流形映射结合响应面法的双频天线优化

随着5G通信技术的快速发展,对于跨频段组网有了更高的要求,多频段天线的高效优化成为重点。传统的空间映射方法对天线进行优化时,要准确地建立一个与之相对应的等效电路模型是非常困难的,因此寻找一种简单快速的方法来建立可靠的粗模型至关重要。通过响应面近似算法来构造粗模型,解决了传统优化方法建立等效电路的困难,进一步节省了计算时间。最后,通过使用流形空间映射算法优化单层跨频段双频天线的设计实例,证明了该方法的可行性。

基于流形等距映射的矩阵信息几何检测方法

雷达目标检测常面临复杂的杂波特性,经典的检测方法通常适合于某些特定的场景,当检测背景发生变化时,其检测性能急剧下降。为有效提升不同杂波背景下的检测性能,提出一种基于流形等距映射(ISOMAP)的矩阵信息几何检测器。该方法首先将信号检测问题转化为矩阵流形上两点之间的区分性问题;然后基于样本数据和流形等距映射原理,自适应地学习出矩阵流形的投影变换矩阵,将矩阵流形变换为可区分的低维流形,最大程度地保持每一个矩阵与其邻域内矩阵之间几何距离大小,增强矩阵流形的可分性;最后利用仿真杂波和实测数据对算法进行验证。实验结果表明,相比于经典的检测方法,所提方法能有效提升目标检测性能。

进入辛流形映射的Schrdinger流

自然地引出了进入辛流形映射的Schr dinger流的概念 .建立了从单位圆周S1 进入K hler流形映射的Schr dinger流的光滑解的局部存在性 .若靶流形为具常截面曲率的紧K hler流形 ,借助于一个守恒律 ,建立了从S1 进入此种K hler流形的Schr dinger流的光滑解的大范围存在性 .

关于代数流形及其性质

k是一个固定的代数闭域,文给出了k~n的仿射代数簇的概念.本文讨论了一种特殊的仿射代数簇——代数流形,并给出了一系列性质.

监督式谱空间分类器

提出了一种非线性的监督式谱空间分类器(supervised spectral space classifier,简称S3C).S3C首先将输入数据映射到融合了训练数据判别信息的低维监督式谱空间中,然后在该监督式谱空间中构造最大化间隔的最优分割超平面,并把测试数据以无监督的方式也映射到与训练数据相同的新特征空间中,最后,直接应用之前构建的分类超平面对映射后的测试数据进行分类.由于S3C使研究者可以直观地观察到变化后的特征空间和映射后的数据,因此有利于对算法的评价和参数的选择.在S3C的基础上,进一步提出了一种监督式谱空间分类器的改进算法(supervised spectral space transformation,简称S3T).S3T通过采用线性子空间变换和强迫一致的方法,将映射到监督式谱空间内的数据再变换到指定的类别指示空间中去,从而获得关于测试数据的类别指示矩阵,并在此基础上对其进行分类.S3T不仅保留了S3C算法的各项优点,而且还可以用于直接处理多分类问题,抗噪声能力更强,性能更加鲁棒.在人工数据集和真实数据集上的大量实验结果显示,S3C和S3T与其他多种著名分类器相比,具有更加优越的分类性能.

LLE与ISOMAP降维的对比研究

局部线性嵌套和等距流形映射是两个基本的非线性降维方式,各自的优点和不足在人脸识别上值得做出深入的对比研究。因此对比测试这两种降维方式在不同参数下的执行效率,分析和总结这两种降维方式的适用特点和范围,选择局部线性嵌套和主成分分析,通过应用于人脸识别中,并总结人脸识别的识别率。

一种改进的ISOMAP算法在图像检索中的应用

传统的核化ISOMAP(K-ISOMAP)算法对于多个分散类簇数据集的低维映射不能较好地表现数据集的内在拓扑结构。针对此缺点,本文将对基于ISOMAP的多类多流形算法(MCMM-ISOMAP)进行核化,提出核化的多类多流形ISOMAP算法(K-MCMM-ISOMAP),该算法不仅使得多类数据集在降维后保持较好的内在拓扑结构,而且具备了K-ISOMAP算法的泛化能力,可以将测试数据直接映射到低维空间。因此,该算法可以在多类图像数据集中实现图像检索的功能。实验结果表明该算法与K-ISOMAP相比更具有效性。

Biharmonic product maps between doubly warped product manifolds

The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.

