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This paper compares periodic set with almost periodic set, and properties of periodic function with that of almost periodic function through analysing the definitions of periodic function and almost perodic function, and then draws some important conclusions.

利用周期函数与概周期函数的定义,把周期函数的周期集与概周期函数的概周期集进行了比较,把周期函数与概周期函数的性质进行了比较,并得出一些重要结论。

A main feature in developing the theory is that the scope is expanding: from almost periodic function, asymptotically almost periodic function, weakly almost periodic function to pseudo almost periodic function which was introduced by Professor Zhang in 1992. Every extension consumedly enlarges the theory and their applications.

从概周期函数、渐进概周期函数、弱概周期函数,一直到张传义教授在上世纪九十年代初提出的伪概周期函数,每一次函数范围的扩展都大大地丰富了概周期函数的理论和其应用前景。

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理,将一致概周期函数与有限三角多项式联系起来;第二,在恒同定理的基础上,给出了一致B~2概周期函数的Fourier级数,并且级数是唯一的;第三,讨论了一致B~2概周期函数的Parseval方程,建立了函数与其Fourier级数的系数之间的联系;接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

On the applications of the uniformly Besicovitch almost periodic functions to differential equations, the main works are as follows:First, the paper proves that the space of the uniformly B2 almost periodic functions, with a special norm, is a Banach space, and then the Fixed Point Methods could be used in this function space.Second, since the space of the uniformly B2 almost periodic functions is per-fect, the paper investigates the existence and uniqueness of uniformly B2 almost periodic solution of a wave equation involving reflection of the argument by the principle of contraction mapping.

关于一致Besicovitch概周期函数在微分方程中的应用,本文主要做了以下工作:第一,证明了一致B~2概周期函数空间在其特定范数下构成Banach空间,从而可以在此函数空间上应用不动点定理;第二,由一致B~2概周期函数空间的完备性,应用压缩映像原理,讨论了一类满足一定初始条件的带反射变量的波方程一致B~2概周期解的存在唯一性。

Though the almost unbiased estimator was still a biased estimator, it has smaller bias than corresponding biased estimator.In this paper, we first study the properties of the almost unbiased generalized ridge estimator and the almost unbiased generalized Liu estimator.

但有偏估计毕竟偏离参数的真值,因此学者们又提出了几乎无偏估计的概念,虽然几乎无偏估计仍然是有偏估计,但是它比相应的有偏估计有更小的偏度。

And then some ellipses that AUGR estimator is better than the OLS estimator and AUGL estimator is better than the OLS estimator are given, respectively.Second, the definition of the almost unbiased unified biased estimator is proposed. This definition includes the familiar almost unbiased estimators in literatures, and it is the unified expression of the familiar almost unbiased estimators. Followed the biased and variance are compared of AUUB estimator and the unified biased estimator, respectively. AUUB estimator has smaller bias than UB estimator and the variance of AUUB estimator is between the variance of UB estimator and 4 times of the variance of UB estimator. Finally the properties of AUUB estimator are discussed. The conclusion is gained that there are parameters made AUUB estimator is better than OLS estimator in terms of their mean square error. The sufficient and necessary condition that AUUB estimator is admissible is given. The ellipse is given that AUUB estimator is

然后给出了几乎无偏统一有偏估计的定义,该定义包括了文献中常见的几乎无偏估计,实现了常见几乎无偏估计的统一表达式;接下来我们比较了几乎无偏统一有偏估计与统一有偏估计的偏度与方差,得出了几乎无偏统一有偏估计比统一有偏估计有较小的偏度,几乎无偏统一有偏估计的方差介于统一有偏估计的方差与统一有偏估计的方差的四倍之间的结论;最后我们对统一有偏估计的主要性质作了讨论,证明了存在参数K,S使得几乎无偏统一有偏估计在均方误差意义下优于最小二乘估计的结论,给出了几乎无偏统一有偏估计为可容许估计的充要条件,还给出了在均方误差阵意义下几乎无偏统一有偏估计优于最小二乘估计的椭球。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征,讨论了其几乎处处连续与极限存在的关系,从而得到了从函数可积性到连续性,从连续性到极限存在性的函数特性理论,即可积函数中极限的几乎处处存在与几乎处处连续是等价的,得出比正规函数更加宽泛的统一条件,得出了有界变差函数是可积函数的结论。

Metz: Almost every night over there...

almost:几乎在那儿,几乎每个晚上。。。

McDormand is as comfortable and convincing as an aging rock sybarite as she was playing the worrywart mother of a teenage rock fan in "Almost Famous" is further evidence of her exceptional dramatic range .

McDormand在"Almost Famous"中扮演了一个年轻摇滚爱好者的自寻烦恼的母亲,她在演一个老牌摇滚享乐者时非常自如和令人信服,这进一步证明了她有非常广的戏路。

McDormand is as comfortable and convincing as an aging rock sybarite as she was playing the worrywart mother of a teenage rock fan in "Almost Famous" is further evidence of her exceptional dramatic range .

McDormand在&Almost Famous&中扮演了一个年轻摇滚爱好者的自寻烦恼的母亲,她在演一个老牌摇滚享乐者时非常自如和令人信服,这进一步证明了她有非常广的戏路。

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