查询词典 theorem of alternative

When proving the differential mid-value theorem,"Higher Mathematics" does know to make the auxiliary function ф in order to apply Rolle Theorem.

在证明微分中值定理时，《高等数学》作辅助函数ф的目的是为了应用罗尔定理。

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。

In chapter II,an extended strongly equivalent theorem forgerms with parameters is proved.The theorem is useful to constructthe factoring map between any unfoldings and universal unfolding.

在第二章中，对带有参数的核证明了一个推广的强等价性定理，这个定理在构造任意开折和普适开折因式相通的变换中有一定的应用。

Chapter 4 is devoted to the existence and multiplicity of homoclinic for self-adjoint nonlinear second order difference equations by using "Mountain Pass " theorem and "Symmetry Mountain Pass "theorem in critical point theory.

第四章应用临界点理论中的山路引理与对称山路引理研究了一类自共轭非线性二阶差分方程的同宿轨的存在性与多重性。

Based on the tree martingale decomposition theorem and the con-vergence of locally finite tree martingales,a tree martingale convergence theorem isverified.

再基于树鞅分解定理和局部有限树鞅收敛定理，证明了一个树鞅收敛定理。

In this paper, a fixed value theorem for direct areas of height triangle s in circular inscribed polygons is obtained, and some results, including the famous height theorem in a triangle, are deduced.

给出圆内接 2n +1边形中高线三角形有向面积的定值定理及其推论，其中包括著名的三角形的高线定

The discriminance methods and expression of generalized alternative optimum solutions of linear programming is given by proving that the equivalent of optimum extreme point and extreme point of optimum solution sets of linear programming and applying the theorem of convex polyhedron.

通过证明线性规划最优解集的极点与线性规划最优极点的等价性，利用凸多面体的表达定理，给出了广泛意义下线性规划无穷多最优解的判别方法及表达式。

First, under G -convexity, the alternative theorem is proved.

首先，在G-凸的条件下，证明了择一定理。

By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.

在线性空间中，定义了广义次似凸映射的概念，并讨论了它的一些性质，建立了此映射的择一定理。

Under the G-differentiable ,using the alternative theorem of generalized subconvexlike map and other some conclusions in locally-convex Hausdorff topological spaces, the optimality conditions of vector extremum problems with set constraint are established.

在局部凸Hausdorff拓扑空间中，在G-可微的意义下，运用广义次似凸映射的择一定理和其他一些结论，建立了带集合约束的向量极值问题的最优性条件。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48