Lagrange系统Lie点变换下的共形不变性与守恒量

研究Lagrange系统Lie点变换下的共形不变性与守恒量,给出Lagrange系统的共形不变性定义和确定方程,讨论系统共形不变性与Lie对称性的关系,得到在无限小单参数点变换群作用下系统共形不变性同时是Lie对称性的充要条件,导出系统相应的守恒量,并给出应用算例. 关键词： Lagrange系统 Lie点变换 共形不变性 守恒量     

共形整流罩像差特性分析及校正方法

共形结构不仅具有良好的空气动力学性能,且不存在由于表面不连续造成的热梯度等问题,因而采用该结构的导弹整流罩更有利于导弹系统作战性能的提高。但共形结构中采用的非球面罩曲面使整流罩表现出许多不同于球形结构的动态特性,这给导引头中光学系统的设计带来很多困难。在分析共形结构一阶特性的基础上,利用矢量像差理论详细分析该结构中初级像差产生的原因及特点,并提出通过控制元件的倾斜和偏心来平衡所有观察视场中像差的方法。软件分析结果表明：加入倾斜偏心元件后可适当放大小观察视场中的像差,共形整流罩在各观察视场中具有较为稳定的像差特性,有效地改善了该结构的成像质量。     

Regularity and Rigidity for Nonlocal Curvatures in Conformal Geometry

In this paper, we will explore the geometric effects of conformally covariant operators and the induced nonlinear curvature equations in certain nonlocal nature. Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations.     

Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions

ABSTRACT

We consider a certain family of CIFSs of the generalized complex continued fractions with a complex parameter space. We show that for each CIFS of the family, the Hausdorff measure of the limit set of the CIFS with respect to the Hausdorff dimension is zero and the packing measure of the limit set of the CIFS with respect to the Hausdorff dimension is positive (main result). This is a new phenomenon of infinite CIFSs which cannot hold in finite CIFSs. We prove the main result by showing some estimates for the unique conformal measure of each CIFS of the family and by using some geometric observations.     

Leibniz Conformal Algebras of Rank Two

We classify all Leibniz conformal algebras of rank two.     

On a certain class of locally conformal symplectic structures of the second kind

We study locally conformal symplectic (LCS) structures of the second kind on a Lie algebra. We show a method to construct new examples of Lie algebras admitting LCS structures of the second kind starting with a lower dimensional Lie algebra endowed with a LCS structure and a suitable extension. Moreover, we characterize all LCS Lie algebras obtained with our construction. Finally, we study the existence of lattices in the associated simply connected Lie groups in order to obtain compact examples of manifolds admitting this kind of structure.     

Atomic Layer Deposition of the Metal Pyrites FeS2, CoS2, and NiS2

Atomic layer deposition (ALD) of the pyrite‐type metal disulfides FeS₂, CoS₂, and NiS₂ is reported for the first time. The deposition processes use iron, cobalt, and nickel amidinate compounds as the corresponding metal precursors and the H₂S plasma as the sulfur source. All the processes are demonstrated to follow ideal self‐limiting ALD growth behavior to produce fairly pure, smooth, well‐crystallized, stoichiometric pyrite FeS₂, CoS₂, and NiS₂ films. By these processes, the FeS₂, CoS₂, and NiS₂ films can also be uniformly and conformally deposited into deep narrow trenches with aspect ratios as high as 10:1, which thereby highlights the broad and promising applicability of these ALD processes for conformal film coatings on complex high‐aspect‐ratio 3D architectures in general.     

λ-Automorphisms of a Riemannian Foliation II

In Pak (Ann. Global Anal. Geom.13 (1995), 281–288), the notion of -automorphisms of a harmonic Riemannian foliation was extended to a general Riemannian foliation. By applying the characterization obtained in Pak of a -automorphism to be transversal Killing, we here consider the problem that a transversal conformal or projective field is transversal Killing. A special condition, namely _{B B} = 0, is discussed.