Geodesics算法在雷达投影转换中的应用检验

基于上海市气象局布设于临港的X波段移动式双线偏振雷达观测资料,利用反射率因子、差分反射率和相关系数等变量识别出东海大桥固定地物回波位置,进而采用Geodesics和HRAP(Hydrologic Rainfall Analysis Project)投影转换算法将雷达回波的极坐标位置转换至地理坐标。以国家测绘局利用GPS技术测量的沪芦高速(东海大桥段)地理坐标作为真值,将环境大气分为晴空回波-低湿度情况和降水回波-高湿度情况分类检验两种算法的效果。检验算法包含经投影转换后地物回波样本位于桥面主体内部的数目(多边形检验)和样本偏离桥体中心线的距离(中心线检验)。其结果表明:Geodesics算法在多边形和中心线检验方面表现均优于HRAP算法,其在雷达投影转换的实际业务中具备一定的应用价值。

The properties and geodesics related to the NUT-Taub-like spacetime

Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊ 〈〈 M, respectively.

Circular geodesics and accretion disk in the spacetime of a black hole including global monopole

We study circular time-like geodesics in the spacetime of a black hole including global monopole. We show that when the range of parameter changed the properties of the circular geodesics and the radiation of accretion disks are different. It follows that the properties of the accretion disk around black hole including global monopole can be different from that of a disk around Schwarzschild black hole.

Schwarzschild Geodesics in Terms of Elliptic Functions and the Related Red Shift

Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.

Null Geodesics, Raychaudhuri Equation, Trapped Surfaces, and Penrose Singularity Theorem

We review the concept of congruence of null geodesics, the Raychaudhuri equation for the expansion, its harmonic oscillator version and associated “quantum” propagator, the role of the equation in the derivation of the Penrose singularity theorem, the definition of trapped surfaces, and the derivation of the theorem itself.

MORSE CONCAVITY FOR CLOSED GEODESICS

In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.

An Implementation Method for the Geodesics with Constraints on Heisenberg Manifolds

In this paper we address the implementation issue of the geodesics method with constraints on Heisenberg manifolds. First we present more details on the method in order to facilitate its implementation and second we consider Mathema-tica as a software tool for the simulation. This implementation is of great importance since it allows easy and direct determination of Ricci tensor, which plays a fundamental role in the Heisenberg manifold metric.

Morse index and the stability of closed geodesics

Let ind(c) be the Morse index of a closed geodesic c in an(n+1)-dimensional Riemannian manifold M.We prove that an oriented closed geodesic c is unstable if n + ind(c) is odd and a non-oriented closed geodesic c is unstable if n + ind(c) is even.Our result is a generalization of the famous theorem due to Poincar'e which states that the closed minimizing geodesic on a Riemann surface is unstable.

Some Remarks on the Geodesics in Infinite Dimensional Teichmuller Spaces

Let B denote the set of those points p in an infinite dimensional Teichmiiller space such that a geodesic between the zero point and p is not unique. Some properties of the set B are given.

On Nonuniqueness of Geodesics and Geodesic Disks in the Universal Asymptotic Teichmüller Space

Abstract The non-uniqueness on geodesics and geodesic disks in the universal asymptotic Teichmfiller space AT（D） are studied in this paper. It is proved that if # is asymptotically extremal in [[#]] with h （μ） 〈 h＊ （μ） for some point ζ∈D, then there exist infinitely many geodesic segments joining [[0]] and [[μ]], and infinitely many holomorphic geodesic disks containing [[0]] and [μ]] in AT（D）.

Geodesics in the Engel Group with a Sub-Lorentzian Metric——the Space-Like Case

Let E be the Engel group and D be a bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, the author constructs a parametrization of a quasi-pendulum equation by Jacobi functions, and then gets the space-like Hamiltonian geodesics in the Engel group with a sub-Lorentzian metric.

凸复Finsler流形上的Hopf-Rinow定理

Suppose(M,F) is a convex complex Finsler manifold. We prove that geodesics of(M,F) are locally minimizing. Hence, F introduces a distance function d such that(M,d) is a metric space from topology. Next, we prove the classical Hopf-Rinow Theorem holds on(M,F).

Formation Mechanisms of Some Features in Siliceous Upper Cretaceous-Lower Tertiary Beds of Jordan-Undulations, Geodes, Boudinages

Geode, boudinage, and undulation structures are widely distributed in the siliceous beds of the Upper Cretaceous/Tertiary rocks in Jordan. Their formation was attributed to tectonic forces, syngenetic processes, organic disintegration processes, subaquatic gliding, compaction and settlement, and meteoritic impacts. In this work, the structural features in the siliceous beds of Jordan are attributed to an interplay of load and directed pressures, and mineralogical transformation processes (opal-A to opal-CT to quartz), governed by pH changes. Tectonic directed pressure was acting in an ESE-WSW direction and is common in the silicified limestone of Upper Cretaceous.

