Optimal nonlinear filtering with constraints—Part II

The impulse response of nonlinear systems with bounded memory and energy have been considered. On the base of the minimum mean square error criterion a generalization of the Wiener-Hopf equation is developed.     

Zernike多项式展开系数的时间相关性

 分析了受大气湍流扰动的光波波前在系统接收孔径上的Zernike多项式展开系数的时间相关性,在此基础上进一步分析了从不同方向到达系统接收孔径的光波波前整体倾斜之间的相关性,并给出了光波在水平均匀大气中传播时的结果。     

透镜抛光机主轴转速与摆架摆速的匹配

从计算得出的浮动上模作往复周期摆动时工件表面上任一点的相对线速度表达式看出，线速度幅值是一个多变量函数，在这些参数中，只有主轴转速与摆架摆速是机床本身的固有参数，从均匀抛光角度出发，提出主轴转速与摆架摆速匹配的观点，为抛光机换代设计提供了依据。     

Performance Analysis of the Spectral Correlation Discriminator Array

Mobile communications suffer from cochannel interference, adjacent channel interference and fading. The cell capacity or the number of users per cell is limited by the interference. In this paper we analyze a new blind adaptive array structure called the spectral correlation discriminator array (SCDA), designed to reject cochannel interference for advanced mobile phone service (AMPS) signals. The blind adaptive array exploits the spectral redundancy in the AMPS signals which arises due to the presence of the supervisory audio tone (SAT). SCDA is shown to provide an improvement of 25–30 dB in signal-to-interference plus noise ratio (SINR) in static multipath channels and 10–15 dB improvement of SINR in Rayleigh fading channels. The SCDA is compared to the least squares constant modulus array (LSCMA) and is shown to have better signal selectivity properties. The reduction in interference power can significantly reduce the frequency reuse factor.     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Evaluation of time correlation functions from a generalized Enskog equation

Numerical results for the density and current correlation functions in dense hard-sphere fluids are obtained from a kinetic equation which is the extension of the linearized Enskog equation to finite wavelengths in order to demonstrate the convergence of the method of solution. Comparison is made to a previously proposed approximate solution.This work was performed in part under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract number W-7405-ENG-48 and in part supported by the National Science Foundation.     

Noise-sustained structure,intermittency, and the Ginzburg-Landau equation

The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested.     

Equivalent measures of dependence

The maximal correlation between a pair of σ-fields $\text{A}$ and $\text{B}$ becomes arbitrarily small as sup{|P(A ? B) ? P(A) P(B)|/[P(A) P(B)]^1/2, A ∈ $\text{A}$, B ∈ $\text{B}$, P(A) > 0, P(B) > 0} becomes sufficiently small.     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.