1) defect
[英][di'fekt] [美]['di,fɛkt, dɪ'fɛkt]
亏数
1.
The authors investigated the properties of two subspaces N(A ∞) and R(A ∞) definded by a bounded linear operator A on a Banach space, mainly the relations with the ascent, descent, nullity and defect of operator A and applied the results to the determinations of chain_finite Fredholm operators.
研究了Banach空间上由算子A定义的两个子空间N(A∞)和R(A∞)与算子A的升标、降标、零度和亏数的关系及其性质 ,并应用于链有限Fredholm算子的判
2.
A finitely generated soluble group G has derived length at most 5 and Fitting length at most 4 if the defect of every subnormal subgroup of G does not exceed 2.
由此可以证明次正规子群的亏数均≤ 2的有限生成可解群的导出长度至多为 5 ,其幂零长度至多为 4 ,这推广了McCaughan -Stonehewer、Casolo等人的结
3.
Then every nonlinear ir reducible character of G has a degree divisible by p if and only if G has a normal p-complement suchthat is abelian and It is also investigate that how all linear characters of G are distributed among the p-blocks of high est defect when G has a normal p-complement.
那么，Ｇ的每一个非线性不可约特征标的次数被ｐ整除当且仅当Ｇ有正规ｐ－补，使得Ｏｒ（Ｇ）∩ＣＧ（Ｐ）为Ａｂｅｌ群并且｜Ｇ：Ｇ″｜＝｜Ｐ：Ｐ′｜·｜Ｏｒ′（Ｇ）∩ＣＧ（Ｐ）｜还研究了当Ｇ有正规ｐ－补时，Ｇ的全体线性特征标是如何分配在具有最高亏数的ｐ－块中的。
2) Betti deficiency
亏数
1.
Abstract Combined with the edge-connectivity of graphs, this paper gives an upperbound of Betti deficiency on a graph in terms of chromatic number of its complement, provesthat this bound is the best possible, and obtains some new results on the lower bounds of themaximum genus of graphs.
结合边连通性,本文给出了一个图的Ｂｅｔｔｉ亏数由这个图的补图的着色数所确定的上界式,证明了所给出的上界式是最好的,得到关于图的最大亏格下界的若干新结果。
3) relative defect of function
相对亏函数亏量
1.
In the paper, the defective values are replaced by some slowly increasing functions the defective funtions, the note of the relative defect of function and the absolute defect of function are introduced.
将亚纯函数值分布理论中的相对于复数的两种亏量，即相对亏量与绝对亏量，推广到相对于涉及慢增长函数的亏量，得到相对亏函数亏量及绝对亏函数亏量，并研究了两者之间的关系，得出两个结论，以及在亏量的值一定的条件下，亚纯函数的ｋ阶导数无非零相对亏函数及非零绝对亏函数的结
4) absolute defect of function
绝对亏函数亏量
1.
In the paper, the defective values are replaced by some slowly increasing functions the defective funtions, the note of the relative defect of function and the absolute defect of function are introduced.
将亚纯函数值分布理论中的相对于复数的两种亏量，即相对亏量与绝对亏量，推广到相对于涉及慢增长函数的亏量，得到相对亏函数亏量及绝对亏函数亏量，并研究了两者之间的关系，得出两个结论，以及在亏量的值一定的条件下，亚纯函数的ｋ阶导数无非零相对亏函数及非零绝对亏函数的结
5) Betti deficiency
Betti亏数
1.
Spanning Trees, Basic Cycles and Betti Deficiency of a Graph;
图的生成树,基本圈与Betti亏数
2.
It is known that the maximum genus of a graph is mainly determined by its Betti deficiency ξ(G) .
一个连通图G的最大亏格γM(G)主要由它的Betti亏数 ξ(G)确定。
3.
The maximum genus of a connected graph is determined by its Betti deficiency.
一个连通图G的最大亏格γM(G)可由其Betti亏数ξ(G)确定。
6) defect index
亏指数
1.
In this paper,several lemmas in [3] are improved,the method used in [2]and [3] is generalized,the complete description of all the possibility of self-adjoint area is given,and the limitation on the equal condition of defect index at the both ends in text [4] is reduced,thus making the analytic description of selfadjoint differential operators at the both strange ends solved completely.
关于对称微分算子在最大算子域内界定自伴域的边界条件问题,去掉了两端亏指数相等的限制条件,给出线性流形为自伴扩张域的充分必要条件,从而使两端奇异的自伴微分算子的解析描述得到完满解决。
2.
In this paper,the largest defect index of the singular Hamilton differential expression is investigated.
讨论了奇异Hamilton微分系统的最大亏指数,主要结果是对Weyl H,Atkinson F V给出的最大亏指数定理相应结果的改进与推广。
3.
For a semi-bounded operator with defect index (1, 1 ), we solve von Neumann s problem in a explicit way based on Krein s formula and rank one perturbation theory of a positive selfadjoint operator, only assuming the Friedrichs extension is obtained.
对亏指数(1，1)的下半有界闭对称算子的von Neumann问题，作者利用实参数形式的Krein公式和自伴正算子的秩1扰动理论给出了一个仅依赖于Friedrichs延拓的显式解答，并且证明了对每个这类算子，在它的全体自伴延拓集合到单位圆周S~1的一个自然的双射下，它的von Neumann问题解集的像一定处于1/4单位圆周内。
补充资料：数不胜数
1.数也数不清。形容很多。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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