2-Harmonic Curves Isometrially Immersed in a Surface

In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.

Some Growth Rates of Certain Holomorphic Maps

In this paper we discuss some properties of h olomorphic maps between Kahler manifolds with certain curvature restrictions.

Stochastic bifurcations in the SD (smooth and discontinuous) oscillator under bounded noise excitation

Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.

FATOU PROPERTY ON HARMONIC MAPS FROM COMPLETE MANIFOLDS WITH NONNEGATIVE CURVATURE AT INFINITY INTO CONVEX BALLS

The author considers harmonic maps on complete noncompact manifolds, solves the Dirichlet problem in manifolds with nonnegative sectional curvature out of a compact set, and proves the Fatou theorem for harmonic maps into convex balls.

CR submanifolds in a sphere and their Gauss maps

The relationship between CR submanifolds in a sphere and their Gauss maps are investigated.Let V be the image of a sphere by a rational holomorphic map F with degree two in another sphere.It is show that the Gauss map of V is degenerate if and only if F is linear fractional.

Research on the transfers to Halo orbits from the view of invariant manifolds

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invafiant manifolds and the altitude of the perigee is investigated using a Poincare map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust （acceleration or deceleration） near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all con- trolled manifolds are captured because they lie inside the boundary of Eatlh＇s gravity trap in the configuration space. The evo- lutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single-impulse flyby trajectories.

ON FACTORIZATION THEOREMS OF PLURIHARMONIC MAPS INTO THE UNITARY GROUP

The authors give some constructive factorization theorems for pluriharmonic maps from a Kaehler manifold into the unitary group U(N) and obtain some optimal upper bounds of minimal uniton numbers.

f-Harmonic Morphisms Between Riemannian Manifolds

f-Harmonic maps were first introduced and studied by Lichnerowicz in 1970.In this paper,the author studies a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions.The author proves that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map.This generalizes the well-known characterization for harmonic morphisms.Some properties and many examples as well as some non-existence of f-harmonic morphisms are given.The author also studies the f-harmonicity of conformal immersions.

BOUNDARY REGULARITY FOR WEAK HEAT FLOWS

The partial regularity of the weak heat flow of harmonic maps from a Riemannian manifold Al with boundary into general compact Riemannian manifold N without boundary is consid-ered. It is shown that the singular set Sing(u) of the weak heat flow satisfies H(Sing(u)) 0, with is = dimensionM. Here is Hausdorff measure with respect to parabolic metric ρ(x,t),(y,s)=max{|x-y|, }.

THE HEAT FLOW OF HARMONIC MAPS FROM NONCOMPACT MANIFOLDS

The authors consider the global existence of the heat flow of harmonic maps from noncompact manifolds while imposing restrictions on the initial data.

On the Regularity Theories for Harmonic Maps from Finsler Manifolds

The author studies the regularity of energy minimizing maps from Finsler manifolds to Riemannian manifolds. It is also shown that the energy minimizing maps are smooth, when the target manifolds have no focal points.

Holomorphic Maps from Sasakian Manifolds into Khler Manifolds

The authors consider ±（Φ, J）-holomorphic maps from Sasakian manifolds into Koihler manifolds, which can be seen as counterparts of holomorphic maps in Kiihler ge- ometry. It is proved that those maps must be harmonic and basic. Then a Schwarz lemma for those maps is obtained. On the other hand, an invariant in its basic homotopic class is obtained. Moreover, the invariant is just held in the class of basic maps.