特殊光学元件的新型子孔径拼接检测方法研究

使用新型的特殊整流罩窗口可以明显地提升飞行器的空气动力学性能,但由于这种共形窗口光学表面的复杂性,传统的非球面检测技术已经较难满足要求.本文提出了一种新型子孔径拼接检测技术,在建立新的检测原理基础上,还重点介绍了这种检测方法的设计.同时基于补偿法的原理,文中还针对一个口径70 mm的共形窗口,设计了相应的特殊补偿器,其最终剩余波像差(RMS)为0.0515λ(λ=632.8 nm),可以满足实际使用要求. 关键词： 共形窗口 共形检测 子孔径拼接检测 补偿器     

CPT violation does not lead to violation of Lorentz invariance and vice versa

We present a class of interacting nonlocal quantum field theories, in which the CPT invariance is violated while the Lorentz invariance is present. This result rules out a previous claim in the literature that the CPT violation implies the violation of Lorentz invariance. Furthermore, there exists the reciprocal of this theorem, namely that the violation of Lorentz invariance does not lead to the CPT violation, provided that the residual symmetry of Lorentz invariance admits the proper representation theory for the particles. The latter occurs in the case of quantum field theories on a noncommutative space–time, which in place of the broken Lorentz symmetry possesses the twisted Poincaré invariance. With such a CPT-violating interaction and the addition of a C-violating (e.g., electroweak) interaction, the quantum corrections due to the combined interactions could lead to different properties for the particle and antiparticle, including their masses.     

Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime

We study complete noncompact spacelike hypersurfaces immersed into conformally stationary spacetimes, that is, Lorentzian manifolds endowed with a timelike conformal vector field V. In this setting, by using as main analytical tool a suitable maximum principle for complete noncompact Riemannian manifolds, we establish new characterizations of totally umbilical hypersurfaces in terms of their higher order mean curvatures. For instance, supposing an appropriated restriction on the norm of the tangential component of the vector field V, we are able to show that such hypersurfaces must be totally umbilical provided that either some of their higher order mean curvatures are linearly related or one of them is constant. Applications to the so‐called generalized Robertson‐Walker spacetimes are given. In particular, we extend to the Lorentzian context a classical result due to Jellett  29 .     

Boundary of Anosov dynamics and evolution equations for surfaces

We show that a compact surface of genus greater than one, without focal points and a finite number of bubbles (“good” shaped regions of positive curvature) is in the closure of Anosov metrics. Compact surfaces of nonpositive curvature and genus greater than one are in the closure of Anosov metrics, by Hamilton's work about the Ricci flow. We generalize this fact to the above surfaces without focal points admitting regions of positive curvature using a “magnetic” version of the Ricci flow, the so‐called Ricci Yang‐Mills flow.     

Projective vector fields on Finsler manifolds

In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold.     

关于SOL流形具有常平均曲率旋转曲面的注记

研究非欧流形SOL 空间上共形平均曲率方程的可解性,通过研究轮廓曲线对具有平均曲率的旋转曲面进行分类。当这些旋转曲面的平均曲率为给定函数时,计算出相应轮廓曲线的微分方程。通过求解这些微分方程,给出旋转函数是其上共形平均曲率的充分条件。     

Diffusion from within a Spherical Body with Partially Blocked Surface: Diffusion through a Constant Surface Area

Diffusion from spherical bodies has been a subject of interest since the earliest times of modern sciences and a few equivalent analytical formulations of the problem are taught in engineering textbooks dealing with cooling rates of hot spheres. However, all these former studies assume that the diffusing material is transferable to/from the surrounding space through the whole surface of the spherical body. Conversely, the development of nanoscience and the improved knowledge of microscopic biological events have evidenced that diffusion from spherical bodies is a ubiquitous problem. It often occurs in situations where the nanosphere surfaces are not isotropic and partly impermeable to diffusing materials. This work elaborates on this issue and theoretically establishes that—with some specific allowance—the basic analytical equation of diffusion from/to fully accessible spherical bodies may be used.     

曲面调和映照的广义Frenet公式及其应用

本文建立了从曲面到复Grassmamn流形调和映照的广义Frenet公式。作为应用，我们得到了调和映照为强共形的一个等价条件。我们也讨论了等距调和映照的曲率pinching性质。从而改进了有关伪全纯曲线的相应结果。     

On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria

In this paper we study the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to a given σ-algebra, as done in Gordin (Dokl. Akad. Nauk SSSR 188, 739–741, 1969) and Heyde (Z. Wahrsch. verw. Gebiete 30, 315–320, 1974). These conditions are well adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.     

二维Finsler空间是共形平坦的若干判定条件

本文利用Finsler约度量函数与度量张量获得了二维Finsler空间是共形平坦的若干令新的充要条件．此外，还推导了在共形映射下，局部Minkowski空间、常曲率Finsler空间与零曲率Finsler空间保持不变的新的充要条件．