Energy theorems for solving equations of deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano’s Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.     

On Conformal Invariants Built from Spinor Fields

By means of a conformal covariant differentiation process we construct generating systems for conformally invariant symmetric (r, s)–spinors in an arbitrary curved space–time. Extending this method to conformally invariant linear differential operators acting on symmetric spinor fields some classes of such operators are derived.     

de Sitter空间S1m+1中具有平行Blaschke张量的正则类空超曲面

本文引入两个以de Sitter空间为模型的非齐性坐标来覆盖共形空间Q₁^m+1.利用球面S^m+1中超曲面的Möbius几何的方法,本文研究了Q₁^m+1中正则类空超曲面的共形几何.作为其结果,本文对所有具有平行Blaschke张量的正则类空超曲面进行了完全分类.     

共形光学技术

共形头罩可大大减小空气阻力,提高导弹在速度与射程方面的性能。介绍了精确共形光学技术,设计的关键在于校正共形头罩在全部视场的动态像差,讨论了采用旋转/平移位相板、拱形校正器等像差校正方法。简要说明了共性头罩加工、试验及应用状况,指出共形光学技术是未来高速导弹整流罩技术的发展方向。     

A novel electromagnetism‐assisted imprinting technology to replicate microstructures onto a large‐area curved surface using a flexible magnetic mold

Replication of microstructures from a mold onto a curved surface is difficult. The conformal contact between the mold and the substrate has to be ensured. The present study proposes an innovative mechanism, which employs an electromagnetic disk to provide magnetic force and a PDMS flexible mold with a layer compounded magnetic powder. This mechanism provides not only the gradual contact from center to edge to avoid air entrapment but also conformal contact between the mold and the substrate during the imprinting operation. A system based on this electromagnetic soft imprinting technology has been implemented, and imprinting to replicate microstructures from the mold onto a curved surface has been carried out. The results reveal that the PDMS magnetic mold and the electromagnetic disk‐controlled magnetic force can successfully perform the imprinting and accurately replicate the microstructures onto the large‐area, curved surface glass. The PDMS flexible magnetic mold incorporated with the magnetic disk can be employed to achieve the conformal contact between the mold and the substrate. In addition, due to the low surface free energy of the PDMS, the de‐molding without sticking can be easily accomplished. Copyright © 2008 John Wiley & Sons, Ltd.     

四元数的复数形式及其在6R机器人反解中的应用

把四元数应用于平面旋转的特殊情况,并把旋转角度的正弦、余弦改写为复指数形式,导出平面四元数的两个复数形式的基.利用这两个基可以把表示三维变换的四元数和对偶四元数改造为复数形式,得到复数形式四元数的4个基和复数形式对偶四元数的8个基,以及它们之间乘法运算的运算法则.通过把它们应用到空间$6R$机器人的位移反解问题,证明了Dixon结式展开后的次数为16次,而不是形式上的24次,并且得到单变量的16次方程.     

ℝ-Conformal invariants of curves

In this paper we describe the structure of the algebra of scalar differential invariants of curves in a plane with Euclidean or Minkowski metric with respect to ?-conformal transformations.     

Reduction of Vaisman structures in complex and quaternionic geometry

We consider locally conformal Kähler geometry as an equivariant (homothetic) Kähler geometry: a locally conformal Kähler manifold is, up to equivalence, a pair $(K,\Gamma )$, where $K$ is a Kähler manifold and $\Gamma$ is a discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invariant of a locally conformal Kähler manifold $(K,\Gamma )$ as the rank of a natural quotient of $\Gamma$, and prove its invariance under reduction. This equivariant point of view leads to a proof that locally conformal Kähler reduction of compact Vaisman manifolds produces Vaisman manifolds and is equivalent to a Sasakian reduction. Moreover, we define locally conformal hyperKähler reduction as an equivariant version of hyperKähler reduction and in the compact case we show its equivalence with 3-Sasakian reduction. Finally, we show that locally conformal hyperKähler reduction induces hyperKähler with torsion (HKT) reduction of the associated HKT structure and the two reductions are compatible, even though not every HKT reduction comes from a locally conformal hyperKähler reduction.