导弹发射姿态测量方法研究

针对导弹发射姿态测量问题,提出采用高速摄像机通过斜瞄和平瞄姿态测量方法求解导弹中轴线俯仰角和方位角,仿真典型导弹起飞段近距离姿态测量,分析两种测量方法对导弹飞行姿态测量精度和适用性。仿真结果表明:平瞄和斜瞄姿态测量方法,测量误差在0.2°以内。斜瞄方式使用更便捷,通用性好。平瞄方式测量精度高,数据处理方法、机械结构相对简单,在适合的应用场合优势明显。此分析方法、分析结果为姿态测量方法选取和研究等提供一种可行的途径,也可为其它运动目标的姿态测量提供借鉴。     

拓扑材料中的超导

近来,人们在凝聚态体系中发现了由拓扑不变量定义的物相,其中最重要的有拓扑绝缘体、拓扑半金属和拓扑超导体等.这些物相的拓扑性质由非平凡的拓扑数描述,相应的材料被称为拓扑材料,具有诸多新奇的物理特性.其中拓扑超导体由于边界上有满足非阿贝尔统计的Majorana零能模,成为实现拓扑量子计算的主要候选材料.除了探索本征的拓扑超导体外,由于拓扑性质上的相似性,在不超导的拓扑材料中调制出超导自然成为了实现拓扑超导的重要手段.目前,人们发展了栅极调制、掺杂、高压、近邻效应调制和硬针尖点接触等多种技术,已经成功地在许多拓扑绝缘体和半金属中诱导出了超导,并对超导的拓扑性和Majorana零能模进行了研究.本文回顾了本征拓扑超导候选材料,以及拓扑绝缘体和半金属中诱导出超导的代表性工作,评述了不同实验手段的优势和缺陷、分析了其超导拓扑性的证据,并提出展望.     

Batalin–Vilkovisky algebra structures on Hochschild cohomology of generalized Weyl algebras

We devote to the calculation of Batalin–Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi–Yau generalized Weyl algebras. We first establish a Van den Bergh duality at the level of complex. Then based on the results of Solotar et al., we apply Kowalzig and Krähmer's method to the Hochschild homology of generalized Weyl algebras, and translate the homological information into cohomological one by virtue of the Van den Bergh duality, obtaining the desired Batalin–Vilkovisky algebra structures. Finally, we apply our results to quantum weighted projective lines and Podleś quantum spheres, and the Batalin–Vilkovisky algebra structures for them are described completely.     

ALGEBRAIC EXTENSION OF ＊-A OPERATOR

In this paper, we study various properties of algebraic extension of *-A operator.Specifically, we show that every algebraic extension of *-A operator has SVEP and is isoloid.And if T is an algebraic extension of *-A operator, then Weyl's theorem holds for f(T), where f is an analytic functions on some neighborhood of σ(T) and not constant on each of the components of its domain.     

Wavelets in Banach Spaces

We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus.     

Weyl Pseudo-Differential Operator and Wigner Transform on the Poincaré Disk

The purpose of this paper is to investigate some relations between the kernel of a Weyl pseudo-differential operator and the Wigner transform on Poincaré disk defined in our previous paper [11]. The composition formula for the class of the operators defined in [11] has not been proved yet. However, some properties and relations, which are analogous to the Euclidean case, between the Weyl pseudo-differential operator and the Wigner transform have been investigated in [11]. In the present paper, an asymptotic formula for the Wigner transform of the kernel of a Weyl pseudo-differential operator as 0 is given. We also introduce a space of functions on the cotangent bundle T ^* D whose definition is based on the notion of the Schwartz space on the Poincaré disk. For an S ¹-invariant symbol in that space, we obtain a formula to reproduce the symbol from the kernel of the Weyl pseudo-differential operator.     

Extremal Almost-Kähler Metrics and Seiberg–Witten Theory

We show that there exist compact non-Kähler almost-Kähler4-manifolds whose metrics minimize L ²-norm of(2/3) s + 2w among all metrics compatible with a fixeddecomposition H ²(M, = H ⁺ H ^–, where s is the scalar curvature and w is the lowest eigenvalue of self-dual Weyl curvature at each point. In particular, the moduli space of such metrics modulo diffeomorphisms is infinite dimensional. This example also shows that LeBrun's estimate of L ²-norm of (1 – )s + · 6won a compact oriented Riemannian4-manifold with a nontrivial Seiberg–Witten invariant cannot beextended over = 1/3.     

-Weyl's theorem for operator matrices

If is a upper triangular matrix on the Hilbert space , then -Weyl's theorem for and need not imply -Weyl's theorem for , even when . In this note we explore how -Weyl's theorem and -Browder's theorem survive for operator matrices on the Hilbert space.

     

q-Painlevé Systems Arising from q-KP Hierarchy

A system of q-Painlevé type equations with multi-time variables t ₁,...,t _M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type . Its rational solutions are constructed in terms of q-Schur functions.     

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.