Computational and dynamic NMR investigation of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane

The structure and rotational barrier for the mesityl-silicon bond of 2,2-dimesityl-1,1,1,3,3,3-hexamethyltrisilane have been investigated by ¹H- and ¹³C-variable temperature nuclear magnetic resonance (NMR) as well as by density functional theory structural calculations. The calculations show that the lowest energy structure has C₂ symmetry with nonequivalent ortho methyl groups, consistent with the crystal structure and solution NMR. The nonequivalent ortho methyl groups exchange through a C_s transition state with a calculated relative free energy of 11.0 kcal mol⁻¹. The barrier for this rotation found by dynamic NMR is 13.4 ± 0.2 kcal mol⁻¹ at 298 K.     

Numerical Evaluation of a Two-Loop Diagram in the Cutoff Regularization

The sunset diagram of λφ4 theory is evaluated numerically in cutoff scheme and a nonzero finite term(in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This findingdramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in ourprevious work.     

New Electroweak Model Without a Higgs Particle

A new unified electroweak model is proposed in this paper. In this unified electroweak model, Higgsmechanism is not used, so no Higgs particle exists in the model. In order to keep the masses of intermediate gaugebosons non-zero, two sets of gauge fields will be introduced. In order to introduce symmetry breaking and to help tointroduce the masses of all fields, a vacuum potential is needed. Except for those terms concerning Higgs particle, thefundamental dynamical properties of this model are similar to those of the standard model. And in a proper limit, thismodel will approximately return to the standard model. The purpose of this paper is not to say that the Higgs particledoes not exist in Nature, it is only to prove that, without a Higgs particle, we can also set up a unified electroweak modelwhich is consistent with present experiments.     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

Patterns and Symmetries in the Visual Cortex and in Natural Images

As borders between different entities, lines are an important element of natural images. Indeed, the neurons of the mammalian visual cortex are tuned to respond best to lines of a given orientation. This preferred orientation varies continuously across most of the cortex, but also has vortex-like singularities known as pinwheels. In attempting to describe such patterns of orientation preference, we are led to consider underlying rotation symmetries: Oriented segments in natural images tend to be collinear; neurons are more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underlying topography. This is verified by direct statistical tests in both natural images and in cortical maps. Using the statistics of natural scenes we construct filters that are best suited to extracting information from such images, and find qualitative similarities to mammalian vision. PACS84.35+i 89.70.+c 87.57.Nk     

1+1/2对转涡轮叶排轴向间距对性能影响的研究

木文对1+1/2对转涡轮中轴向间距影响进行了初步研究。对不同轴向间距叶栅流场进行了大量时间精确模拟。研究表明,1+1/2对转涡轮高低压转叶间轴向间距成为追求高效率的制约因素,轴向间距为高压转叶喉部宽度是关键点。因此有关小轴向间距下强激波/叶排干扰的研究应该加强。     

轴流风扇叶片端导叶作用的研究

本文采用数值方法研究了叶片端导叶对轴流风扇性能的影响。通过与普通开式轴流风扇比较,分析了叶片端导叶对内部流动作用的机理.数值计算结果表明:叶片端导叶的安装位置将影响轴流风扇气动效率,安装叶片端导叶不能提高风扇静压升,但是在压力面安装时能有效地减小风扇叶顶泄漏流与主流的掺混损失;在设计流量下,压力面安装叶片端导叶使泄漏涡的作用范围较小,涡核更靠近吸力面;吸力面安装叶片端导叶弱化了泄漏涡的强度但没有减小泄漏涡的作用范围。     

张量对称类上诱导线性算子的数值半径

设V是一个n维线性空间,V_x~m(G)为V上的张量对称类.A为V的线性算子T的矩阵,K(A)为V_x~m(G)上的诱导线性算子K(T)的矩阵.本文从K(A)的数值半径Υ(K(A))和可分数值半径Υ_x(K(A))定义出发,研究了Υ(K(A))、Υ_x(K(A))与范数||A||_p(1≤p≤2)、广义矩阵函数d_x~G(A)的关系,得到了它们之间的两个不等式.     

全内反射荧光显微术应用于单分子荧光的纵向成像

利用这种显微术中激发场的纵向强度呈指数衰减的分布特性，测得的荧光强 度将强烈依赖渗透深度（强度衰减到1/e时的距离），从而快速直接的确定单分子荧光 团间的纵向间隔、每个荧光团的纵向绝对位置和荧光团的半径大小，即实现荧光分子三维分 布的重构.在整个重构的过程中，只需要改变一次入射角的大小，即只需探测两幅荧光分子 的全内反射成像. 关键词： 全内反射荧光显微术 纵向重构