numerical range造句
例句與造句
- The numerical range of non - negative matrix
非負(fù)矩陣的數(shù)值域 - In the second part : the emphasis is put on the n - numerical range
第二部分：研究了二次數(shù)值域的推廣： n次數(shù)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：研究了數(shù)值域與算子補(bǔ)問(wèn)題。 - 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
結(jié)果表明，同軸光信號(hào)幅值的眾數(shù)在不同間隙的焊縫段，聚集在線性可分的不同的區(qū)間，可以有效分開(kāi)焊接質(zhì)量不同的類、類、類焊縫；信號(hào)的分段功率譜分析能夠較為直觀地反映焊接狀態(tài)的變化。 - 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，受前面的引理的啟發(fā)，根據(jù)一個(gè)算子的數(shù)值域和它的譜之間的關(guān)系，研究了數(shù)值域與譜擾動(dòng)問(wèn)題，在本章的最后，我們給出了幾個(gè)證明的改進(jìn) - It's difficult to find numerical range in a sentence. 用numerical range造句挺難的
- 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
對(duì)它們的研究涉及到了基礎(chǔ)數(shù)學(xué)及應(yīng)用數(shù)學(xué)許多不同的分支，諸如算子理論，泛函分析， c ~ * -代數(shù)， banach代數(shù)，矩陣范數(shù)，不等式，數(shù)值分析，擾動(dòng)性理論，矩陣多項(xiàng)式，系統(tǒng)論，量子物理等等，并且在這些分支上面得到了廣泛的應(yīng)用。近年來(lái)，為了上述某些數(shù)學(xué)分支發(fā)展的需要，人們?cè)谘芯糠謮K算子矩陣譜理論的過(guò)程中引入了數(shù)值域的一個(gè)重要推廣：二次數(shù)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年首先證明了toeplitz - hausdorff定理以后，有關(guān)數(shù)值域、數(shù)值半徑以及各種廣義數(shù)值域及其數(shù)值域半徑的研究變得非?；钴S。 - 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
我們知道，研究譜理論的一個(gè)重要目的就是了解譜的位置特征，通過(guò)對(duì)比可知，二次數(shù)值域較之?dāng)?shù)值域能夠更好地給出所給算子的譜的位置特征，這引起了我們的研究興趣，本文將著重就二次數(shù)值域的相關(guān)問(wèn)題進(jìn)行較深入地研究，同時(shí)我們還提出了一些有待解決的問(wèn)題，我們認(rèn)為這些問(wèn)題是值得大家共同去研究和探討的。 - 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 ? ?
首先給出了n次數(shù)值域的定義，我們發(fā)現(xiàn)n次數(shù)值域不但具有一系列和二次數(shù)值域類似的性質(zhì)，而且在給定的條件下還有n次數(shù)值域包含在二次數(shù)值域當(dāng)中，另外當(dāng)是n維hilbert空間時(shí)，它的n次數(shù)值域就等于它的譜集，前面的結(jié)論促使我們猜想，當(dāng)是無(wú)限維hilbert空間時(shí)，對(duì)的任意的空間分解d _ n ，都應(yīng)該有下面的式子成立： ( 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
為了對(duì)數(shù)值域的本質(zhì)有更進(jìn)一步地了解，首先根據(jù)toeplitz - hausdorff定理的證明方法，得到了數(shù)值域的一個(gè)等價(jià)刻畫(huà)： w ( a ) ： u _ ( p _ n p _ n ) w ( p _ na | e _ n ) ，接著引入了二次數(shù)值域的定義，從二次數(shù)值域的定義我們可以看出，一般說(shuō)來(lái)，在不同的空間分解下，一個(gè)算子的二次數(shù)值域也會(huì)截然不同，但是當(dāng)所給的兩種空間分解有某種關(guān)系時(shí)，它在這兩種空間分解下的二次數(shù)值域是相等的。