查询词典 replacement theorem

Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results.

利用Liapunov中心定理，进一步得到了周期解的存在性定理，并举例说明结果的应用。

In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression.

在最后一部分讨论了带有特征值的非线性二阶差分方程正解存在性问题，利用锥压缩与拉伸不动点定理及逼近性理论，在一定的假设条件下，得到了差分方程正解存在性。

By changing differential equations into nonlinear integral equation,we study the existence of positive solution of a class of second order differential equations problems by the fixed point theorem of cone expansion and compression,and the fixed point index theorem,then we obtain two multiple positive .

通过将常微分方程转化为非线性积分方程，利用锥拉伸和锥压缩不动点定理和不动点指数讨论了一类二阶常微分方程的正解存在性问题，在一定条件下，得到了几个多重正解定理，同时证明了与此相关的主要引理

The method includes a "Theorem of General Expansion" for a complicated network and a "Theorem of Minimizing Expansion" for a logical expression.

本文提出了复杂网络的"大展开定理"和逻辑表式的"最小化展开定理"，并简要地叙述了本文作者已发表在"继电器"杂志(1978年1、2期)上的"逻辑——概率变换"和"单幂变换"等法则。

By using the theorem on cone expansion and compression and a fixed point theorem on cone,this paper is concerned with the existence of positive solutions for some boundary value problem of singular nonliear semipositive second-order three-point boundary value problem,which improve many known results.

运用锥拉伸与压缩不动点定理研究非线性奇异半正二阶三点边值问题正解的存在性，推广了一些已知的结果。

We prove an extension of the representation theorem of the convex pricing rule. We also give the corresponding probabilistic repre-sentation theorem of the convex pricing rule in a financial market with convex constraints.

我们证明了凸价格算子相应的表示定理，并给出了在凸约束的金融市场下凸价格算子的一个概率表达式。

Automated geometric theorem proving, as a byproduct of the completion of geometric theorems, is further developed into automated quantitative description of geometric relations. The recovery of the geometric meaning of this quantitative description leads to a natural extension of the geometric theorem.

几何定理的机器证明作为几何定理完全化的副产品，被发展成几何定理的关系定量化，这种量化的几何还原就是几何定理的自然推广。

Through presentation and discussion of traditional wavelet construction with lifting scheme, the multiwavelet construction with lifting scheme is introduced. The extension of Vetterli-Herley theorem under multiwavelet condition is overall proved in detail. Based on equivalent scalar filters banks, a kind of multiwavelet construction with lifting scheme and corresponding theorem are proposed.

通过介绍基于提升格式构造传统小波的内容，引入基于提升格式构造多小波的研究，对Vetterli-Herley定理在多小波中扩展进行详细全面地证明，提出了一种基于等效标量滤波器组的提升格式构造多小波的实现框架和定理，并通过实例验证该方案的可行性。

Meantime, the Namioka-Bauer's and Wong's positive extension theorem are generalized to ordered locally convex spaces (see Theorem 5.1) and hence some new necessary and sufficient conditions of positive extension in ordered locally convex spaces are obtained

同时Namioka-Bauer 定理和 Wong定理也被推广到半序局部凸空间中(定理5.1)，从而得到了一些新的关于半序局部凸空间中正延拓的充分必要条件

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

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