查询词典 mapping theorem

Trivial Solution conception is put forwarded based on the theorem of K〓nig and forbidden node----for the n×n 0-1 degeneracy matrix, the solution under the condition that all element 1 can not be covered completely by n lines that must have intersects or can be covered completely by n lines that must have cross, without forbidden node, are called TS matrix.

本文在K〓nig定理和禁点定理的基础上，提出了平凡解的概念，即对于n×n阶的退化矩阵，全部1元素不可能被n条有交叉的直线全部覆盖或能用n条直线覆盖全部1元素，但无禁点的情况称为平凡解。并证明了如下的平凡解产生的充分必要条件：对退化矩阵A〓，若

We can prove trivially that this theorem is false .

我们可以轻易地证明这一命题是错的。

At first, in this paper, the concept and type were introduced; afterwards, how to apply counter-examples in the higher mathematics was expatiated particularly in such aspects: concept、theorem、rule、formula and distinguishing true and false of the proposition; Finally, the construction of counter-examples was explored using special example、character、the method of approach as well as intuitional geometrical graphics.

本文首先简要介绍了反例的概念和类型；然后从概念、定理、法则、公式以及判别命题真假等几个方面，详细阐述了在高等数学中如何应用反例；最后，从利用特例、性质，采用逼近的方法以及直观的几何图形几个方面探讨反例的构造。

The empirical Bayes estimation for parameters of the one-side truncated distribution family with convergence rate which can close to 1 arbitrarily is investigated using NA samples and an example that satisfies the conditions of theorem is given.

运用NA样本密度函数核估计构造了一类截断型分布族参数的经验Bayes估计，建立了它的收敛速度，证明了在适当条件下该收敛速度可以任意接近于1，文中还给出了适合定理条件的例子。

This paper was concerned with the Dirichlet-Neumann mixed boundary value problem of bipolar quantum hydrodynamic model in thermal equilibrium. By truncation method and Leray-Schauder fixed point theorem, the existence of solution to the problem is proved. In addition, the uniqueness of the solution was proved as the Plank constant was large enough.

研究了热平衡状态下双极量子流体动力学模型的Dirichlet-Neumann混合边值问题，利用截断方法和Leray-Schauder不动点定理证明了其解的存在性，另外还证明了当普朗克常数充分大时其解是唯一的。

In the condition of no loop and no twoness, the auto update theorem is justified. At the same time, a locally best algorithm is given and additional validation is conducted.

在没有回路问题和二重性问题的条件下，本文证明了自动更新定理，并进一步提出了一个局部最优的自动更新算法，还给出了这个算法的证明。

Theorem 10.3: Under assumptions TS.1 – 5, the unbiased estimator of σ2 is

定理10.3：在假定TS.1-5下，σ2的无偏估计量为

In parameter estimation, the Minimum Variance Unbiased Estimator of a parameter θ can be characterized by sufficient statistics and the Rao-Blackwell Theorem.

但匪夷所思的是，有人还再加上"生肖"这样一个中国特有的"统计量"，再对各星座的性格做出统计判断。

Second theorem shows that the existence of solution is possible under suitable conditions when the limit of growth of nonlinear term at infinity is an unbounded function.

第二个定理表明当非线性项在无穷远处增长的极限是一个无界函数时在适当条件下这问题仍可能有一个解。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proof on the uncountability of real number set and the proof on the Cantor's Theorem of , a mysterious error was found:the very same logic contradiction was applied in both Russell and Cantor's work.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托在这两个非构造性证明中所依赖的、用对角线法所构造出的矛盾其实就是罗素悖论中所揭示的逻辑矛盾。

He paid $5,000 for this cupcake.

他我这个纸杯蛋糕花了5000美元。

I mean, if you want to, that is

我的意思是，如果你们想吃的话。