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     For a boolean function f(x), let Rf be the set of vectors which do not satisfy the propagation criteria and zf be the set of vectors which do not satisfy the correlation immunity, i.e Rf={ai|(ai)0,0≤i≤2n-1},zf={ai|0, 0≤i≤2n-1}.
     对于布尔函数f(x),设不满足扩散准则的元素之集为Rf,不满足相关免疫的元素之集为zf ,即Rf={ai|(ai)0,0≤i≤2n-1},zf={ai|0,0≤i≤2n-1}。
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     In this paper we prove the following theorem Theorem: Let G be a finite group Then G≌L 3(8) if and only if π e(G)=π e (L 3(8)) , where π e(G) denote the set of element orders in G
     证明了如下定理:定理设G是有限群,则G≌L3(8)的充要条件是πe(G)=πe(L3(8)),其中πe(G)表示G中元的阶之集
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     In this paper, the following theorem is proved: Let G be a finite group, then GL 3(8)i f and only if π e(G)=π e(L 3(8)), where π e(G) denotes the set of element orders in G.
     文中证明了如下定理:设G是有限群,则GL3(8)的充要条件是πe(G)=πe(L3(8)),其中πe(G)表示G中元的阶之集
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     In this paper we prove that if G be a sporadic simple group, M be a finite group and Z(M)=1, N(G)=N(M), then G≌M, where N(G) is the set of orders of the conjugacy classes in G.
     本文证明了:如果G为散在单群,M为有限群且Z(M)=1,N(G)=N(M),那么M≌G。 此处N(G)为G中共轭类的阶之集
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     Proves: Let G be a finite group. Then GL 3(8) if and only if π e(G)=π e(L 3(8)), where π e(G) denotes the set of element orders in G .
     证明若 G 是有限群, 则 G L3(8)的充要条件是πe( G)= πe( L3(8)), 其中 πe( G)表示 G中元的阶之集
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     Let the set of experimental points be X={x(t)=kt+b, t∈[0, 1], |k|≤B_1, |b|≤B_2}, where B_1>0 and B_2>0 are real and given. The paramater space is Θ={θ:θ∈L_2[0, 1]}.
     设试验点集是X={x(t)=kt+b:t∈[0,1],|k|≤B_1,|b|≤B_2},其中B_1>0,B_2>0都是已知数,参数空间={θ:θ∈L_2[0,1]}。
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     ON THE SET OF SMOOTH POINTS OF ORLICZ SEQUENCE SPACES 1_((M))
     Orlicz 序列空间1_(M)的光滑点集
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     We prove that the chromatic index X'(G) of a simple graph G satisfies X'(G)=X'(G[F∪N(F)]) where F={v|d(v)=△(G)}is the set of maximum degree vertices, N(F)is the set of neighbors of F, G[S] denotes the induced subgraph of SV(G).
     (G[F∪N(F)])。 这里F={v|d((v)=△(G)}是G的最大度点集,N(F)是F的邻点集,G[S]记G中由S(?)
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     Let f be a continuous self-map of a graph G and P(f), AΓ(f),ω(f),Ω(f), sα(y, f) denote the set of periodic points of f, the set of unilateral γ-limit points of f, the set ofω-limit points of f, the set of nonwandering points of f, the set of special aaaaaaaaaaaaaa- limit points of f relative to y, respectively.
     设f是图G上的连续自映射, P(f),AΓ(f),ω(f),Ω(f),sα(y,f)分别表示f的周期点集,单侧γ-极限点集,ω-极限集,非游荡集,相对于y的特殊α-极限点集.
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     Suppose that the set of common fixed points of T_1, T_2, … , T_N be nonempty, we prove that explicit viscosity iterative sequence for N nonexpansive mapping converges strongly to the common fixed point of T_1, T_2, … , T_N, which solves some variational inequality.
     在假设T_1,T_2,…,T_N的公共不动点集非空的前提下,我们证明了N个非扩张映射的显格式黏滞迭代序列强收敛到T_1,T_2,…,T_N的公共不动点,并且此不动点是某一变分不等式的解。
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     The Total volume for the Set of Cosets{o~+}
     关于傍系集合{O~+}的总体积的计算
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     RESEARCH ON COMPUTER AIDED INSTRUCTION ON THE SET OF Z-80 INSTRUCTIONS
     z-80指令的计算机辅助教学研究
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     A Numerical Calculation Method of Solving the Set of Transcendental Equations in the Meshing Principles of Worm Gearing
     蜗杆传动啮合原理中超越方程组的数值解法
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     Pansystem Analysis of the Set of Functional Dependence in Database
     数据库中函数依赖集的泛系分析
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     A New Algorithm for Calculating the Set of Boundary Pixels of Linear Octree
     计算线性八叉树边界象素集的新算法
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We define a map from an affine Weyl group to the set of conjugacy classes of an ordinary Weyl group.
      
Xi defined a partition ofWf into canonical right cells and the right order ≤R on the set of cells.
      
Let ζ-1/2 be the inverse on the set of regular elements ofu of a square root of the discriminant of.
      
