查询词典 unique factorization theorem

Unitil fairly recently, Burnside's paqb theorem was another outstanding exemple of this.

特别地，Burnside paqb定理是一个非常出色的例子，它用特征标理论活得了证明。

As functions of the function of mathematics, the Key theorem of calculus of variations is Euler LaGrange, it can be used to the pan-seeking function of the maximum and minimum of mathematical.

变分法是处理函数的函数的数学领域，关键定理是欧拉－拉格朗日方程，用来求的泛函数的极大值和极小值的数学方法。

In this thesis, sound wave path equation is derived from Fermat's theorem and the calculus of variations, and then the temperature field is reconstructed by the combination least-square method and the modified sound wave path.

本文通过求解由费马定理和变积分原理确定的声波路径方程，结合最小二乘法实现了声波路径的修正。

Applied with the holistic analysis method, based on the theorem of maximal probability multiplication and the principle of cannikin, the paper establishes a coordination model between the sub-systems (river, wetland, lake, city, dryland) within the ecological water allocation system of the river basin.

本文应用整体分析法，基于最大概率乘积定理和"木桶法则"，构造了流域生态用水分配系统的协调性评价模型，分析了各子系统生态用水分配的合理度，完善了流域生态用水分配合理性的评价内容和方法。

Based on the projection theorem in the finite-dimensional inner product space, by making use of the generalized singular value decomposition and the canonical correlation decomposition of matrix pair simultaneously, we transform the least-squares problems of the abovementioned inconsistent matrix equations into the problems of solving the consistent matrix equations over given matrix set, and obtain the general expressions of the corresponding least-squares solutions.

S使得‖-X~*‖=‖-X~*‖，其中‖·‖为Frobenius范数，S分别表示矩阵方程 AXB=D，AXA~T+BYB~T=D，AXB+CYD=E和矩阵方程组=，=在一般矩阵集合或对称矩阵集合上不相容时的最小二乘解集合。

In this paper,the author deduces the basic equation of statistical Mechanics- Liouville Theorem in two different ways from analytical mechanics′ concepts of phase space and the Hamilton Canonical Equation.

本文笔者用两种不同思路由分析力学的相空间概念和哈密顿正则方程推导了统计力学的基本方程———刘维定理。

It has been showed that the quantum PCII can be still valid for the general case Jacobi J 1, which is different from quantum Noether theorem. The equivalence between quantum canonical equation and PCII is deflved at the quantum level. The comparisons of these results in quantum level with those in classical theories are discussed in detail. The relationship of canonical transformation with quantum PCII is obtained.

结果表明，当变换的Jacobi行列式不为1时，量子PC积分不变量仍然存在，从而把PC积分不变量推广到了最一般情形；在量子水平上，证明了量子正则方程与该积分不变量之间的等价性；比较了经典与量子PC积分不变量以及PC积分不变量与Noether定理；给出正则变换与量子PC积分不变量间的关系。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

What was it that made you want to change sider ?

是什么使你临阵倒戈？

I don't know what he wants, but let's play along with him.

我不知道他要干什么，可我