受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cram&#...受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cramér-Rao Bound,CRB),提出了一种基于克拉美罗界的小孔径阵列性能评估和构型优化方法。首先,梳理了宽带信号波达方向估计的发展历程和典型的二维阵列结构,建立了基于频带分解的标量阵列及极化敏感阵列宽带信号模型;接着,针对标量阵列,给出了宽带二维波达方向估计克拉美罗界闭式表达式;随后,推导出极化敏感阵列宽带二维波达方向估计克拉美罗界的通用框架及闭式表达式,建立了极化敏感阵列二维测向性能评估准则;最后,结合制导系统平台对阵元数量和布阵孔径的限制,提出了基于所推导克拉美罗界的二维阵型优化方法,通过构建阵型优化集合和理论性能评估,实现阵列布局的定量优化。研究结果为小孔径制导测向系统的阵列构型设计与性能评估提供了理论支撑和技术指导。展开更多
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of...It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.展开更多
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applyin...Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.展开更多
We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of...We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.展开更多
文摘受平台资源(重量、体积、布阵空间等)限制,制导测向系统在小孔径布阵约束下测向性能受限,阵型优化成为提升系统性能的关键环节。本文推导了标量阵列和极化敏感阵列的宽带二维波达方向(Direction of Arrival,DOA)估计的克拉美罗界(Cramér-Rao Bound,CRB),提出了一种基于克拉美罗界的小孔径阵列性能评估和构型优化方法。首先,梳理了宽带信号波达方向估计的发展历程和典型的二维阵列结构,建立了基于频带分解的标量阵列及极化敏感阵列宽带信号模型;接着,针对标量阵列,给出了宽带二维波达方向估计克拉美罗界闭式表达式;随后,推导出极化敏感阵列宽带二维波达方向估计克拉美罗界的通用框架及闭式表达式,建立了极化敏感阵列二维测向性能评估准则;最后,结合制导系统平台对阵元数量和布阵孔径的限制,提出了基于所推导克拉美罗界的二维阵型优化方法,通过构建阵型优化集合和理论性能评估,实现阵列布局的定量优化。研究结果为小孔径制导测向系统的阵列构型设计与性能评估提供了理论支撑和技术指导。
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.
基金Supported by Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
基金Supported by the National Natural Science Foundation of China (10571035,10871141)
文摘Under the assumption that the ordering cone has a nonempty interior and is separable （or the feasible set has a nonempty interior and is separable）, we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions.
文摘We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.
