A Domain of Spacetime Intervals in General Relativity

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. We obtain a mathematical setting in which one can study causality independently of geometry and differentiable structure, and which also suggests that spacetime emerges from something discrete.     

Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions

We extend the method of Balister, Bollobás and Walters (Phys. Rev. E 76:011110, 2007) for determining rigorous confidence intervals for the critical threshold of two dimensional lattices to three (and higher) dimensional lattices. We describe a method for determining a full confidence interval and apply it to show that the critical threshold for bond percolation on the simple cubic lattice is between \(0.2485\) and \(0.2490\) with \(99.9999\,\%\) confidence, and the critical threshold for site percolation on the same lattice is between \(0.3110\) and \(0.3118\) with \(99.9999\,\%\) confidence.     

Intervals of an unsteady electrohydrodynamic Kelvin-Helmoltz stability

An analysis is made of the stability of a basic flow of streaming fluids in the presence of an oblique periodic electric field. The particular profile investigated is the classical Kelvin-Helmholtz profile modified by the addition of the influence of mass and heat transfer across the interface. The intervals of electrohydrodynamic Kelvin-Helmholtz instability are considered. It is shown that a linear model of the interface is governed by Hill's differential equation. Characteristic values and intervals of stability are discussed. The special case of the Mathieu differential equation type is obtained. From the latter equation, the various criteria are discussed for both Rayleigh-Taylor and Kelvin-Helmholtz problems in the presence of an oblique periodic electric field, with and without mass and heat transfer across the interface.     

OCDMA系统二维RS地址码的设计方案及性能分析

首次在有限伽罗瓦域GF(7)上以本原元3构造出RS地址序列码.在一维RS素数码的基础上,给出基于二素数的二维RS矩阵码(2D-RSC)的设计方案.系统地研究了2D-RSC的OCDMA系统总体性能：分析了2D-RSC码字的相关性;导出了系统的最大用户容量;研究了2D-RSC系统以多址干扰为主的误码性能.结果表明：2D-RSC系统性能较之一维RS码有明显的改进. 特别是在大信息量传输时,采用两个较大的素数,基于2D-RSC的OCDMA系统的总体性能远优于一维素数码.     

Large Deviations,Fluctuations and Shrinking Intervals

This paper concerns the statistical properties of hyperbolic diffeomorphisms. We obtain a large deviation result with respect to slowly shrinking intervals for a large class of Hölder continuous functions. In case of time reversal symmetry, we obtain a corresponding version of the Fluctuation Theorem.     

Distribution of Periods of Closed Trajectories in Exponentially Shrinking Intervals

For hyperbolic flows over basic sets we study the asymptotic of the number of closed trajectories γ with periods T _γ lying in exponentially shrinking intervals ${(x - e^{-\delta x}, x + e^{-\delta x}), \; \delta > 0, \; x \to + \infty.}${(x - e^{-\delta x}, x + e^{-\delta x}), \; \delta > 0, \; x \to + \infty.} A general result is established which concerns hyperbolic flows admitting symbolic models whose corresponding Ruelle transfer operators satisfy some spectral estimates. This result applies to a variety of hyperbolic flows on basic sets, in particular to geodesic flows on manifolds of constant negative curvature and to open billiard flows.     

Length of the Instability Intervals for Hill's Equation

The length of instability intervals is investigated for the Hill equation y′′+ω(ω− 2∈p(x)y = 0, where p(x) has an infinite Fourier series of coefficients c _n. For any small ∈ it is shown that these lengths are completely characterized by the c _n's.     

等间距线性数据的标准偏差

对大学物理实验中两种不同类型的等间距线性数据进行了区分。第一类线性数据中,等权独立的误差来源于对每一位置的测量而与其它位置的测量无关,应该把每一测量点对最佳直线的偏离作为研究对象,其它参量的标准偏差应该从该对象的标准偏差为出发点求得;第二类线性数据等权独立的误差来源于每一次测量过程的增加量,应该把每一次测量的增加量同最佳增加量的偏离作为研究对象,其它参量的标准偏差应该从此对象的标准偏差为出发点求得。针对这两类数据,分别按照算术平均值法、逐差法和最小二乘法的原则进行处理,给出了符合其数据类型对象的最佳斜率表达式和它们的标准偏差表达式.给出了它们的比较:第一类线性数据的最小二乘法处理的最佳斜率的标准偏差最小;第二类线性数据的算术平均值处理给出的标准偏差最小。     

Lattices and Quantum Logics with Separated Intervals, Atomicity

It is well known that a Boolean algebra B isatomic (atomistic) iff the interval topology on B isHausdorff. But this no longer holds for orthomodularlattices (quantum logics). There exist (even complete) atomic orthomodular lattices the intervaltopology of which is not Hausdorff. We show that anothercharacterization of atomicity for Boolean algebras isthe following: A Boolean algebra B is atomic iff B has separated intervals. Furthermore, we showthat the interval topology on a complete orthomodularlattice L is Hausdorff iff L has separated intervals iffL is atomic and it has separated intervals. An orthomodular lattice L with orthomodularMacNeille completion has separatedintervals iff L is atomic and it has separated intervalsiff the interval topology on isHausdorff.     

Short notices

The coming into operation of the Intersecting Storage Rings (ISR) at the European Centre of Nuclear Research (CERN), near Geneva, has made it possible in the past two years to study the behaviour of matter at the highest densities ever obtained artificially, hundreds of times greater than the density of matter in nuclei and even in the densest stars. An account is given of some of the results obtained thus far; this is followed by a brief discussion of possible future developments.