The six semifield planes associated with a semifield flock

In 1965 Knuth (J. Algebra 2 (1965) 182) noticed that a finite semifield was determined by a 3-cube array (a_ijk) and that any permutation of the indices would give another semifield. In this article we explain the geometrical significance of these permutations. It is known that a pair of functions (f,g) where f and g are functions from GF(q) to GF(q) with the property that f and g are linear over some subfield and g(x)²+4xf(x) is a non-square for all x∈GF(q)∗, q odd, give rise to certain semifields, one of which is commutative of rank 2 over its middle nucleus, one of which arises from a semifield flock of the quadratic cone, and another that comes from a translation ovoid of Q(4,q). We show that there are in fact six non-isotopic semifields that can be constructed from such a pair of functions, which will give rise to six non-isomorphic semifield planes, unless (f,g) are of linear type or of Dickson-Kantor-Knuth type. These six semifields fall into two sets of three semifields related by Knuth operations.     

On uniformity of exponential dichotomies for delay equations

It is shown that there cannot exist a uniform exponential dichotomy for any linear delay equation with a positive finite delay.     

Uniform persistence for nonautonomous and random parabolic Kolmogorov systems

The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems.     

On a stochastic hyperbolic integro-differential equation

In this paper we study an initial-boundary-value problem for a hyperbolic integro-differential equation with random memory and a random noise. We establish the existence, uniqueness and exponential stability of solutions. Our method consists of finite-dimensional approximation and energy estimates.     

Effect of Nuclear Binding Energy to K Factor

We modify the square of virtual photon four-momentum by using nuclear binding energy formula, and calculate the effect of nuclear binding energy to K factor and Compton subprocess and annihilate subprocess in A-A collision Drell-Yan process. The outcome indicates that the effect of nuclear binding energy to K factor is obvious in little x region and it would disappear gradually as x increases.     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

e+e-实验中ψ(2S)能区连续态单光子湮没过程的贡献

研究了e+e-实验中ψ(2S)能区连续态单光子湮没过程的截面对观测总截面的贡献. 针对ψ(2S)质量处ωπ0和π+π-两个观测末态,利用唯象模型估计了单光子湮没过程贡献的大小. 分析表明,对于ψ(2S)→ωπ0和ψ(2S)→π+π-,以及其他电磁末态分支比的确定,单光子湮没过程的贡献必须认真考虑. 通过研究,我们认为对于BES实验来说,为了获得共振态电磁末态分支比的正确结果,至少需要在低于ψ(2S)共振峰的能量点采集10pb-1的数据.     

Diffraction of transverse horizontal waves in Fibonacci piezoelectric superlattices

The transfer matrix and global matrix techniques are used in the analysis of diffraction of transverse horizontal waves in piezoelectric superlattices. The system is composed of a set of different piezoelectric layers with quasiperiodic structure according to the Fibonacci sequence. The diffraction spectrum of different configurations of piezoelectric Fibonacci structures is studied. Numerical results for the diffraction spectrum for the piezoelectric Fibonacci superlattice are obtained and a comparison between the results of the transfer and global matrix methods is given, exhibiting the advantage of the latter.     

光双二进制传输系统的性能研究

光双二进制信号的谱宽是传统二进制信号的一半,采用双二进制传输比二进制传输色散限制的中继距离可增加一倍.本文对采用传统光接收机的光双二进制传输系统用MATLAB进行了通信仿真.结果表明:在完全消光条件下,10 Gb/s双二进制信号在常规单模光纤上传输可达160 km,40 Gb/s双二进制信号在非零色散光纤上为30 km,均比二进制增加了一倍;详细考察了消光比对传输的影响,只有消光比大于25 dB时,双二进制相对于二进制传输的优越性才呈现出来.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.