The Non-contractibility of Closed Geodesics on Finsler RP^(n)

Let(RP^(n),F)be a bumpy and irreversible Finsler n-dimensional real projective space with reversibilityλand flag curvature K satisfying(λ/1+λ)^(2)<K≤1 when n is odd,and K≥0 when n is even.We show that if there exist exactly 2[n+1/2]prime closed geodesics on such(RP^(n),F),then all of them are non-contractible,which coincides with the Katok’s examples.

3D Face Similarity Measure by Frechet Distances of Geodesics

3D face similarity is a critical issue in computer vision, computer graphics and face recognition and so on. Since Fr@chet distance is an effective metric for measuring curve similarity, a novel 3D face similarity measure method based on Fr^chet distances of geodesics is proposed in this paper. In our method, the surface similarity between two 3D faces is measured by the similarity between two sets of 3D curves on them. Due to the intrinsic property of geodesics, we select geodesics as the comparison curves. Firstly, the geodesics on each 3D facial model emanating from the nose tip point are extracted in the same initial direction with equal angular increment. Secondly, the Fr@chet distances between the two sets of geodesics on the two compared facial models are computed. At last, the similarity between the two facial models is computed based on the Fr6chet distances of the geodesics obtained in the second step. We verify our method both theoretically and practically. In theory, we prove that the similarity of our method satisfies three properties： reflexivity, symmetry, and triangle inequality. And in practice, experiments are conducted on the open 3D face database GavaDB, Texas 3D Face Recognition database, and our 3D face database. After the comparison with iso-geodesic and Hausdorff distance method, the results illustrate that our method has good discrimination ability and can not only identify the facial models of the same person, but also distinguish the facial models of any two different persons.

Homogeneous Finsler spaces with only one orbit of prime closed geodesics

When a closed Finsler manifold admits continuous isometric actions,estimating the number of orbits of prime closed geodesics seems a more reasonable substitution for estimating the number of prime closed geodesics.To extend the results of Duan,Long,Rademacher,Wang and others on the existence of two prime closed geodesics to the equivariant situation,we propose the question if a closed Finsler manifold has only one orbit of prime closed geodesics if and only if it is a compact rank-one Riemannian symmetric space.In this paper,we study this problem in homogeneous Finsler geometry,and get a positive answer when the dimension is even or the metric is reversible.We guess the rank inequality and the algebraic techniques in this paper may continue to play an important role for discussing our question in the non-homogeneous situation.

A Note on the Stability of Geodesics on Diffeomorphism Groups with One-side Invariant Metric

In this note,we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric.We showed that for non-Beltrami fields on a three-dimensional compact manifold,there does not exist Eulerian stable flow which is Lagrangian exponential unstable.We noticed that a stationary flow corresponding to the KdV equation can be Eulerian stable while the corresponding motion of the fluid is at most exponentially unstable.

Self-intersecting Geodesics and Entropy of the Geodesic Flow

Given a symmetric Finsler metric on T^2 whose geodesic flow has zero topological entropy, we show that the lift in the universal covering R^2 →T^2 of any closed geodesic on T^2 must be an embedded curve in R^2.

基于改进的Hessian和Live-wire算法的岩石节理裂隙检测

在图像处理中,由于岩石节理裂隙是最复杂的线状目标之一,针对该对象的检测算法的研究一直是一个难题。故此,研究了一种新的跟踪裂隙边缘线的算法。首先,若图像尺寸太大,进行有选择的图像缩小,然后采用基于Geodesic Shadow Removal的算法进行图像平滑,再用一种基于Hessian矩阵算法增强模糊及微细节理裂隙;用一种基于Live-wire Contour思想的节理裂隙边缘线特征点提取的算法进行边缘特征点提取;最后基于特征点之间的距离及相应线段夹角来连接特征点以形成完整的线段。选择了200幅图像进行实验,通过与十多种传统和新近的算法相比,新算法能够在复杂的岩石节理裂隙图像中,准确快速地提取节理裂隙边缘线,为在该领域引进深度学习等方法奠定基础。

Spherical and Circular Non-Equatorial Photon Orbits around Kerr Black Holes

By analytically solving the equation of azimuthal null geodesics for spherical photon trajectories, a parametric representation of the corresponding segment of the orbit is obtained. The solution parameter is the latitude coordinate. The dependences of the orbital radius on the black hole spinning parameter and the angle of inclination of its plane with respect to the rotation axis are calculated for flat circular non-equatorial orbits. It is proved that all spherical photon trajectories in the Kerr spacetime are unstable, as well as equatorial ones, and the critical photon orbits in the Schwarzschild metric.