Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators

Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown.     

Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation

Nonlinear Dynamics - A new method named bilinear neural network is introduced in this paper, and the corresponding tensor formula is proposed to obtain the exact analytical solutions of nonlinear...     

Nondimensional frequency scaling of aerodynamically-tensioned membranes

Membrane wings have applications that involve low Reynolds number flyers such as micro air vehicles. The time-averaged and time-dependent deformations of the membrane affect the aerodynamic characteristics of the wing, primarily in the region beyond the maximum aerodynamic efficiency of the wing. This paper investigates an appropriate nondimensional vibration frequency scaling of a spanwise tensioned membrane with free (unattached) leading and trailing edges at low Reynolds numbers relative to nondimensional aeroelastic parameters. Silicone rubber membranes with varying spanwise pre-tension, aerodynamic tension (due to wing angle-of-attack and flow dynamic pressure), modulus of elasticity, span, and thickness are studied. Experimental results are compared to a proposed scaling that simplifies the aerodynamic loading as a uniform pressure distribution acting on the membrane. Data is further compared and discussed relative to previous published results of membrane wings with finite wing spans (three-dimensional flow) and fixed (rigid) leading edges.     

炔桥联不对称苯基取代双二茂铁衍生物的设计合成和电化学性质

以四苯基环戊二烯酮为起始原料,经过八步连续反应,成功地合成了3个炔桥联不对称五苯基取代双二茂铁衍生物Fc''-C≡C-Fc（1）、Fc''-C≡C-C≡C-Fc（2）和Fc''-C≡C-C≡C-Fc''（3）（Fc''=五苯基二茂铁基,Fc=二茂铁基）。在设计合成双二茂铁衍生物的过程中,首先经过4步反应,制备出已知化合物Fc''-H（4）,再连续进行3步反应,分别得到3个中间化合物Fc''-COCH₃（5）,Fc''-CCl=CHCHO（6）和Fc''-C≡CH（7）,最后利用偶联反应,得到目标化合物1~3。利用X射线单晶衍射和循环伏安法,测定了化合物1、2和5、7的晶体结构,研究了化合物1~7的电化学性质。研究结果表明,分子的C-H…π键相互作用和空间位阻是导致化合物1和2分子中Fc''和Fc基空间排布取向不同的主要原因。当二茂铁的一个环戊二烯环上引入5个苯取代基时,铁中心的氧化还原电位将升高（E_p^a（Fc''-H）=0.658 V,E_p^a（Fc-H）=0.511 V）。与已知化合物Fc-C≡C-Fc（ΔE=0.215 V）和Fc-C≡C-C≡C-Fc（ΔE=0.134 V）相比,化合物1~3的氧化电位差值（ΔE）均有不同程度地提高（ΔE₁=0.236 V;ΔE₂=0.170 V;ΔE₃=0.146 V）。将1与Fc-C≡C-Fc,2与Fc-C≡C-C≡C-Fc和3进行比较发现,当炔桥两端连接不同的基团Fc''和Fc时,其氧化电位差值（ΔE）将明显提高。     

两个dpa类配体的铜(Ⅱ)配合物的合成、结构、核酸酶活性及细胞毒性

以dpa衍生配体合成2个单核铜配合物[CuL（NO₃）₂]（1）和[CuL（OAc）（H₂O）]ClO₄（2）,并对其进行了表征。单晶结构显示,配合物1中的Cu中心可以描述为畸变的五角双锥构型,而2的Cu中心为畸变的八面体构型。运用电子吸收和发射光谱法研究了配合物与CT-DNA的键合作用,结果表明2个配合物与DNA的相互作用均为部分插入模式。通过改变浓度、时间进一步检测配合物切割DNA的能力,以及验证其切割机理,结果表明在外界诱导剂存在下,2个配合物均表现出强的切割DNA的能力,其作用机理为氧化切割机理,其中活性氧可能为·OH和1O2。利用MTT法测定了配合物对体外HeLa、HepG-2和SGC-7901肿瘤细胞增殖的抑制能力。     

电感耦合等离子体质谱(ICP-MS)法同时测定荞麦秸秆中的8种重金属元素

基于硝酸-盐酸-氢氟酸消解体系,建立了马弗炉-微波消解-电感耦合离子体质谱(ICP-MS)法同时测定荞麦秸秆中的Cr、Cu、Ag、Mn、Fe、As、Ni、Pb等重金属含量测定方法。在微波消解的过程中,分别考察5种不同组合的混合酸体系及两种消解方法对荞麦秸秆中8种重金属测试结果的影响。实验结果表明,浓硝酸-浓盐酸-氢氟酸(6∶2∶2)混酸体系和马弗炉-微波消解样品前处理优于其他方法。在优化条件下,8种重金属加标回收率为91.2%~102%,相对标准偏差(RSD,n=5)为0.22%~4.7%,检出限为0.18~9.41μg/L。方法操作简便、快速、准确,结果可靠,能同时测定荞麦秸秆中8种重金属元素。     

Thermal behaviors and kinetic analysis of two natural kaolinite samples selected from Qingshuihe region in Inner Mongolia in China

Journal of Thermal Analysis and Calorimetry - The thermal characteristic behaviors of two kaolinite samples selected from Qingshuihe region in Inner Mongolia in China were studied through...     

一锅法可控合成金属有机框架材料Mn-荧光素用于核磁共振/荧光成像

通过一锅法,首次将核磁共振成像试剂Mn²⁺和荧光成像试剂荧光素（FSD）自组装于一个简单的金属有机框架材料（Mn-FSD）上。实验结果表明,Mn-FSD的粒径可被控制在微纳米水平内并进行生物成像。体外和体内实验结果证实,Mn-FSD可在细胞和裸鼠中显示强绿色荧光。同时,Mn-FSD表现出较高的弛豫值（r₁=4.95 L·mmol^-1·s^-1）。