An Efficient Synthesis of Stable Phosphorus Ylides Derived from Hydantoin and 5,5-dialkylhydantoins

Stable crystalline phosphorus ylides are obtained in excellent yields from the 1:1:1 addition reaction between triphenylphosphine and dialkyl acetylenedicarboxylates in the presence of strong NH-acids, such as hydantoin and 5,5-dialkylhydantoins. These stable ylides exist in solution as a mixture of two geometrical isomers as a result of restricted rotation around the carbon-carbon partial double bond resulting from conjugation of the ylide moiety with the adjacent carbonyl group.     

Static analysis of functionally graded beams using higher order shear deformation theory

Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal–ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped–clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal–ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same.     

The 30° rotation domains in wurtzite ZnO films

The 30° rotation domains in ZnO films were studied by transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). The cross-section and plane-view observations reveal that the 30° rotation domains have elliptical cylindrical shape, with the longitude axis along one of the 1 1 2¯ 0 directions and the short axis along one of the 1¯ 1 0 0 orientations, respectively. The volume fraction of the 30° rotation domains is about 1%. Due to the elliptical shape of the domain boundaries along the [0 0 0 1]_ZnO direction, partially disordered superlattice-like structures are formed. As shown by the HREM images and Zn elemental mapping, these super-lattices are most likely caused by periodical segregation and depletion of Zn along the domain boundary for compensating the mismatched lattice strain.     

The effect of inversely unstable solutions on the attractor of the forced pendulum equation with friction

Consider the attractor A of a periodically forced equation of pendulum type with linear friction, in the cylinder. Levi and independently Min, Xian and Jinyan show that if the friction coefficient is larger than a certain bound then A is homeomorphic to the circle. We shall give a topological version of the definition of inversely unstable solution of N. Levinson and show that the appearance of such solutions imply that A is not homeomorphic to the circle. As an application we shall show that the bounds on the friction coefficient obtained before are optimal.     

Gottlieb groups of spheres

This paper takes up the systematic study of the Gottlieb groups of spheres for k≤13 by means of the classical homotopy theory methods. We fully determine the groups for k≤13 except for the 2-primary components in the cases: k=9,n=53;k=11,n=115. In particular, we show if n=2ⁱ−7 for i≥4.     

Polar actions on compact Euclidean hypersurfaces

Given an isometric immersion of a compact Riemannian manifold of dimension n ≥ 3 into Euclidean space of dimension n + 1, we prove that the identity component Iso ⁰(M ⁿ ) of the isometry group Iso(M ⁿ ) of M ⁿ admits an orthogonal representation such that for every . If G is a closed connected subgroup of Iso(M ⁿ ) acting polarly on M ⁿ , we prove that Φ(G) acts polarly on , and we obtain that f(M ⁿ ) is given as Φ(G)(L), where L is a hypersurface of a section which is invariant under the Weyl group of the Φ(G)-action. We also find several sufficient conditions for such an f to be a rotation hypersurface. Finally, we show that compact Euclidean rotation hypersurfaces of dimension n ≥ 3 are characterized by their underlying warped product structure.      

非分辨空间目标光谱双向反射分布函数的实验室平行测量

为了克服非分辨空间目标识别研究中外场观测和计算机仿真手段的局限性,采用实验方法模拟了天基光照场景,用仪器和技术平行类比望远镜观测时光源-目标-探测器方位,并测量了某高保真卫星模型的光谱双向反射分布函数.分析了空间目标光谱散射模型、实验场旋转轴系和环境模拟设备布局.根据在轨卫星的轨道和姿态建立了外场观测几何到室内5轴旋转系统的角度映射关系.利用该关系控制旋转系统实现了对某卫星过境观测的平行模拟,并对目标混合光谱进行了测量和定标.实验结果发表明:目标光谱数据中存在"闪光"和峰值波长迁移现象;旋转系统各轴定位精度为0.5°,光谱数据相对测量误差为0.018%.该方法能实现空间目标观测的全角度平行模拟,测量结果为非分辨目标外形、材料、旋转等特性的识别提供参考.     

Determining if a System is Heterogeneous: The Analysis of Single Molecule Rotational Correlation Functions and Their Limitations

Single molecule spectroscopy can be utilized to measure distributions of individual molecular properties that may be averaged out in the ensemble measurement. For example, complex dynamics in disordered systems can be investigated by observing single molecule rotations via fluorescence spectroscopy. The rotational time of a single transient can be calculated from the correlation function of the reduced linear dichroism signal which fluctuates over time as the molecule reorients in its surroundings. Distributions of rotational time constants can be used to characterize the heterogeneity of molecular environments in the material. This paper reviews some theoretical studies on (1) the high numerical aperture effects on the final correlation function, and how it can be related to optical anisotropy decays in a bulk measurement; (2) the statistical errors resulting from the finite observation length that will propagate into distributions of rotational times. These lead to the discussions on how to interpret correctly the distribution of properties measured from a set of single molecule data, and to determine if in fact the system is heterogeneous.