For a smooth oriented surface Σ, denote byM(Σ) the set of all ways to represent Σ as a result of gluing together standard spheres with holes ("the Lego game").
      
We introduce a notion of transversality for pairs of elements inS, and then study the action ofG on the set of triples of mutually transversal points inS.
      
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Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear...

Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear terms in the dynamical equations can be neglected. Furthermore the size of vortices which form the turblent flow is regarded small, so within the range of each vortex the mean turbulent velocity and its gradient can be considered to be independent of the changes of the space coordinates. We now seek the following approximate solution of the linearized equations of turbulent velocity fluctuation; one part of the turbulent velocity fluctuation represents the final stage motion of homogeneous isotropic turbulence, while the other is proportional to the gradient of mean velocity, the latter part being smaller than the former. From this approximate solution the shearing component of the Reynolds stress is found to be directly proportional to the gradient of mean velocity. As a special example of the general solution we consider the case of the two-dimensional wake. Within the wake we put, furthermore, a plane grid normal to the plane of symmetry of the wake. This grid then creates in its downward stream a homogeneous isotropic turbulence field superimposed upon that of the wake. Our solution is applicable to places far downstream both from the body which creates the wake and from the grid. Since the flow here is nearer to the grid, so the turbulence level of the homogeneous isotropic turbulence would be higher than that of the wake. Consequently the conditions of the general solution can be satisfied. The present paper presents the solutions of the mean velocity and the mean squares of turbulent velocity fluctuation of the wake. These theoretical results can all be tested by experiment. On account of that we only discuss the final stage motion of free turbulence, the question how to lay down the upstream boundary condition of the flow field when solving the differential equations of the mean flow needs further consideration by other methods.

具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速...

具有剪应力的自由湍流到下游相当远的地点由于能量的逐渐耗损将衰变成为类似均匀各向同性湍流的后期运动。如同处理后一种流动问题一样,我们现在根据湍流是由涡旋所组成的概念来求自由湍流的后期运动解。求涡旋运动解的动力学的基础是湍流速度涨落方程。在后期湍流场中湍流Reynolds数比较小,故方程中的非线性项可以略去。再考虑到组成湍流的涡旋尺寸比较小,在每个涡旋范围内平均湍流速度和它的坐标梯度可以近似地认为和坐标的改变无关。我们求线性化了之后的湍流速度涨落方程如下的近似解:涨落速度的一部分代表均匀各向同性湍流的后期运动:另一部分是和平均流速的坐标梯度成正比,后一部分要比前一部分为小。从这样的近似解得出的Reynolds剪应力是和平均流速的坐标梯度成正此。当作这一般解的特例我们求一个二元尾流的后期运动。在产生尾流的物体的后面还置放一个平面与尾流对称平面成垂直的栅格。这个栅格在它的下游可产生一个迭加在物体所产生的尾流场上的均匀各向同性的湍流(?)。我们的解是适用在离物体和栅格相当远处的后期运动,但此处的流场距栅格较近,所以栅格所产生的均匀各向同性湍流要比尾流的湍流度为高,因此一般解的近似条件是可以满足的。本论文给出尾流平均流速和速度涨落平方平均值的解。?

Let S denote the family of star-like functions f{z), that arc regular and univalent inthe unit circle |z|<1, with the expansion f(z)=z+a2z2+…about z=0.In this paper, we use the extremal property of the function W=(1+c)c+1/(1-c)c-1 F(z),where F(z) is compounded by two functions (4) and (5), and the principle of circular symmetrization to prove the following two results:1. Let L(r,f) denote the length of the set of values on |W|=r,not covered byvalues of f(z)∈S for|z|<1. Then for 1/4

Let S denote the family of star-like functions f{z), that arc regular and univalent inthe unit circle |z|<1, with the expansion f(z)=z+a2z2+…about z=0.In this paper, we use the extremal property of the function W=(1+c)c+1/(1-c)c-1 F(z),where F(z) is compounded by two functions (4) and (5), and the principle of circular symmetrization to prove the following two results:1. Let L(r,f) denote the length of the set of values on |W|=r,not covered byvalues of f(z)∈S for|z|<1. Then for 1/41 under f(z)∈S, Af=area D(f)∩(|W|16π0.l6π.

这篇短文中;通过星形极值区域的结构,利用从圆到这个区域的共形映照的极值函数,得出了单位圆内单?星象函数族取不到圆周|W|=r(1/4

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering...

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and three coupled modes succesively. For the two coupled-modes case, our results agree with those by Louisell and Unger. Solution for the three coupled-modes problem has not been appeared in literatures heretofore. A numerical evaluation of the spurious modes in an S-shaped bend is given. Further applications are discussed.

在本文中作者提出了耦合本地正规波型的广义理论;它建立在作者在另一篇论文中提出的数学方法——“缓变系数法”的基础上。为了说明这种方法的应用,依次解出了考虑两个及三个耦合波型的缓变曲率波导弯曲问题。在两个耦合波型的情形下,所得结果与Louisell及Unger已得结果相符合。三个耦合波型的问题在以前的文献中尚未讨论过。本文讨论了所提出的理论及数学方法在其它方面的应用。

 
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