On the null geodesics from the viewpoint of space-time singularities

We examined the complete form of the propagation equation of the expansion for null geodesies and we found some restrictions in integral form on the Ricci and Weyl tensors near a singularity.     

Decomposition of Quasi-regular Representations Induced from Discrete Subgroups of Nilpotent Lie Groups

We describe the direct integral decomposition of a quasi regular representation of a connected and simply connected nilpotent Lie group G, which is induced from a discrete subgroup Γ. The solution is given explicitly in terms of orbital parameters. That is, the spectrum, multiplicity and spectral measure that constitute the decomposition are described completely in terms of natural objects associated to the co-adjoint orbits of G. We conclude with a study of the multiplicity function in certain cases.      

激光技术在引信中的应用

 激光就是对受激辐射的光源采取适当的措施后,获得光强度极高、光能量集中在某一方向上,而且相干性极好的传播光源。激光的特性可概括为:单色性、相干性、方向性和高亮度。激光测距是激光技术在军事方面的最早应用。当激光器和激光技术刚跨出实验室之时,激光在引信中的应用发展,与激光在测距中的应用发展一样受到各国的重视。一、激光引信工作原理激光引信目前大多采用主动式,发射部分由激光器和发射装置组成,激光朝着目标发射后,碰到目标而被漫发射,其中的一部分就沿着原路返回,进入激光接收系统。     

一个二次多项式混沌系统的均匀化及其熵分析

利用已有理论给出了一个二次多项式混沌系统,证明了该系统与Tent映射拓扑共轭,给出了该混沌系统的概率密度函数;并根据此概率密度函数,得到了轨道均匀分布的反三角函数映射;对均匀化前后的混沌系统在不同参数下产生序列的信息熵、Kolmogorov熵、离散熵的特性进行了分析,结果显示均匀化后产生的混沌序列混沌程度不改变且具有更好的均匀性.     

Lissajous singularities

Coherent optical Lissajous states are easily created by nonlinear processes such as second-harmonic generation (SHG). Singular properties of such states are discussed and illustrated theoretically with non-phase-matched SHG of an ellipse field containing a C point.     

Space-time singularities

A set of conditions for the reasonableness of space-time is proposed and investigated. Using these, together with strong causality and an assumption of genericness, it is shown that future timelike or null geodesically incomplete space-times contain either curvature or intermediate singularities, or primordial singularities.     

超导简史

 超导现象最初是1911年由荷兰物理学家昂内斯(Onnes)发现的。1908年,昂内斯首次获得液化的氦,并且在液氦温度(4.2K)下研究各种物质的电学特性。他发现,在温度为4.2K时,汞的电阻突然消失。1933年,迈斯纳(Meissner)和奥森菲尔德(Os-chenfeld)发现,处于弱磁场中的超导体会将磁场从内部排斥出来(见图1),这就是迈斯纳效应。1945年,俄罗斯物理学家阿卡迪也夫(Arkadiev)利用这一特性首次演示了将一块小的条形磁铁悬浮于超导体的上方的实验(见图2)。随后而来的几十年,其他超导材料--金属、合金、化合物的超导材料相继找到。     

铀氢锆脉冲反应堆

 1989年4月6日,我国核工业第一研究设计院,在铀氢锆脉冲反应堆零功率装置上,成功地实现了首次临界.标志我国在研制开发这一新型反应堆方面,迈出了重要的一步.什么是脉冲反应堆脉冲反应堆,是一种具有稳态和脉冲运行特殊功能的核反应堆.核反应堆,是中子使原子核发生链式反应,并伴随放出大量粒子和巨大能量的可控核反应器.     

