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There are series of papers studying the solvability of an incompressible, viscous, instationary fluid contained in a domian bounded entirely by a free surface. In 1977, Solonnikov proved its local solvability in a Holder space for any initial date but without surface tension. In 1984, he considered the same problem in a Sobolev space with surface tension being taken into account. In I992, Mogilevskii and Solonnikov treated the same problem in a Holder space, where the coefficient of surface tension is not a constant. There are also short-time existence results for the solvability of an incompressible, vicous, unsteady fluid bounded above by a free surface and below by a fixed bottom which approach horizontal planes at infinity. In 1981, Beale proved its local solvability in a Sobolev space for any initial date but without surface tension. In 1983, Allain were concerned with the same problem in R〓 with surface tension but under the assumption that the initial fluid domain was near a horizontal strip. In 1987, he obtained the same result without the preceding assumption. In 1996, Tani solved the same problem in R with surface tension. For the solvability of an incompressible viscous instationary fluid in Ω R bounded inside by a free surface S and outside by a rotating boundary S, in 1995 Ciuperca proved its local existence in a Sobolev space for any initial date but without surface tension. In this paper, we consider the same problem with surface tension.

对于边界完全是由自由边界组成的有界区域中粘性不可压流体的非定常运动问题,Solonnikcv于1977年在忽略表面张力情况下证明了初值问题小时间解在Holder空间的存在性,于1984年在有表面张力情况下证明了初值问题问题小时间解在Sobolev空间的存在性,Mogilevskii和Solonnikov于1992年在表面张力系数可以不是常数情况下证明了初值问题小时间解在Holder空间的存在性;对于上面是自由边界、下面是固定边界且两边界在无限处趋于水平的无限区域中粘性不可压流体的非定常运动问题,Beale于1981年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性,Allain于1983年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性,但其中假定初始区域近似是个水平条,他于1987年去掉了这个假定得到同样的结果,Tani于1996年在有表面张力情况下证明了R中初值问题小时间解在Sobolev空间的存在性;对于R中内面是自由边界、外面是旋转边界S的有界区域中粘性不可压流体的非定常运动问题,Ciuperca于1995年在忽略表面张力情况下证明了初值问题小时间解在Sobolev空间的存在性,本文考虑了在有表面张力情况下初值问题可解性问题。

The content of this course is divided into four chapter, the normed linear space and bounded linear operator on the normed space; the character of finite dimensional linear space; the basic theorems on Banach space.

本课程主要分为四章,赋范线性空间与内积空间;赋范线性空间上的有界线性算子,有限维赋范线性空间的特征。Banach空间中的基本定理:泛函存在定理,一致有原理,开映象,闭图象、逆算子定理。

It is necessary to point out that our results not only extend the classical results of composition operators C〓 on Hardy spaces, Bergman space, Dirichlet space and Nevanlinna class, but also expand composition operator C〓 to sequence {C〓} or C〓C〓 and C〓C〓, and expand basic spaces to the vector-valued analytic function spaces, etc.

应该指出的是,本文不仅涵盖了经典Hardy空间、Bergman空间、Dirichlet空间、Nevanlinna类上复合算子C〓的原有结果,而且进一步弄清了不同空间之间的复合算子的性质,同时扩展了单个复合算子C〓至复合算子序列{C〓}及乘积算子C〓C〓与C〓C〓的情况,基本空间扩展至向量值解析函数空间的情形等等。

Chapter 3 Some properties in Cesaro-Orlicz sequence spaces: In this chapter, the dual spaces of the Cesaro-Orlicz sequence spaces and the criteria for the extreme point are studied and the sufficient and necessary condition of which the spaces has theλ- property and the uniformλ- property is given by the above results.

第三章Cesaro-Orlicz序列空间中的一些基本性质:本章我们主要讨论了Cesaro-Orlicz序列空间的对偶空间,同时给出此空间中端点的判据,然后由此端点的判据我们证明了Cesaro-Orlicz序列空间具有λ-性质,最后我们得到了此空间中一致λ-性质的等价条件。

In the fifth chapter,we mainly discuss the relationship of the metric space induced by a Loeb measure space and the metric space induced by a internal finitely additive measure space.

在第五章,我们重点讨论了由有限测度空间导出的度量空间和由内有限可加测度空间导出的度量空间的关系,然后在此关系的基础上研究了由内有限可加测度空间导出的度量空间的性质。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先,构造二维张量积空间,并证明该空间具有再生核;其次在再生核空间中,建立多尺度分析,获得该空间的一个标准正交基,使得再生核空间可以由小波空间来刻画,进而得到小波级数和相应的采样公式,而且给出的小波级数形式简单易于数值分析,进一步完善了有限区间上的多尺度分析方法,也为实际应用提供了良好的理论基础和算法。

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Chapter 4 -rotundity and nearly strict convexity of quotient spaces. It is proved that ifis a -rotund or nearly strict convex Banach space andis a closed and proximinal subspace of, then the quotient spaceis also -rotund or nearly strict convex.

第四章 商空间的-严格凸性和近严格凸性:本章证明了若是Banach空间的任意可逼近子空间,则商空间对原空间的-严格凸性和近严格凸性都具有遗传性。

This paper presents aconcept of " Space for Brightness Perception ", and transforms the design of lightand space into the design of Space for Brightness Perception correspondingly, andbrings forward a method of dynamic integrative design of light and space.

在此基础上,提出了&光视空间&的概念,把空间的视觉设计归结为光视空间的设计,并进而采取现象学的方法,对光视空间的本质进行还原,探讨光视空间设计的基本观念和源泉,提出了光与空间一体化设计的方法,提倡光与空间的双向的互动的设计模式。

This method first maps training data into a high dimensional feature space through kernel function concept in Support Vector Machine and constructs orthogonal space in the feature space. Then it maps the data from feature space into the orthogonal space and computes Fisher criterion based global orthogonal discriminants.

首先应用支持向量机中核函数的概念,将样本隐式地映射到特征空间,然后构造特征空间的正交空间,再将特征空间样本映射到特征空间的正交空间,求解基于Fisher的全局正交鉴别矢量集。

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Finally, according to market conditions and market products this article paper analyzes the trends in the development of camera technology, and designs a color night vision camera.

最后根据市场情况和市面上产品的情况分析了摄像机技术的发展趋势,并设计了一款彩色夜视摄像机。

Only person height weeds and the fierce looks stone idles were there.

只有半人深的荒草和龇牙咧嘴的神像。

This dramatic range, steeper than the Himalayas, is the upturned rim of the eastern edge of Tibet, a plateau that has risen to 5 km in response to the slow but un stoppable collision of India with Asia that began about 55 million years ago and which continues unabated today.

这一引人注目的地域范围,比喜马拉雅山更加陡峭,是处于西藏东部边缘的朝上翻的边框地带。响应启始于约5500万年前的、缓慢的但却不可阻挡的印度与亚洲地壳板块碰撞,高原已上升至五千米,这种碰撞持续至今,毫无衰退。