Effect test spaces and effect algebras

The concept of an effect test space, which is equivalent to a D-test space of Dvurečenskij and Pulmannová, is introduced. Connections between effect test space. (E-test space, for short) morphisms, and event-morphisms as well as between algebraic E-test spaces and effect algebras, are studied. Bimorphisms and E-test space tensor products are considered. It is shown that any E-test space admits a unique (up to an isomorphism) universal group and that this group, considered as a test group, determines the E-test space uniquely (up to an isomorphism).     

Noncommutative space from dynamical noncommutative geometries

We present noncommutative topology as a basis for noncommutative geometry phrased completely in terms of partially ordered sets with operations. In this note we introduce a noncommutative space-time starting from a dynamical system of noncommutative topologies based on the notion of temporal points. At every moment a commutative topological space is constructed and it is shown to approximate the noncommutative space in sheaf theoretical terms; this so called moment space should be the space where observed phenomena should be described, the commutative shadow of the noncommutative space is to be thought of as the usual space-time.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper.Firstly,since the Dirac equation is described as a matrix equation in phase space,it is necessary to define the Wigner function as a matrix function in spinor space.Secondly,the matrix form of the Wigner function is proven to support the Dirac equation.Thirdly,by solving the Dirac equation,energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Wigner function for the Dirac oscillator in spinor space

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained.     

Conservation laws in de Sitter space from action principles in five-space

By recognizing the resemblance of the de Sitter group algebra to that of the conformal group, the method by which manifestly conformally covariant field equations in sixdimensional space are rewritten in Minkowski space is adapted to fields in flat five-dimensional space, the embedding space of de Sitter space. A quantum action principle based solely on rotational invariance in five-dimensional space is devised, and the resulting commutation relations are shown to correspond to the correct ones in curved four-space. As well as recovering the ten conservation laws associated with de Sitter group invariance, the five extra conservation laws present whenever conformal symmetry holds are determined directly in five-space. The derivation is found to be complicated by a new feature—the Lagrangian density does not transform as a field either for special conformal transformations or for dilations; this is true only for the former transformations in flat space.     

On the state space of the dipole ghost

A particular representation of SO(4, 2) is identified with the state space of the free dipole ghost. This representation is then given an explicit realization as the solution space of a 4th-order wave equation on a spacetime locally isomorphic to Minkowski space. A discrete basis for this solution space is given, as well as an explicit expression for its SO(4, 2) invariant inner product. The connection between the modes of dipole field and those of the massless scalar field is clarified, and a recent conjecture concerning the restriction of the dipole representation to the Poincaré subgroup is confirmed. A particular coordinate transformation then reveals the theory of the dipole ghost in Minkowski space. Finally, it is shown that the solution space of the dipole equation is not unitarizable in a Poincaré invariant manner.     

理想气体中的内势能

本文证明在无壁空间或无束缚力约束空间中,压力是气体以物态存在的束缚力.证明了热力学压力不仅是动量交换的统计平均值的量度,而且也是分子或原子空间位置分布(密度)的表征.理想气体在有限空间中的统计构形空间,具有逸散势-pV.这种系统构形空间内的各能级粒子具有相应的动量空间分布,其统计构形空间具有无序势TS.热力学平衡态具有处处相等p、T和总势能TS-pV.理想气体的二种势能具有对称性,总势能等于零;但其相应的无序势和逸散势都不等于零.     

Canonical quantization of classical mechanics in curvilinear coordinates. Invariant quantization procedure

In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed.     

空间光学的发展与波前传感技术

摘要：进入21世纪，国际上一些发达国家和有关部门都已制定了空间发展战略规划，如美国航空航天局（NASA）、欧洲空间局（ESA）和俄罗斯政府相关部门等都提出空间发展战略规划，这些规划提出了今后一段时间内空间科学要解决的问题和发展的方向，而解决这些问题并推进空间技术的发展很大程度上依赖于先进的光学和无线电望远镜及仪器设备。因此，本文介绍本世纪初国际上空间科学应用的大型天文望远镜的发展情况，重点描述了大口径光学望远镜的光学系统以及实现这类天文望远镜的关键技术之一一波前传感技术。     

The geometric phase and ray space isometries

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be realised as projections of unitary or anti-unitary transformations on the Hilbert space. We suggest that the construction involved in Wigner’s proof is best viewed as an use of the Pancharatnam connection to ‘lift’ a ray space isometry to the Hilbert space.     

“神舟”四号中的空间环境研究

空间环境 ,特别是日地空间环境是人类航天活动关系极为密切的环境 .文章以“神舟”四号为背景 ,概要介绍了为“神舟”四号飞船所作的空间环境安全保障服务 ,包括在“神舟”四号飞船上进行的空间环境探测、空间环境分布及变化规律的研究、空间环境对人类航天活动及“神舟”飞船的影响 (空间环境效应 ) ,以及为保障“神舟”飞船发射安全、正常运行、顺利返回所作的空间环境预报等 .此外 ,概要评述了国内外上述研究领域的研究现状与进展     

O8h结构磁空间群C-G系数的计算

磁空间群相对于以往的空间群,在对物理图像的描述上更准确、更深刻。如它可在考虑晶体对称性的同时,也考虑到自旋磁矩的作用,因而它的C－G系数更加重要。本文利用本征函数法,计算了面心立方结构Oh^8磁空间群的C－G系数,以及波矢选择规则和C－G序列。     

