定理

Theorem 1 constructs a set of universal measure zero using continuous extension; Theorem 2 verifies absolutely continuous function being of good property under some condition; Theorem 3 reveals some relation between real function and meager.

定理1 主要运用了连续延拓构造了一个泛测度零集；定理2 证明绝对连续函数在一定条件下具有良好的性质；定理3 揭示了实函数与第一纲集的某种关系。

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

Under the instruction of the schur axioms, many reasoning concerning schur axiomses produced then, and became a theories system of the schur axioms of integrity, coming up the certificate that the schur axioms and many of its reasonings expanded the likeness of the matrix and the characteristic of the matrix to be worth.

在 定理的指导下，许多关于定理的推论便产生了，并且形成了一个完整的定理理论体系，把定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces.

通过应用G-凸空间的乘积空间内一族GB-优化映象的极大元的存在定理，在G-凸空间的非紧设置下证明了某些重合点定理，Fan-Browder型不动点定理和极小极大不等式组的解的存在性定理。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

This result is browden to n-dimentional case in chapter 2 first and an existence theorem (theorem 2.1) for linearly increasing solutions is given.

第二章将此结果推广到高维情形，给出了一个线性增长解的存在性定理(定理2.1)；另外，本章还给出了方程存在对数增长解的两个定理(定理2.2—2.3)。

The main work is done as following: 1.A model of dynamic fuzzy multi-dimensional data is proposed. The compose and the categoricalness theorem of the model of dynamic fuzzy multi-dimensional data is proposed. The provement of both is proposed.

主要工作有以下几方面： 1、给出了动态模糊多维数据模型，包括动态模糊多维数据模型合成定理和动态模糊多维数据模型完备性定理，对该模型的合成定理和完备性定理作了证明。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对&中间点&的渐近性进行了研究，得出了一系列&中间点&的渐近性的结果，概括了有关文献对微分中值公式的&中间点&的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新