单链和gemini表面活性剂的NMR研究

应用核磁共振技术,对几种典型的表面活性剂在水溶液中的聚集行为、结构特征、动力学特性和相互作用等进行了研究. 
利用1D ¹H NMR方法测得4-癸基萘磺酸钠（SDNS）在313 K温度时的临界胶束浓度（CMC）在0.82~0.92 mmol/L之间,与报道的298 K时的CMC范围相同. 弛豫时间和2D NOESY实验结果表明,与298 K时的SDNS胶束相比,313 K温度时,SDNS胶束中烷烃链排列得更紧密,其中与萘环相连的第一和第二个亚甲基参与了胶束紧密层的形成,更紧密地堆积在萘环之间. SDNS质子T₂值随温度的变化表明,在单体和胶束两种状态下,质子运动对温度的敏感性明显不同. 由自扩散系数分析得到,SDNS胶束的水合半径约为其单体水合半径的5.3倍. 而在十二烷基磺酸钠（SDSN）胶束中,由于静电排斥力的作用,在同样温度下SDSN的胶束紧密层排列比SDNS更疏松. 
NMR实验表明,在SDNS/Triton X-100 (TX-100)和SDNS/SDSN体系中形成了混合胶束. 在SDNS/TX-100混合胶束中,TX-100的苯环靠近SDNS的烷烃链,而它的聚烷氧链除与苯环相连的第一个乙氧基基团以外都被限制在SDNS的萘环附近. 在SDNS/SDSN混合胶束中,SDSN的磺酸基比SDNS分子更靠近胶束内部. 而SDNS的萘环将SDSN的磺酸基分隔开,在降低带负电荷的磺酸基极性头之间的静电排斥力中起到了积极的作用,有助于混合胶束的形成.
从自扩散系数、横向弛豫和质子距离等NMR测定参数推测,在浓度为0.26 mmol/L（318 K）的N,N′-双(十六烷基二甲基)-α,ω-丙烷溴化铵(16-3-16)溶液中形成了近似球形的胶束,胶束表面的带正电荷的铵基极性头呈锯齿状排列以减弱分子间静电排斥力的影响. 弛豫时间测定表明,与N,N′-双(十六烷基二甲基)-α,ω-丁烷溴化铵(16-4-16)相比,16-3-16在胶束表面的spacer链段更僵硬, 在胶束核区的烷烃侧链排列的更紧密. NMR共振峰的线形分析表明,16-3-16和16-4-16侧链末端的甲基在胶束中位于两个不同的位置.      

Generalized Toda Mechanics Associated with Loop Algebras (L)(Cr) and (L)(Dr) and Their Reductions

We construct a class of integrable generalization of Toda mechanics with long-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) in the sense that their Lax matrices can be realized in terms of the c=0 representations of the affine Lie algebras C⁽¹⁾_r and D⁽¹⁾_r and the interactions pattern involved bears the typical characters of the corresponding root systems. We present the equations of motion and the Hamiltonian structure. These generalized systems can be identified unambiguously by specifying the underlying loop algebra together with an ordered pair of integers (n,m). It turns out that different systems associated with the same underlying loop algebra but with different pairs of integers (n₁,m₁) and (n₂,m₂) with n₂<n₁ and m₂<m₁ can be related by a nested Hamiltonian reduction procedure. For all nontrivial generalizations, the extra coordinates besides the standard Toda variables are Poisson non-commute, and when either $n$ or m≥3, the Poisson structure for the extra coordinate variables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand side of the Poisson brackets). In the quantum case, such generalizations will become systems with noncommutative variables without spoiling the integrability.     

Theory of Electrorotation of Clustered Colloidal Particles

When a colloidal suspension is exposed to a strong rotating electric field, an aggregation of the suspended particles is induced to appear. In such clusters, the separation between the suspended particles is so close that one could not neglect the multiple image effect on the electrorotation (ER) spectrum. Since so far the exact multiple image method exists in two dimensions only, rather than in three dimensions, we investigate the ER spectrum of the clustered colloidal particles in two dimensions, in which many cylindrical particles are randomly distributed in a sheet cluster. We report the dependence of the ER spectrum on the material parameters. It is shown that the multiple image method predicts two characteristic frequencies, at which the rotation speed reaches maximum. To this end, the multiple image method is numerically demonstrated to be in good agreement with the known Maxwell-Garnett approximation.     

关于2×2矩阵代数保立方幂等的单射

刻画了2×2全矩阵代数保立方幂等映射,利用保立方幂等映射象与原象矩阵对应元素相等这个特点计算出相应的结果,得出特征不等于2,3,5域上2×2全矩阵代数保立方幂等单射的一个具体的刻画.     

四阶方程两点边值问题变号解的存在性

利用一个已有的抽象结论,证明了一类非线性四阶方程两点边值问题变号解的存在性.     

超分辨重建技术及其研究进展

超高分辨成像技术一直是航天、遥感、目标识别等领域的研究热点。随着光学成像到光电数字成像的转变,如何提高CCD的几何分辨率,已成为研制高分辨光电成像系统亟待解决的问题。本文从理论和工程实现的角度介绍了超分辨成像的技术原理,分析了实现超分辨重建技术的几种方法,主要描述了微扫描和亚像元两种重建技术的实现方式,指出了目前超分辨技术存在的缺陷。最后,针对超分辨技术中无混淆重建带宽较窄的问题,提出了一种新的技术方案。该方案将光学编码技术与目前的亚像元技术相结合,可将重建带宽拓展3倍。研究结论指出：融合了光学,光电子学和信号处理的成像系统的综合设计,将是未来成像领域的一个重要研究方向。     

High Performance Micro-Structure Sensor Based on TiO2 Nanofibers for Ethanol Detection

TiO2 nanofibers are synthesized via a simple electrospinning method and coated on a silicon substrate with Pt electrodes to fabricate a micro-structure sensor. This sensor exhibits high ethanol sensing properties at 300℃. The sensitivity is up to 4 when the sensor is exposed to 1 ppm ethanol, the response time is about 3s, and the recovery is about 5 s.     

处处不可导连续函数的构造法

为了方便向大学生介绍处处不可导的连续函数的构造,对van derWaerden的级数构造法和Bush直接定义函数的构造法分别进行推广并给出证明.     

利用激光诱导荧光来探测远程宽带太赫兹波

远程太赫兹光谱分析在国土安全和环境监测方面的应用有着巨大的潜力.然而由于大气中的水气在太赫兹频率范围内的强吸收,远程宽带太赫兹探测一直以来都是一个挑战.文章介绍了一种通过相干控制非对称电离气体荧光来实现远程宽带探测太赫兹波的全光学技术.由于荧光在大气中的高透过率以及全方位辐射特性,该技术可用于太赫兹波的远程探测,具有最小水气吸收以及不受光信号收集方向限制两个优点.实验上已经获得了距离为10m量级的太赫兹波相干探测.