Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.     

OSCILLATION FOR NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＦＯＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ（申建华）（王志成）湖南大学，邮编：４１００８２ＳｈｅｎＪｉａｎｈｕａ；ＷａｎｇＺｈｉｃｈｅｎｇ（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，）Ａｂｓｔｒａｃｔ...     

用于双光子激发荧光寿命显微成像的高重复频率皮秒扫描相机

建立了一台基于新研制的高重复频率皮秒扫描相机的双光子激发荧光寿命显微成像系统,重点介绍所研制的高重复频率皮秒扫描相机。为了在高时间分辨力的同时扩大时间测量范围,实现大面积两维空间高时间分辨取样测量,从而提高采样速率和更有效地发挥扫描相机的作用,设计和研制了一种大面积、高时间分辨力扫描变像管和一种重复频率高达1MHz的斜坡电压扫描电路。基于上述关键部件所研制的扫描相机具有重复频率高、扫描速度可调、时间分辨力高、工作面积大、非线性低、触发晃动小等优点。用钛宝石飞秒激光器作为激光脉冲源,通过脉冲提取器将76MHz的高重复频率降低为1MHz,采用可调延时器和标准具对扫描相机的时间分辨力、扫描速度和非线性进行标定。该系统的时间分辨力达到6.5ps,非线性为2.60%,可测量的时间范围从十几皮秒到几十纳秒。测量了若丹明6G和香豆素314两种标准荧光染料的荧光寿命,取得了与参考文献一致的实验结果。     

半正二阶三点边值问题的解和正解

考察了非线性二阶三点边值问题的n个解和正解的存在性,其中允许非线性项有一个负的下界并且n是一个任意的自然数．主要结论表明该问题可以具有n个解或者正解,只要非线性项在某些有界集上的“高度”是适当的．     

Theoretical Analysis of the Motional Model of Nonlinear Heterogeneous Catalysis

In this paper, a model of the motional nonlinear heterogeneous catalysis process is discussed using the characteristic line method, the analytical results of elution profile are obtained and the formula which determines the parameters of reaction rate and adsorption isotherm through the motional measurement data under the nonlinear condition is given.     

Optical Nonlinearity of Hybrid and Nanocomposite Materials Prepared by the Sol-Gel Method

In this paper the nonlinear refractive index, optical limiting effect, photoinduced and electroinduced second harmonic generation of dye-doped hybrid and nanoparticle-doped composite materials prepared by the sol-gel process have been reported. The origin of these nonlinear optical effects has been discussed.     

Theoretical and Experimental Studies on a Metallorganic Complex of (Isopropylxanthato)(Phenyl)Mercury(I) [Hg(I)(C<Subscript>6</Subscript>H<Subscript>5</Subscript>)(C<Subscript>4</Subscript>H<Subscript>7</Subscript>OS<Subscript>2</Subscript>)]

The title compound, (isopropylxanthato)(phenyl)mercury(I), was synthesized and characterized by elemental analysis, IR and thermogravimetric analysis. Density functional theory (DFT) method calculations were performed at B3LYP/CEP-121G and B3LYP/CEP-31G levels of theory, respectively. Vibrational frequencies were predicted, assigned, compared with the experimental values, and they are supported each other. The calculated results show that the strength of bond Hg—C is stronger than that of Hg—S, which is good agreement with the experimental data. The calculations of the second order optical nonlinearity and electronic absorption spectra are also performed.     

Crystallization and second harmonic generation in thermally poled niobium borophosphate glasses

Crystallization of glasses with compositions (1−x)(0.95 NaPO₃+0.05 Na₂B₄O₇)+xNb₂O₅, x=0.4, 0.43, 0.45, 0.48 was investigated by differential scanning calorimetry and X-ray powder diffraction. Crystallization of two phases was observed in the glasses with x=0.43-0.48. First phase is a sodium niobate with the structure of tetragonal tungsten bronze () and second phase is Na₄Nb₈P₄O₃₂ (). The crystallization of sodium niobate is correlated with increasing of nonlinear optical efficiency reported for thermally poled glasses with x>0.4. The results of Raman spectroscopy show the formation of three-dimensional (3D) niobium oxide framework in the glasses with increase of niobium concentration. This framework is supposed to have tetragonal tungsten bronze structure and to be responsible for nonlinear optical properties of the glass. Second harmonic generation signals of as prepared and crystallized glass after thermal poling are compared. The nucleation and crystallization do not improve the NLO properties of the glasses under study.     

Cu2(μ-dppb)2(μ-Cl)2的合成、晶体结构及非线性光学性质

The complex Cu₂(μ-dppb)₂(μ-Cl)₂ has been synthesized from the reaction of CuCl， dppb and (n-Bu)₄NCl. The crystal belongs to the triclinic with space group P1. The unit cell parameters are: a=9.939(4)?， b=10.083(6)?， c=14.104(5)?， α=76.46(3)°， β=71.02(2)°， γ=70.87(5)°. The single crystal X-ray diffraction analysis reveals that it has a bi-ring structure with a symmetry center at the middle of two Copper atoms. The outer ring is a 14-membered ring of Cu-dppb-Cu-dppb， and the inner ring is a 4-membered ring composed of two Cl^- and two Cu(Ⅰ). Investigation of third-order optical nonlinearity shows that it exhibits considerable nonlinear absorptive and self-defocusing effect with α₂=1.75×10^-13m·W^-1 and n₂=3.19×10^-18m²·W^-1. CCDC: 193113.     

Asymptotic behavior of non-autonomous Lamé systems with subcritical and critical mixed nonlinearities

This paper deals with the asymptotic behavior of solutions to a class of non-autonomous Lamé systems modeling the physical phenomenon of isotropic elasticity. The main feature of this model is that the nonlinearity can be decomposed into a subcritical part and a critical one. We first show that the system generates a non-autonomous dynamical system, and then prove that the system has a minimal universe pullback attractor. The upper-semicontinuity of these pullback attractors is also established as the perturbation parameter of the external force tends to zero. The quasi-stability ideas developed by Chueshov and Lasiecka (2010, 2008, 2015) are used to prove the pullback asymptotic compactness of the solutions in order to overcome the difficulty caused by the critical growthness of the nonlinearity.