range vt. 1.排列;整理(頭發等)。 2.使歸類[班、行、隊];把…分類。 3.〔用被動形或反身形〕加入,站住…的一邊 ( with against)。 4.〔古、詩〕在…徘徊,在…走來走去,到處尋找;【航海】巡邏(沿岸等)。 5.(用槍、望遠鏡等)對準(目標);瞄準;(炮術)試(炮),試(射程)。 range books on a shelf 把書排列在書架上。 range the forest for game 在森林中跑來跑去獵取獵物。 be ranged according to size 按大小順序排列。 be ranged against 站在…的反對方向[…的一伙內]。 range oneself 1. (放蕩后因結婚而)改過自新。 2. 得到固定職業。 range oneself on the side of 做…的伙伴。 range oneself with 做…的伙伴,與…做伙伴。 vi. 1.開列,進行;成直線 (with) (山脈等)相連,連綿;(動植物等)分布,蔓延,散布 (from... to) (子彈)能打到,達到。 2.加入,站在…的一邊 (with against) 與…為伍 (with)。 3.徘徊,走來走去,跋涉 (in over through) 【航海】巡航。 4.(思想、研究等)到達,涉及。 5.【軍事】測距,試射測距;射程為。 6.(在某范圍內)變動,升降 (betweenfrom...to ...)。 range north and south 綿亙南北。 The gun ranges 3 miles. 這炮能打三英里遠。 The thermometer ranges from 45° to 50°. 溫度表的升降幅度是從45度到50度。 ranging fancy 動搖的愛情,水性楊花。 n. 1.(山脈、房屋等的)排列;連續;綿亙。 2.(同種物的)一批,一套,一堆。 3.方向;范圍,區域;(動植物的)分布區域;生存期間;放牧區域,牧場;知識范圍;音域;幅度,差度;限度,極限;【數學】變程,量程;值域;全距。 4.作用[有效]半徑,距離;射程;靶子場,射擊場。 5.等級,類別,種類,部類。 6.徜徉,徘徊。 7.(能同時利用余熱燒水、烤面包的)多用鐵灶;火格子;梯級。 8.〔美國〕公地測量中相距六英里的兩子午線間的一排市鎮。 a range of buildings 一排房子。 the range of politics 政界。 a high [lower] range 大[小]比例,大[小]刻度。 the range of a thermometer 溫度表的(升降)幅度。 the range of one's voice 音域;聲音所能達到的范圍。 the effective range 有效射程。 foul the range finding (放煙幕)擾亂測距工作。 a projectile [proving, rocket] range 炮兵[軍用、火箭]靶場。 a range boss 〔美國〕(在某一地段內)看守放牧牲畜的人。 a range rider 〔美國〕牧童;山村看守人。 range cattle 放牧的牲畜。 a range forecast 【商業】(棉花的)收成估計。 a range of the cable 拋錨時所必需的一定長度的錨鏈。 an electronic range 電子爐。 a low range of prices 低檔價錢。 at long [short] range 在遠距離[近距離]。 go over the range 〔美國〕死。 in range with 和…開排著;和…同一方向。 in the range of 在…范圍內。 out of one's range 能力達不到的;在知識以外的,不能辦到的。 out of [within] range 在射程外[內]。 within the range of 在…的射程內,…能力達得到的,…所能的。
The numerical range of non - negative matrix 非負矩陣的數值域
In the second part : the emphasis is put on the n - numerical range 第二部分:研究了二次數值域的推廣: n次數值域。
In the last part : the emphasis is put on the relations between the numerical range and operator completion problem 第三部分:研究了數值域與算子補問題。
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 結果表明,同軸光信號幅值的眾數在不同間隙的焊縫段,聚集在線性可分的不同的區間,可以有效分開焊接質量不同的類、類、類焊縫;信號的分段功率譜分析能夠較為直觀地反映焊接狀態的變化。
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,根據一個算子的數值域和它的譜之間的關系,研究了數值域與譜擾動問題,在本章的最后,我們給出了幾個證明的改進
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 對它們的研究涉及到了基礎數學及應用數學許多不同的分支,諸如算子理論,泛函分析, c ~ * -代數, banach代數,矩陣范數,不等式,數值分析,擾動性理論,矩陣多項式,系統論,量子物理等等,并且在這些分支上面得到了廣泛的應用。近年來,為了上述某些數學分支發展的需要,人們在研究分塊算子矩陣譜理論的過程中引入了數值域的一個重要推廣:二次數值域。
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,有關數值域、數值半徑以及各種廣義數值域及其數值域半徑的研究變得非常活躍。
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,研究譜理論的一個重要目的就是了解譜的位置特征,通過對比可知,二次數值域較之數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值域的相關問題進行較深入地研究,同時我們還提出了一些有待解決的問題,我們認為這些問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次數值域的定義,我們發現n次數值域不但具有一系列和二次數值域類似的性質,而且在給定的條件下還有n次數值域包含在二次數值域當中,另外當是n維hilbert空間時,它的n次數值域就等于它的譜集,前面的結論促使我們猜想,當是無限維hilbert空間時,對的任意的空間分解d _ n ,都應該有下面的式子成立: ( a ) = _ ( d _ n d ) w _ ( d _ n ) ~ n ( a ) 。
In the mathematical field of linear algebra and convex analysis, the numerical range of a square matrix with complex entries is a subset of the complex plane associated to the matrix. If A is an n?×?n matrix with complex entries, then the numerical range of A is the set