A Radial Derivative with Boundary Values of the Spherical Poisson Integral

A formula of a radial derivative is obtained with the aid of derivatives with respect to and to of the functions closely connected with the spherical Poisson integral and the boundary values are determined for . The boundary values are also found for partial derivatives with respect to the Cartesian coordinates .     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

Large Deviations Behavior for the Quadratic Error of Density Estimate

For a projection estimator f_n of an unknown density f we investigate the behavior of large deviations probability P{T_n > r_n} when r_n , where T_n is appropriately centered and normed quadratic error f_n-f)².     

平面多项式系统及其相伴系统

引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 .     

关于积分上限函数的几个定理

变上限积分是积分学的一个重要理论，其运算结果仍以函数的形式体现．研究这类函数，得出几个颇有理论意义的定理。     

低杂波电流驱动的密度极限分析

用低杂波的可的性条件，参量不稳定条件和功率耦合谱分析了低杂波电流驱动。由于波的可近性条件限制耦合谱中平行相速度较大的波进入等离子体中心，参量不稳定性使平行相速度较低的波与离子相互作用，随着等离子体密度的增中，这些作用越来越明显，最终导致低杂波不能在中心与电子相互作用，驱动电流消失，这就是所谓密度极限。在本文建立的模型基础上的计算结果与实验结果符合较好。     

Asymptotic theorems for estimating the distribution function under random truncation

Representation theorem and local asymptotic minimax theorem are derived for nonparametric estimators of the distribution function on the basis of randomly truncated data. The convolution-type representation theorem asserts that the limiting process of any regular estimator of the distribution function is at least as dispersed as the limiting process of the product-limit estimator. The theorems are similar to those results for the complete data case due to Beran (1977, Ann. Statist., 5, 400–404) and for the censored data case due to Wellner (1982, Ann. Statist., 10, 595–602). Both likelihood and functional approaches are considered and the proofs rely on the method of Begun et al. (1983, Ann. Statist., 11, 432–452) with slight modifications.Division of Biostatistics, School of Public Health, Columbia Univ.     

Asymptotic behavior of fluctuations for the 1D Ising model in zero-temperature limit

Fluctuation of the average spin for one-dimensional Ising spins with nearest neighbor interactions are studied. The distribution function for the average spin is calculated for a finite volume, finite temperature, and finite magnetic field. As the volume increases and the temperature diminishes at zero magnetic field, there are two limits in which the probability distribution shows quite different behaviors: in the thermodynamic limit as the volume goes to infinity for finite temperature, small deviations of the fluctuations are described by a Gaussian distribution, and in the limit as the temperature vanishes for a finite volume, the ground states are realized with probability one. The crossover between these limits is analyzed via a ratio of the correlation length to the volume. The helix-coil transition in a polypeptide is discussed as an application.     

对冲击电流计测直螺线管磁场的两项改进措施

通过一些具体数据，对冲击电流计测直螺线管磁场的实验进行了分析，指出了两个重要误差来源，并介绍了改进措施。     

THE VARIATION OF INVARIANT LINES AND LIMIT CYCLES FOR A QUADRATIC DIFFERENTIAL SYSTEM

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