权为任意正实数的Poincare级数（II）解析的情形

设ｒ为一个正实数，１＜ｒ＜２，是一个Ｈ－群，υ：Γ→Ｃ是一个乘子系（定义见文［８］）．本文在［８］的基础上讨论了Ｐｏｉｎｃａｒｅ级数的存在性．令Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）＝Ｐ＿（ｎｒ）（ｚ，０，υ，Γ，ｋ＿ｊ）．这里Ｐ＿（ｎｒ）（ｚ，ｓ，Ａ＿ｊ，Γ，ｋ＿ｊ）如文［８］中定义．我们有：定理｛Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）｝ｎ＋ｋ＿Ｋ＞０是群Γ的，权为ｒ的具有乘子系υ的全纯歧点型模形式，且它们张成歧点型模形式所成的空间．应用这个结果，我们证明了一些模形式的性质并推导出一个重要的恒等式．该恒等式在半整权模形式的Ｆｏｕｒｉｅｒ系数估计中有极重要的地位．     

q超几何级数 2Φ0[a,b;z]的两个基本恒等式及其一些应用

本文由有限域上交错矩阵方程ＸＫ_２υＸ′＝０的解数公式得到ｑ超几何级数 ₂Φ₀的一个基本恒等式，并且用它能直接把一些特殊矩阵的这类方程的解数由函数 ₂Φ₀表出．另外还用 ₂Φ₀的一个恒等式得出Ｆ_q上ｍ阶特殊矩阵的个数．     

特征≠2的有限域上对称矩阵方程解的计数公式及其q超几何级数表达

设Ｆｑ是特征≠２的有限域．本文利用Ｆｑ上奇异正交几何的理论，给出当Ａ，Ｂ分别是Ｆｑ上阶ｎ秩２ν＋δ和阶ｍ秩２ｓ＋γ的对称矩阵时，Ｆｑ上适合方程ＸＡＸ′＝Ｂ的秩ｋ的解Ｘ的个数和解Ｘ的个数的明显公式，并且用ｑ超几何级数简化表达解数公式．     

Analysis of pseudo-periodic chronological series with irregularly time-spaced data in view to their prediction. I. Proposed problem

The problem originates from the necessity to predict luminosities of large-amplitude variable stars that are to be observed by the astronomical satellite HIPPARCOS. The data have a specific character: they are unequally time-spaced and can be missing during a long time in comparison to the pseudo-period. So the classical method of time-series analysis must be adapted and new methods are to be searched. In the following papers we present two solutions: a numerical one derived from a Fourier analysis and a symbolic one.     

Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I²), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category.     

我国水路货运量短期预测模型

本文对我国逐月水路货运量进行了趋势、季节分析，并利用时间序列分析方法建立了简单、实用的短期预测模型。     

双重时序AR—MA模型的高价平稳性

本文讨论双重时序AR－MA模型的高价（4阶，8阶及一般2m阶）平稳解存在的充分条件，这些结论对建立模型参数的矩估计及讨论估计量的渐近性质都是必不可少的．     

Factors for ¦N,pn;δ¦k summability of Fourier series

In this paper two theorems on | N,p_n;δ|_k summability factors, which generalize the results of Bor [4] on | N,p_n|k summability factors, have been proved.     

Nonlinear waves in two-dimensions generated by variable pressure acting on the free surface of a heavy liquid

The development of nonlinear waves on the free surface of a heavy liquid initially at rest is treated analytically in cases where the external pressure force of limited power is distributed over a large area in the free surface but is otherwise arbitrary. In [1] approximate (up to small terms of higher order) solution of the problem is obtained in the form of functional series. In the present article the convergence theorems for the series are proved. When the pressure varies with time sinusoidally, the sums of the series are found in closed form. By passing to the limit in the solution as time goes to infinity, the form of the nonlinear steady-state wave is found. According to the solution, when the steady-state wave gets away from the variable pressure zone, a long chain of structures develops similar to so called Kelvin-Helmholtz billows. The existence of nonlinear standing waves is discovered, which have a finite number of nodes in the free surface infinite in extent, and the frequency spectrum and the form of these waves are found explicitly.     

关于二重三角级数的有关讨论

文 [1 ]对形如 ∑∞n =0 ∑∞m =0amncosmxcosny等二重三角级数的和函数进行了研究 ,并证明了其范数‖f(x ,y)‖ p =∫π-π∫π-π｜f(x ,y) ｜p1 dx p2 /p1 dy1/p2 <∞所满足的几个不等式 .本文在此基础上对有关问题作了讨论并得到进一步的结果