乘积

In this paper, the adjointness of the product of two differential operators generated by a third order normal and singular symmetric differential expression in the limit-circle case is discussed. The necessary and sufficient conditions which make the product operators being the adjoint operators obtained by the matrix analysis and calculation. At the same time, the adjointness of the product of the power and adjointness operator obtained.

本文首先讨论了正则和奇异两种情况下两个极限圆型三阶对称微分算式生成的微分算子的乘积的自共轭性，运用矩阵分析和计算，得到了乘积算子为自共轭算子时边界应满足的充分必要条件，同时得到了幂算子的自共轭性、自共轭算子乘积的自共轭性等乘积算子的其它若干性质。

Firstly, we analyze the deficiencies ofexisting ones, extend domains of fuzzy logical operators from the cap product withtwo sets to them with arbitrary (finite, enumerable, or non-enumerable) number ofsets to form two general mappings so as to conform them to the fuzzy conjunctionand infimum, and to fuzzy disjunction and supremum, respectively, and fuzzify theset inclusion of fuzzy sets. Similar to the classical adjunction, the concept of fuzzyadjunction is introduced.

首先分析了原有"模糊形态学"框架的缺陷，进而将模糊合取和模糊析取算子的定义域从两个集合的笛卡儿乘积推广到任意多个集合的笛卡儿乘积，形成两个一般的映射，使得模糊合取与下确界、模糊析取与上确界保持一致，以此将模糊集的包含关系一般化。

Bordered matrix has very wide applications in the matrix theory, many specialists and scholars had studied bordered matrices before.

本节在P-SVD中通过构造特殊的非奇异矩阵，详尽地揭示了两个矩阵乘积{1，3}-和{1，4}-逆的结构，从而最终解决了两个矩阵乘积{1，3}-和{1，4}-逆的反序律，并得到了两个矩阵乘积伪逆反序律的一个新的等价性条件。

Firstly, the paper sets up a rational function model for the long run relationship between economic growth rate and the inflation rate by adding the cross product term of the both into the traditional model of "output-price" Phillips curve. The empirical analysis shows that the product term has substantial impact on the model\'s stability.

第一，本文在传统"产出一物价"型Phillips曲线长期模型中，加入了表现经济增长率与通货膨胀率乘积效应的交叉乘积项，建立了表现二者之间长期关系的有理函数模型。

By using the partition theorem of unity, a continuous selection theorem for a multimap from a compact Hausdorff topological space to a finitely continuous topological spaces (simply, FC-spaces) without any convexity structure was obtained, and from which and Tychonoff fixed point theorem, a collectively fixed point theorem for a family of multimaps on the product space of compact FC-spaces and several collectively fixed point theorems for a family of multimaps on the product space of non-compact FC-spaces were given.

利用单位分解定理得到从紧的Hausdorff拓扑空间到没有任何凸结构的有限连续拓扑空间的集值映射的连续选择定理，并从该结果和Tychonoff不动点定理，得到紧的FC-空间的乘积空间上映射族的集族不动点定理和若干个非紧的FC-空间的乘积空间上的映射族的集族不动点定理，对文献中的相应结果进行了改进和一般化。

On the product of unit spheres,we give a kind of natural embeddings from the product unit spheres to the unit sphere in which the product of unit spheres can be viewed as a hypersurface.

第一个是在乘积单位球面上，我们给出自然的由乘积单位球面到高一维球面的嵌入映射，然后考虑了在乘积单位球面上预给定Gauss-Kronecker曲率后，我们所考虑的嵌入的存在性。

In this paper,the law of iterated logarithm for product sums of positive as- sociated sequences with the strong stability and the strong law of large numbers for product sums of positive associated sequences with different distributions are proved.

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律，指出了部分和服从强大数律但乘积和未必服从强大数律这一事实，并讨论了定理2中一个条件的必要性。

However, the fact that SICp category does not exist establishes the basis of further study work on the Cartesian closedness of categories for semicontinuous lattices .

讨论了两类半连续格范畴有限乘积性的存在性，得到了SIC_P范畴具有有限乘积性而SIC_q范畴有限乘积不存在的结果，为进一步研究半连续格范畴的Cartesian封闭性奠定了一定的基础。

In Chapter 2, we recapitulate some fundamental definitions and propositions of topological degrees and some fundamental results about the computation of topological degrees;in Chapter 3, applying relative definitions and propositions of topological degrees, we establish product formulae of topological degrees in product space, in particular, the product formula of fixed point index on product cone, moreover, combining with the fundamental propositions and the computation of fixed point index, we obtain some fixed point theorems on product cone.

为此，在第二章中，我们给出了拓扑度的基本概念和性质以及拓扑度计算方面的基本结果；在第三章中，运用拓扑度的有关知识，我们建立了乘积空间中各类映射的拓扑度的乘积公式，特别是乘积锥上的紧连续映射的不动点指数的乘积公式，进一步，结合不动点指数的基本性质和不动点指数计算方面的基本结果，得到了乘积锥上的若干不动点定理。

In Chapter 3, we discuss the self-adjoint boundary-value problems for products of m differential operators generated by the same symmetric differential expression of order n defined on a, b

第三章 讨论了m个由同一n阶对称微分算式生成的赋予某种边界条件的微分算子乘积自伴边值问题，结合常微分算子自伴扩张的一般构造理论，分别给出了两个四阶微分算子、两个n阶微分算子、m个n阶微分算子乘积自伴边条件的解析刻划，得到了乘积微分算子是自伴的充分必要条件及与乘积算子自伴性有关的一些有益结果。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了