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非交换
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  noncommutative
     We discuss the distribution problem of the right zeros of the special quadratic equation(x一β)(x一α)= 0 over noncommutative division rings, and whereby we obtain a newmethod for solving the quadratic equation x ̄2 +αx+b=0 over quaternion rings R(i,j,k).
     本文讨论了非交换除环D上的特殊二次方程(x-β)(x-α)=0的右零点分布问题,并且由此而得到了一种求解四元数环R(i,j,k)上的二次方程x ̄2+ax+b=0的新方法。
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     THE STRUCTURE OF HOPF BIGALOIS EXTENSION OVER NONCOMMUTATIVE RINGS
     非交换环上Hopf Bigalois扩张的结构
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     Unitary and Noncommutative Wavelet
     酉基和非交换小波
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     On Noncommutative Hopf-Galois Extensions
     关于非交换Hopf-Galois扩张
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     Being different from the existing implementation based on the discrete logarithm problem, the new realization is based on the difficulty of deducing x and y from A and B=x·A·y in a specific monoid (m,·) which is noncommutative.
     与已有的基于离散对数问题的实现方案不同,它是基于在特定的非交换壹半群(m,·)中,由A和B=x·A·y求解x和y的难度;
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  non-commuting
     Let G be a non-abelian group and associate a non-commuting graph ▽(G) with G as follows:the vertex set of ▽(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.
     令G是一个有限群,其非交换图▽(G)如下定义:顶点集合▽(G)是G\Z(G),当两条边x与y的换位子不等于单位元时x与y相连.
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     Unique common fixed point theorem for a family of contractive type non-commuting selfmaps in 2-metric spaces
     2-度量空间上一族收缩型非交换自映射族的唯一公共不动点定理
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     Pure States and Spectra of Tensor Products of Non-commuting C~*-algebras
     非交换C~*-代数张量积的纯态和谱
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     In this paper,the pure state ranges of non-commuting C~*-algebras are discussed and a representation of the essential pure state range of a pair of elements in the tensor products algebra of non-commuting C~*-algebras are obtained.
     讨论了非交换C*-代数的谱与纯态值域,得到了C*-代数张量积中两个元的本质纯态值域的表示.
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  non-abelian
     If Z(G) = 1, M is a non-abelian simple group, such that N(G) = N(M), then G(?)
     如果Z(G)=1,M为非交换的单群,并且N(G)=N(M),则G≌M。
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     In Chapter Two, the author extends the relationship r(G) = |G| + D(G) - 1 in finite abelian groups to some type of finite non-abelian groups.
     其中,在第二章中,作者将对于有限Abel群G成立的关系式r(G)=|G|+D(G)-1推广到一类非交换群上。
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     Let G be a non-abelian group and associate a non-commuting graph ▽(G) with G as follows:the vertex set of ▽(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.
     令G是一个有限群,其非交换图▽(G)如下定义:顶点集合▽(G)是G\Z(G),当两条边x与y的换位子不等于单位元时x与y相连.
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     Using non-abelian cyclic cohomology theory,the isomorphic classes of étale φ-modules are characterized.
     利用非交换循环上同调理论刻画了平展φ-模的同构类.
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     Moreover, all simple basic Hopf quivers of non-abelian groups with order≤ 10 are provided.
     另外,还给出了十阶以下非交换群的简单基本Hopf箭图。
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  “非交换”译为未确定词的双语例句
     Let G be a group of |G:Z(G)| = 4, if G is a nilpotent group, then its sylow subgroups with odd number order are commutative groups, its sylow-2 subgroups are non-commutative groups, and P/Z(G)≌ Z2×Z2.
     G是|G:Z(G)|=4的群,如果G为幂零群,则其奇数阶Sylow子群为交换群,其Sylow-2子群P为非交换群,且P/Z(G)≌Z2×Z2。
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     Let =C_q[x_1~(±1),x_2~(±1)] be the non-commutative torus over the complex field, and A=\C,Der  be the Lie algebra of Derivations over . In this paper we study the automorphism group Aut L_q for the Lie algebra L_q=Der+A.
     =C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数.本文研究李代数L_q=DerA的自同构群Aut L_q.
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     Caiheng Li has proved that[1]: the connected cubic arc-transitive Cayleygraphs on the finite nonabelian simple groups are all normal except A_5, PSL(2,11), M_(11), A_(11), M_(23), A(23) and A_(47).
     李才恒证明[1]:除A_5,PSL(2,11),M_(11),A_(11),M_23,A_(23)与A_(47)外的有限非交换单群的连通3度弧传递Cayley图都是正规的。
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     In this paper, we study the noncommuting graph (G) associated with a finite group G and prove that:Theorem 1 Let p be a prime. If (G)■(D4p), then G■D4p or G■Q4p.
     研究有限群G的非交换图(G),证明了:定理1若(G)■(D4p),p为素数,则G■D4p或G■Q4p.
短句来源
     Let f be a nonnegative operator monotone function on [0,∞). Then for all non-commutative Banach function space norms, we obtain that‖f(A)X-Xf(B)‖54‖f(|AX-XB|)‖,where A,B are τ-measurable positive operators, X is a contraction.
     当f是[0,∞)上的非负算子的单调函数时,得到了对任何非交换Banach函数空间范数都有‖f (A)X - Xf (B)‖ 54‖f ( AX - XB )‖,其中A,B是τ-可测正算子, X是收缩算子.
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  noncommutative
A convexity theorem for noncommutative gradient flows
      