TWO-DIMENSIONAL NUMERICAL SIMULATION OF LOW FREQUENCY OSCILLATIONS OF SPACE CHARGE AND POTENTIAL IN THE GYROTRON ADIABATIC TRAP

The development of oscillations of the space charge and potential in the adiabatic trap of a gyrotron between the cathode and the cavity is studied numerically. The PIC method is applied, with the real two-dimensional distributions of the electric and magnetic fields taken into account. Secondary emission is included into the numerical model, as well as such factors as the electron beam space charge, thermal velocities of electrons, and emitter roughness. The value of the trapped space charge as a function of time is calculated. Time dependences of the potential in various cross-sections of the formation system are traced. The amplitudes of its variable component have been found and then the corresponding frequency spectra have been calculated. The process of cathode bombardment is investigated. The energy distribution and time dependence of the current in the electron beam coming to the operating space are found. Some ways to reduce the oscillations of the potential and the space charge are discussed.     

The geometrical structure of the parameter space of the two-dimensional normal distribution

The differential geometrical consideration of the parameter space, especially as a Riemannian geometry, was initiated by C.R. Rao in 1945. This approach appears to be important for the problem of estimation and test of hypotheses as well as for applications to physical problems. It has been shown that the parameter spaces of univariate normal distribution, univariate exponential distribution and multinomial distribution are Riemannian spaces of constant curvature. In the present paper the discussion is confined to the parameter space of the two-dimensional normal distribution. It has been shown that in general the parameter space is not necessarily of a constant curvature and that, if the correlation coefficient vanishes, the parameter space becomes an Einstein space. In addition, some invariant quantities, as sectional curvature, mean curvature and scalar curvature, have been calculated.     

简立方结构磁空间群耦合系数计算

利用本征函数法（EFM方法）计算了Oh^1结构磁空间群第一布里渊区部分点的C－G系数。     

Dynamical symmetries in mechanics

The object of this review is to discuss methods that enable one to trace the origin of symmetries and conservation laws in mechanics to geometrical symmetries of space-time. Starting with the basic Newtonian assumptions on absolute space and time classical mechanics is developed in configuration space and phase space independently together with the related structures such as force-less mechanics. Heuristic considerations on geometric symmetries in configuration space reveal their intimate relation to conservation laws. Using the methods of differential geometry this relationship is put on a formal footing and symmetry groups of all spherically symmetric single term potentials are classified. The method of infinitesimal canonical transformations is presented as an alternative method of deducing dynamical symmetries of an arbitrary system in phase space. These methods also apply to non-relativistic quantum theory. Possible extension to special and general relatively is also discussed.     

射频放电CO2激光器放电区物理过程的研究

本文认为射频放电CO₂激光器的高增益区是类法拉第暗区,并利用有质动力计算了阴极区和类法拉第暗区电子的能量及类法拉第暗区的尺寸,最后给出了四极放电CO₂激光器的一些实验结果。     

Geometro-Differential Conception of Extended Particles and the Semigroup of Trajectories in Minkowski Space-Time

The semigroup of trajectories in Minkowski space-time and its induced representations are constructed as a generalization of the Galilei case. They describe relativistic pointlike particles and yield the free propagator as a path integral in the space of trajectories parametrized by a fifth parameter. This non physical propagator in a five-dimensional space is integrated over the fifth parameter to yield the physical propagator in Minkowski space. Thereafter, this notion is applied to a model of extended particles with internal Poincaré symmetry and moving in an external Minkowski space. The geometrical structure is of Hilbert bundles and the interaction is introduced as a connection. The propagator is a path integral with respect to either the internal and external trajectories and reduces to a product of an internal and an external propagator when the interaction is ignored, just as has been found in a previous work with representations of the group rather than those of the semigroup.     

Globally hyperbolic flat space–times

We consider (flat) Cauchy-complete GH space–times, i.e., globally hyperbolic flat Lorentzian manifolds admitting some Cauchy hypersurface on which the ambient Lorentzian metric restricts as a complete Riemannian metric. We define a family of such space–times—model space–times—including four subfamilies: translation space–times, Misner space–times, unipotent space–times, and Cauchy-hyperbolic space–times (the last family—undoubtful the most interesting one—is a generalization of standard space–times defined by G. Mess). We prove that, up to finite coverings and (twisted) products by Euclidean linear spaces, any Cauchy-complete GH space–time can be isometrically embedded in a model space–time, or in a twisted product of a Cauchy-hyperbolic space–time by flat Euclidean torus. We obtain as a corollary the classification of maximal GH space–times admitting closed Cauchy hypersurfaces. We also establish the existence of CMC foliations on every model space–time.     

An expansion of system with time delayed feedback control into spatio-temporal state space

Time delayed feedback control is well known as an effective continuous control method for stabilizing the unstable periodic orbit embedded in chaotic attractors. As for the system with time delay, the solution is in a function space and shows characteristics governed by an infinite dimension. Therefore it is difficult to understand the system behavior analytically. In this paper, it is shown that, when the state space for the system with time delay is expanded into the spatio-temporal state space, the solution propagates in the space as a wave theoretically and numerically. The dynamic behavior experimentally obtained in the sinusoidally excited magneto-elastic beam system under time delayed feedback control is also discussed by the transformation into the expanded spatio-temporal state space. (c) 1999 American Institute of Physics.