空间环境之火箭探测

一、探空火箭介绍火箭探空技术是指利用火箭进行近地空间环境探测和近地空间资源利用的技术,在近地空间进行探测和科学试验的火箭称为探空火箭。探空火箭是40～300千米高度范围内进行空间原位探测的唯一手段,是高空气球、人造卫星等航天器所不能及的。利用探空火箭能够进行中高层大气、电离层、磁层的     

从莺莺塔蛙鸣看古代仿生学

 在山西省永济县城附近有座佛教古刹--普救寺。寺内有一闻名中外的古塔,由于《西厢记》中张生戏莺莺的故事就发生在这里,所以人们叫它“莺莺塔”。为什么这一极普通的佛塔却闻名遐迩呢?其主要原因就是它那特殊的声学效应。中央电视台1992年1月21日的“神州风采”节目曾对此做过专门的报道。见过此塔的人都知道,每当人们在塔前拍手或击石,均可听到清晰、悦耳、宏亮的“咯哇、咯哇”的蛙叫声。有趣的是,在不同的地点敲击,听到的蛙声来自不同的地方,如在离塔面15米左右的地方拍手或击石,听到的蛙声好似从塔底传出,而当到离塔面20米以外的地方敲击,听到的蛙声则由上空传来。     

Coulomb effects on single-particle exchange singularities

We consider the singularity in the scattering amplitude arising from the exchange of a massive neutral particle. It is shown that the presence of Coulomb distortion in the entrance or exit channel modifies the exchange pole residue. Within the framework of the Coulomb wave Born approximation the exchange pole residue is modified by an energy-dependent factor that is independent of the orbital angular momentum of the bound states involved in the exchange process. The implications of this result on the polarization observables and on recent determinations of the deuteron asymptotic D- to S-state ratio, by analytic continuation in cos θ to the neutron exchange pole, are discussed.     

A remark on null infinity

It is shown that to each choice of conformal factor for the conformal metric on future null Infinity (₊) there is associated an equivalence class of slicings of ₊. Each slicing in turn gives rise to a family of null hypersurfaces in the physical space-time.Supported by NSF Grant No. GP-35773X1.     

Covariant derivatives on null submanifolds

The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes, conformal transformations are used to construct a covariant derivative on null hypersurfaces, and a condition on the Ricci tensor is given to determine when this construction can be used. Several examples are given, including the construction of a covariant derivative operator for the class of spherically symmetric hypersurfaces.     

Reply to Unnikrishnan on naked singularities

Dwivedi and Joshi (dj) [2] have demonstrated the occurrence of a strong curvature naked singularity in the spherically symmetric gravitational collapse of inhomogeneous dust. In a recent paper Unnikrishnan (u) [8] has claimed that demonstrations such as these are unphysical. According tou, dj arrived at a strong naked singularity because they started the collapse of the cloud from an infinite central density. We show, by means of an explicit demonstration, that this claim ofu is incorrect. In fact, the strong naked singularity arises from a regular initial density profile which has the form(R)= ₀ + ₃ R ³ +O(R ⁴) near the center, where ₀ is the initial central density and is finite.u has missed out on these density profiles, thereby leading to his erroneous conclusion. We also note that in his paperu has given no proof either of the nakedness of the singularity, or of its strength. Thus his claims, besides being wrong, are not based on any mathematical derivation. We also point out other serious mistakes in that paper. In summary,u has no valid mathematical or physical objection to the work of Dwivedi and Joshi.     

Junction conditions on null hypersurface

The analytic extension of the globally regular space-time metric for a Schwarzschild black hole is realized by a Kruskal-like coordinate transformation. The junction conditions on null hypersurface are discussed. The reason why a stable black hole bounded with null hypersurface can exist is explained.     

D-branes on non-abelian threefold quotient singularities

We investigate the classical moduli space of D-branes on a non-abelian Calabi-Yau threefold singularity and find that it admits topology-changing transitions. We construct a general formalism of world-volume field theories in the language of quivers and give a procedure for computing the enlarged Kähler cone of the moduli space. The topology changing transitions achieved by varying the Fayet-Iliopoulos parameters correspond to changes of linearization of a geometric invariant theory quotient and can be studied by methods of algebraic geometry. Quite surprisingly, the structure of the enlarged Kahler cone can be computed by toric methods. By using this approach, we give a detailed discussion of two low-rank examples.     

Recovering singularities of a potential from singularities of scattering data

In this paper we show that the leading singularities of certain potentials can be determined from the leading singularities of the backscattering (as well as other determined sets of scattering data). The potentials in question are conormal with respect to smooth surfaces of arbitrary dimension; the restrictions on their orders allow for unbounded potentials in all dimension greater than or equal to three.Partially supported by NSF Grant DMS-9101298 and an Alfred P. Sloan Research FellowshipPartially supported by NSF Grant DMS-9100178