The paper studies serving extensions of noncommutative groups in the sense of the definition transferred naturally from the theory of Abelian groups.
      
Heredity of radicals in a class of noncommutative Jordan rings
      
We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra ?(L2(0, +∞)) of bounded operators onL2(0, +∞).
      
A noncommutative identity for the appell polynomials
      
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  non-commuting
Let G be a non-abelian group and associate a non-commuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.
      
This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics.
      
Whereas a pure Bose system is comparatively easy to treat in this way, the presence of Fermi fields involves a complication due to the occurrence of non-commuting quantities in the classical action function.
      
We give a definition involving only two non-commuting quantities, and work out some illustrative examples.
      
transformations in which the parameters are functions of the space-time point leads to the necessity of introducingf non-commuting vectors fields.
      
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  non-abelian
Let G be a non-abelian group and associate a non-commuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity.
      
It is proved that for any set of finite non-Abelian simple groups there exists a finite simple group as a result of this set.
      
We know that a group G is functionally complete if and only if it is either trivial or a finite simple non-Abelian group [Ref.
      
It is shown that for n >amp;gt; 1 these notions and the notion of functional completeness are equivalent, and apart from all finite simple non-Abelian groups, only the trivial group and groups of second order are 1-functionally complete.
      
The structure of the totally local formation,?∞ formG, generated by a simple non-Abelian groupG is described.
      
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In this article, we have introduced a new Regge trajectory, αq, with vacuum quantum numbers, α9(0) = αp(0) = 1, but αq'(0)≠ αp'(0). αq as well as αp takes part in the high energy non-exchange processes, and they interfere with each other. The consequence of the two vacuum Regge trajectories is equivalent to an effective trajectory αc, the slope of which at zero energy αs'(0) is dependent on the processes. The essential difference of our theory from the old one deduced from a single vacuum trajectory, αp, is...

In this article, we have introduced a new Regge trajectory, αq, with vacuum quantum numbers, α9(0) = αp(0) = 1, but αq'(0)≠ αp'(0). αq as well as αp takes part in the high energy non-exchange processes, and they interfere with each other. The consequence of the two vacuum Regge trajectories is equivalent to an effective trajectory αc, the slope of which at zero energy αs'(0) is dependent on the processes. The essential difference of our theory from the old one deduced from a single vacuum trajectory, αp, is that αz'(0) will be different for different processes. This does not conflict with the newest experiments.

我们引进一个具有真空量子数的新的Regge轨迹α_q,α_q(0)=α_p(0)=1,但α_q~′(0)≠α_p~(0)。在高能非交换过程中α_q和α_p同时参与贡献且相互干涉,其结果和一个等效的Regge轨迹α_e相当,唯α_e的斜率α_e~′(0)与过程有关,这与单一α_p轨迹的结论有本质的区别。根据我们的看法,由不同过程测得的α_e~′(0)将有不同数值,这点和最近的实验是相容的,并且预期将来K-N散射所测的α_e~′(0)亦将另取他值。α_q轨迹的存在将不改变高能相关过程总截面的关系,但使高能核子极化度随能量增大较缓慢地衰减。

From the determination of exchangeable and non-exchangeable potassium ofthe different soils in Jiangsu Province and the experiments of potash fertilizationon cotton,it was preliminarily established that bleached whitish soils in ChenjiangDistrict,the sandy and sandy loom soils along the Yangtze River and the sandysoils in Xuzhow-Huaiying District are deficient in available potassium(exchange-able K 10—20 jin/mu,non-exchangeable K 65—200 jin/mu),the K supply ofthe permeable paddy soils in Suzhow Distriet is also...

