numerical range造句
例句与造句
- The numerical range of non - negative matrix
非负矩阵的数值域 - In the second part : the emphasis is put on the n - numerical range
第二部分：研究了二次数值域的推广： n次数值域。 - In the last part : the emphasis is put on the relations between the numerical range and operator completion problem
第三部分：研究了数值域与算子补问题。 - It is found that , the modes of coaxial optical emission of dissimilar gaps , clustering at distinct numerical range , can distinguish 1st , 2nd and 3rd class welds of different welding quality effectively
结果表明，同轴光信号幅值的众数在不同间隙的焊缝段，聚集在线性可分的不同的区间，可以有效分开焊接质量不同的类、类、类焊缝；信号的分段功率谱分析能够较为直观地反映焊接状态的变化。 - On the other hand , benefit from the facts above and according to the properties of the numerical range , we study the operator spectrum perturbation problem , in the last , we give some better proofs on some theorems which simplify the original proof much
其次，受前面的引理的启发，根据一个算子的数值域和它的谱之间的关系，研究了数值域与谱扰动问题，在本章的最后，我们给出了几个证明的改进 - It's difficult to find numerical range in a sentence. 用numerical range造句挺难的
- The subject is related and has applications to many different branches of pure and applied science such as operator theory , functional analysis , c " - algebras , banach algebras , matrix norms , inequalities , numerical analysis , perturbation theory , matrix polynomials , systems theory , quantum physics , etc . in recent years , the quadratic numerical range , one of the most important generalizations of the numerical range , was put forward in the course of people studying the spectral theory of the block operator matrix to the need of the development of some branches mentioned above
对它们的研究涉及到了基础数学及应用数学许多不同的分支，诸如算子理论，泛函分析， c ~ * -代数， banach代数，矩阵范数，不等式，数值分析，扰动性理论，矩阵多项式，系统论，量子物理等等，并且在这些分支上面得到了广泛的应用。近年来，为了上述某些数学分支发展的需要，人们在研究分块算子矩阵谱理论的过程中引入了数值域的一个重要推广：二次数值域。 - Research on quadratic numerical range of bounded linear operators zhang jingjie abstract the study of numerical range started in 1918 - 1919 by toeplitz and hausdorff when they first proved that w ( a ) is always convex , since then , the study of numerical range theory had been one of the most active research areas
自toeplitz和hausdorff在1918 - 1919年首先证明了toeplitz - hausdorff定理以后，有关数值域、数值半径以及各种广义数值域及其数值域半径的研究变得非常活跃。 - As we all know , one of the main aim of the spectral theory research is to find out the location of the spectrum , it is just because of the quadratic numerical range gives a better information about the localization of the spectrum than the numerical range and that provoke my interest to study the quadratic numerical range . the aim of this paper is to make a deep investigate in this area , the main content as follows : the first part of this paper pays the emphasis on the quadratic numerical range
我们知道，研究谱理论的一个重要目的就是了解谱的位置特征，通过对比可知，二次数值域较之数值域能够更好地给出所给算子的谱的位置特征，这引起了我们的研究兴趣，本文将着重就二次数值域的相关问题进行较深入地研究，同时我们还提出了一些有待解决的问题，我们认为这些问题是值得大家共同去研究和探讨的。 - After we define the n - numerical range of bounded linear operators on a hilbert space , we find that the n - numerical range have a series properties very similar to that of the quadratic numerical range . at the same time , we prove that under certain conditions , wn ( a ) c w ~ ( a ) and that when h is finite dimensional and dimti = n , we have a ( a ) = wn ( a ) . therefore , it is nature to guess that when h is an infinite dimensional hilbert space , for any space decomposition dn ? ?
首先给出了n次数值域的定义，我们发现n次数值域不但具有一系列和二次数值域类似的性质，而且在给定的条件下还有n次数值域包含在二次数值域当中，另外当是n维hilbert空间时，它的n次数值域就等于它的谱集，前面的结论促使我们猜想，当是无限维hilbert空间时，对的任意的空间分解d _ n ，都应该有下面的式子成立： ( a ) = _ ( d _ n d ) w _ ( d _ n ) ~ n ( a ) 。 - At first we get an equivalence characteristic of the numerical range : w ( a ) = jpn ? pn w ( pna en ) . from the definition of the quadratic numerical range , we can see that the quadratic numerical range depend on the space decomposition . from contrast , we can see that the quadratic numerical range gives a better information about the localization of the spectrum than the numerical range , perhaps just because of this , the quadratic numerical range of an operator need not to be convex , and even that the quadratic numerical range of an operator need not connected , then we give a condition under which the quadratic numerical range of an operator is not connected
为了对数值域的本质有更进一步地了解，首先根据toeplitz - hausdorff定理的证明方法，得到了数值域的一个等价刻画： w ( a ) ： u _ ( p _ n p _ n ) w ( p _ na | e _ n ) ，接着引入了二次数值域的定义，从二次数值域的定义我们可以看出，一般说来，在不同的空间分解下，一个算子的二次数值域也会截然不同，但是当所给的两种空间分解有某种关系时，它在这两种空间分解下的二次数值域是相等的。