On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation

In this paper, we study the well-posedness of the Cauchy problem and the scattering problem for a new nonlinear dispersive shallow water wave equation (the so-called DGH equation) which was derived by Dullin, Gottwald and Holm. The issue of passing to the limit as the dispersive parameter tends to zero for the solution of the DGH equation is investigated, and the convergence of solutions to the DGH equation as ²0 is studied, and the scattering data of the scattering problem for the equation can be explicitly expressed; the new exact peaked solitary wave solutions are obtained in the DGH equation. After giving the condition of existing peakon in the DGH equation, it turns out to be nonlinearly stable for the peakon in the DGH equation.     

High resolution miniaturized stepper ultrasonic motor using differential composite motion

Experiments show that there is a limited minimum stepped angle in ultrasonic motors (USM). The research on the minimum angle of stepper USM with 15 mm in diameter and wobbling mode is being carried out. This paper presents a novel way to decrease the minimum stepped angle of USM based on the principle of differential composite motion (DCM), i.e. clockwise and counterclockwise rotation. The prototype was fabricated and experiments proved that this method is useful and also keeps a high torque for a large stepped angle. The stator of the prototype is steel, and rotor is fiberglass, antifriction material or steel. The prototype can operate well over 150 h with a 5 kHz wide frequency band. The minimum stepped angle is 46" using a coventional method while 12" using DCM method proposed in this paper.     

On the Extension of Isometries between Unit Spheres of E and C（Ω）

In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too.     

Spectroscopic Study of Neodymium-Doped Sodium–Yttrium Double Fluoride Nd<Superscript>3+</Superscript>:Na<Subscript>0.4</Subscript>Y<Subscript>0.6</Subscript>F<Subscript>2.2</Subscript> crystals

Nd³⁺:Na_0.4Y_0.6F_2.2 (Nd³⁺:NYF) crystals are grown by the Stockbarger–Bridgman method for a stoichiometric mixture prepared by the solid-phase method and containing neodymium up to 20 at. %. The absorption spectrum of Nd³⁺:NYF crystals exhibits bands located in the emission region of laser diodes. The peak absorption cross section of the 796.8-nm band is σ _a = 0.96 × 10^–20 cm² and the bandwidth is Δλ = 17.5 nm. The most intense luminescence band is located at 1.05 μ m and the radiative time of the ⁴F_3/2 level is τ₀ = τ_exp ~ 960 μ s. It is shown that the ²P_3/2 and ⁴D_3/2 levels of Nd³⁺:NYF crystals are also radiative with lifetimes τ exp equal to ~110 and 9.5 μ s, respectively. However, these radiative transitions are partially quenched due to nonradiative relaxation. The intensity parameters Ω t are determined by the Judd–Ofelt method to be Ω₂ = 1.18 × 10^–20, Ω₄ = 1.55 × 10^–20, and Ω 6 = 2.85 × 10–20 cm 2. Using these parameters, the probabilities of radiative transitions and branching ratios are calculated, and the probabilities of nonradiative transitions are estimated. A conclusion is made that Nd³⁺:NYF crystals are promising as active media for diode-pumped tunable lasers, in particular, up-conversion-pumped lasers.     

Quasinormal modes of a Schwarzschild black hole surrounded by free static spherically symmetric quintessence: electromagnetic perturbations

In this paper, we evaluated the quasinormal modes of electromagnetic perturbation in a Schwarzschild black hole surrounded by the static spherically symmetric quintessence by using the third-order WKB approximation when the quintessential state parameter w _q in the range of −1/3 < w _q < 0. Due to the presence of quintessence, Maxwell field damps more slowly. And when at −1 < w _q < −1/3, it is similar to the black hole solution in the ds/Ads spacetime. The appropriate boundary conditions need to be modified.     

双δ掺杂In0.65Ga0.35As/In0.52Al0.48As赝型高迁移率晶体管材料子带电子特性研究

研究了基于InP基的In0.65Ga0.35As/In0.52Al0.48As赝型高迁移率晶体管材料中纵向磁电阻的Shubnikov-deHaas(SdH)振荡效应和霍耳效应,通过对纵向磁电阻SdH振荡的快速傅里叶变换分析,获得了各子带电子的浓度,并因此求得了各子带能级相对于费米能级的位置.联立求解Schrdinger方程和Poisson方程,自洽计算了样品的导带形状、载流子浓度分布以及各子带能级和费米能级位置.理论计算和实验结果很好符合.实验和理论计算均表明,势垒层的掺杂电子几乎全部转移到了量子阱中,转移率在95%以上.     

连续波腔衰荡法的一种新理论推导方法及其应用仿真

与多光束干涉的理论推导不同，本文基于无源腔的Q值定义，根据能量守恒原理，对连续波腔衰荡技术测量原理进行了新的推导．根据推导结果，采用数值模拟的方式就入射光开、关时间对腔出射光功率变化线形的影响进行了分析．重点对衰荡腔充光不足情况下的衰荡线形进行了仿真和数据拟合．结果表明，衰荡腔充光不足会给测量带来误差，但进一步缩短入射光关断时间能减小这种误差．     

New series of AB2‐type hyperbranched polytriazoles derived from the same polymeric intermediate: Different endcapping spacers with adjustable bulk and convenient syntheses via click chemistry under copper(I) catalysis

In this article, according to the concept of “suitable isolation group,” six new AB₂‐type polytriazoles containing azo‐chromophore moieties, derived from the same hyperbranched polymer intermediate, were successfully prepared through click reaction under copper(I) catalysis by modifying the synthetic route, in which different isolation groups in different size were introduced to the periphery of the hyperbranched polymers as end‐capping moieties. With the different end‐capping groups, these hyperbranched polymers, P1 – P6 , exhibited different solubility and processability; also, their nonlinear optical properties were modified accordingly, realizing the adjustment of the properties of hyperbranched polymers through the structural design. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011