查询词典 radon nikodym theorem

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。

Letг is a theory,if г has extensions,then the theorem of the theory г is the intersectionof its all extensions;if г has no extension,its theorem is the whole language.

由于非单调逻辑I中出现了一些与直觉相悖的情形，为此，D。

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

In chapter2 we obtain the constructure theorem and intechange theorem of 2-tournaments.wefind the correlation between the number of 3-cycles and 2-cycles in 2-tournament andits score vector,discuss a class of extreme value problem of tournament,answer partlya open problem posed by Brualdi.

第二章讨论了2-竞赛图和竞赛矩阵的一些基本问题：存在性和结构问题，证明了具有相同得分向量的任意两个2-竞赛矩阵可以通过三角形转换而互相得到，得到了2-竞赛图中2-圈与3-圈的数目与得分向量之间的关系式；讨论了2-竞赛中的一类极值问题，部分地回答了Brualdi〓的一个问题。

The reason of our being particularly overjoyed lies primarily on the fact that the subject of this Congress is mathematics, which has been respected as "the queen of sciences" for its brilliant intellectual accomplishments, as suggested by the examples of the discovery of Goedel's theorem and the proof of the Fermat Last theorem in the last century.

我上面说感到"特别高兴"，是因为数学一向以其辉煌的智力成就而被尊为"科学的皇后"，如上一世纪哥德尔定理的提出与费马大定理的证明就是一例。

Schur theorem was discovered by German mathematician Schur in 1916 when researching on the limited domain of Fermat's great theorem.

Schur定理是德国数学家Schur在1916 年研究有限域上的Fermat 大定理时发现的。

Moreover, we also get a fixed point theorem of uniform partial extension mapping and a fixed point theorem of quasi- extension mapping.

另外，我们还得一个一致局部扩张映射不动点定理与一个准扩张映射不动点定理。

Mainly by means of the Hopf bifurcation theorem and the cone fixed point theorem in the functional differential equations.

本文对非线性项为两种形式的时滞Van der Pol方程分别加以比较，利用Hopf分支理论和锥不动点定理，得到相应方程在周期解和Hopf分支方面上的差异。

This theorem, which had challenged mathematicians for centuries, is still called "the fundamental theorem of algebra".

表现最好的孩子是那些其父母为既支持又激励型的。

Integral Calculus: definite and indefinite integrals; fundamental theorem of calculus; techniques of integration; Taylor's Theorem; applications in geometry, physics and engineering.

积分学：定积分与不定积分、本定理、积分的方法、勒定理、分学在几何、理和工程学上的应用。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。