From the determination of exchangeable and non-exchangeable potassium ofthe different soils in Jiangsu Province and the experiments of potash fertilizationon cotton,it was preliminarily established that bleached whitish soils in ChenjiangDistrict,the sandy and sandy loom soils along the Yangtze River and the sandysoils in Xuzhow-Huaiying District are deficient in available potassium(exchange-able K 10—20 jin/mu,non-exchangeable K 65—200 jin/mu),the K supply ofthe permeable paddy soils in Suzhow Distriet is also low(exchangeable K 18—24jin/mu,non-exchangeable K 60—80 jin/mu),and the soils in The Lower RiverBasin and along the coast line are rich in K supply(exchangeable K 40—70 jin/mu,non-exchangeable K 200—300 jin/mu).The results from the cotton potash fertilizaton during 1973—75 had shownthat when the amounts of exchangeable K were less than 25 jin per mu,theapplication of potash fertilizer had a marked eliect in increasing cotton yield.Potash fertilization lessened the wilting disease and prevented the prematurity.Potash fertilization lessened the root diseases during the seedling stage toensure the stand in the field.Potash fertilization increased the boll wight,promoted boll opening and im-proved the fibre quality.The diagnostic technique of potassium on cotton during the square stage wasa very useful tool to decide whether the potash fertilizer should be side-dressed.

根据我们对我省不同土壤交换性钾和非交换性钾的测定以及棉花的钾肥试验,初步确定我省白土类型土壤,沿江沙土和沙壤土,徐淮地区沙土为缺钾土壤(交换性钾含量10—20斤/亩,非交换性钾65—200斤/亩),苏州地区黄泥土钾的供应也不充足(交换性钾18—24斤/亩,非交换性钾60—80斤/亩),里下河地区湖积物发育的土壤和滨海地区土壤钾的供应丰富(交换性钾40—70斤/亩)非交换性钾200—300斤/亩)。三年棉花钾肥试验指出,当土壤交换性钾含量低于25斤/亩时,施用钾肥有显著增产效果。土壤含钾水平愈低,钾肥增产效果愈显著。钾肥能减轻红叶茎枯病,防止早衰。钾肥能减轻苗期病害,保证壮苗全苗。钾肥能增加铃重,促使棉铃吐絮畅,棉花品质好。蕾期田间棉株钾素营养诊断,可作为棉花追施钾肥的参考。

In this paper, the kinetics of shell-progressive reaction in a solution of finite volume is investigated. A more general finite solution volume condition is obtained from material balance. The theoretical treatment supplements what is lacking in the mathematical model proposed by previous authors, who assume that there is no invasion of electrolyte over that of the fixed ionic groups in the resin, and the concentration of counter-ion in solution is independent of reaction time. The description of shell-progressive...

In this paper, the kinetics of shell-progressive reaction in a solution of finite volume is investigated. A more general finite solution volume condition is obtained from material balance. The theoretical treatment supplements what is lacking in the mathematical model proposed by previous authors, who assume that there is no invasion of electrolyte over that of the fixed ionic groups in the resin, and the concentration of counter-ion in solution is independent of reaction time. The description of shell-progressive reaction in ion exchange resin is now more nearly perfect and definite than was before. Some numerical calculations have been done with a computer. On the basis of the great number of calculations, it may finally be concluded that(l) shell-progressive reaction is different from that occurs simultaneously throughout resin beads in the dependence of reaction rate on various factors; (2) as long as the solution volume is finite, there is a necessary condition for the application of the theoretical expressions deduced by former authors; (3) under the ordinary conditions of finite solution volume, the fractional conversion of the resin can be determined experimentally from the concentrations of counter-ion in solution.

本文将前人无限浴条件下层进机理关于离子交换反应速度的理论发展为有限浴条件下的理论。本理论特别考虑了非交换吸入电解质的作用.对所得方程式的数值计算表明,对具有动边界的和没有动边界的两种过程来说,反应速度与某些参数之间存在不同的依赖关系;确定了用无限浴的公式处理有限浴条件下实验数据的必要条件.肯定了,大多数有限浴实验条件下得到的离子交换反应的转换度可以根据溶液中反应离子浓度的变化来确定.本文对层进机理的描述更明确,更完整.

 
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