures in the range of 187–234 °C and could be thermally cyclodehydrated into the corresponding oxadiazole polymers in the range of 300–400 °C. The resulting poly(1,3,4‐oxadiazole)s exhibited T_g's in the range of 252–283 °C, 10% weight‐loss temperature in excess of 470 °C, and char yield at 800 °C in nitrogen higher than 54%. These organo‐soluble polyhydrazides and poly(1,3,4‐oxadiazole)s exhibited UV–Vis absorption maximum at 262–296 and 264–342 nm in NMP solution, and their photoluminescence spectra showed maximum bands around 414–445 and 404–453 nm, respectively, with quantum yield up to 38%. The electron‐transporting properties were examined by electrochemical methods. Cyclic voltammograms of the poly(1,3,4‐oxadiazole) films cast onto an indium‐tin oxide (ITO)‐coated glass substrate exhibited reversible reduction redox with E_onset at ?1.37 to ?1.57 V versus Ag/AgCl in dry N,N‐dimethylformamide solution. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6466–6483, 2006     

Viscometric study of gelatin in dilute aqueous solutions

The viscosities of aqueous solutions of gelatin at different temperatures were carefully measured in a common glass‐capillary Ubbelohde viscometer at dilute to extremely dilute concentrations. The adsorption effect that occurred in the viscosity measurements was theoretically analyzed and discussed. A theory based on Langmuir isotherms could adequately describe the existing data. Some structural information was obtained by the use of an iterative fitting procedure to treat the reduced viscosity data, which disclosed that individual gelatin chains underwent a coil‐to‐helix transition as the solution cooled from 40 to 15 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1804–1812, 2006