一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

PTC热敏电阻器的电阻温度特性及应用

本文从半导体陶瓷PTC热敏电阻器入手，讨论了该热敏材料的电阻温度特性，给出了PTC热敏电阻器的测量结果和应用范围。     

渐变折射率光波导的精确分析

本文利用转移矩阵理论和等效衰减系数的概念，导出了渐变折射率光波导的色散方程，数值计算的结果，赢余方程的精度优于目前存在的所有近似方法。     

Effective potential for water vapour

A suitable temperature dependence is introduced into the force parameters of the Lennard-Jones potential by taking the free-energy average of the Rowlinson potential. The resulting temperature-dependent parameters are used to calculate the effective potential, which is plotted for water vapour at a few different temperatures. The temperature-dependence of the second virial coefficient is shown for the cases of temperature-independent and temperature-dependent parameters of which the latter agrees very well with experimental results.     

Electron and plasma stream reflection at a nonadiabatic mirror

Experimental investigations of the phenomena occurring when low density electron and plasma beams are injected into a nonadiabatic magnetic mirror are presented. Effects of nonadiabaticity and mirror ratio on the reflectivity of the magnetic mirror are measured. Transition of the mirror from adiabatic to strongly nonadiabatic results in setting up of a potential barrier which enhances the reflectivity.     

Magnetotransport in simple metals. An exactly soluble model

The magnetoconductivity tensors of a metal with a weakly anisotropic Fermi surface are determined from analytic solutions to the Boltzmann equation without any restrictions on the magnitude of the cyclotron frequency compared to the collision rate. Results are given for both a two- and a three-dimensional model, the former being analytically simpler to handle. The Hall coefficient and magnetoresistance are obtained as functions of the magnetic field, and we show by explicit calculation how the thermoelectric coefficients at high magnetic fields are determined by the thermodynamic entropy.     

On the correlation dimension of the spectral measure for the thue-morse sequence

Using the relationship between the decay rate of autocorrelation and the characteristics of singular Fourier spectra, we show that the correlation dimension of the spectral measure for the infinite Thue-Morse symbolic sequence equals 3 − log(1 + √17)/log 2=0.64298….     

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.     

激光-钨靶耦合效应的二维模拟研究

利用二维ESCL-CASTOR磁流体力学三温激光靶程序,对激光-钨靶进行了计算机模拟研究。得到了密度、温度(T_e,T_i,T_R)和速度的空间分布以及随时间的变化规律;特别是得到了临界面的运动规律、辐射谱和X光转换效率等结果,并与实验结果进行了比较。     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.