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向量的和
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     The Vectorial Orthogonalization in R~n
     R~n中向量的正交化
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     Independence of Random Vectors
     随机向量的独立性
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     Perturbation Bounds for Eigenvector and Singular Vector
     特征向量奇异向量的扰动界
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     The Differentiation between the Projection of Vector and Image of Vector
     向量的投影射影概念辨析
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  sum of vectors
We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set.
      
Distribution of sum of vectors of 0-1 random variables is discussed generalizing the univariate results obtained in our previous article Takeuchi and Takemura (1987,Ann.
      
The vector partition problem concerns the partitioning of a set A of n vectors in d-space into p parts so as to maximize an objective function c which is convex on the sum of vectors in each part.
      
In particular, it is proved that the direct decompositions of such groups are in bijective correspondence with the decompositions of vectors of some cone in an integer lattice into the sum of vectors in the lattice.
      
In order to compute the chessboard distance securely we can use our protocol for finding the maximum value in a sum of vectors for two parties.
      


Fault plane solutions are obtained from data of the first motions for 24 earthquakes with Ms ≥ 4.0 of the Haicheng earthquake sequence, the mainshock of which occurred on Feb. 4, 1975. One of the nodal planes of the mainshock strikes N 70° W, dipping 80° to the NE. while the other nodal plane strikes N 23° B, dipping 75° to the SE. Based on the data of the spatial distributions of the after shocks and the ground deformations, the N 70° W nodal plane is taken as the fault plane. The faulting is nearly a vertical,...

Fault plane solutions are obtained from data of the first motions for 24 earthquakes with Ms ≥ 4.0 of the Haicheng earthquake sequence, the mainshock of which occurred on Feb. 4, 1975. One of the nodal planes of the mainshock strikes N 70° W, dipping 80° to the NE. while the other nodal plane strikes N 23° B, dipping 75° to the SE. Based on the data of the spatial distributions of the after shocks and the ground deformations, the N 70° W nodal plane is taken as the fault plane. The faulting is nearly a vertical, left-lateral strike-slip with a minor component of normal dip-slip movement. While the focal mechanisms of all the fore-shocks and most of the aftershocks are similar to that of the mainshock, those of 4 aftershocks with Ms ≥ 4.0 are remarkably different from the mainshock. They represent a faulting with slip vector reversed in direction to that of the mainshock. One possible explanation for these exceptions is that during the mainshock the fault movement overshot along some segments of the fault.The source parameters of the mainshock are calculated from the data of field observations and spatial distributions of the aftershocks. The fault length, width, averge dislocation, seismic moment, and stress-drop, of the mainshock, are estimated as 70 km, 20km, 45cm, 2.1 x 1026 dyne·cm, 4.8 bars, respectively. It is a low stress-drop earthquake occurring in a weak zone that is incapable of accumulating higher stresses.For 81 foreshocks and aftershocks the source dimensions, seismic moments, stress-drops as well as average dislocations are calculated from the data of the first half cycles and amplitudes of the seismic P-waves. The results indicate that the stress-drops are rather low, and generally in the range of 0.1-1.0 bars, for both the foreshocks and aftershocks. There are two regions with relatively higher stress-drops ( ≥ 0.8 bars), which correspond to the overshooting portions on the main fracture. These results imply that there might be some intrinsic connections between higher initial stresses before the mainshock, overshooting of fault movment, relatively higher stress-drops, and reverse of the slip vectors of focal mechanisms. It seems that the latter three phenomena are the results of the relatively higher initial stress.

由地震纵波初动符号的资料,求得了海城地震系列中Ms≥4.0的24个地震的断层面解。主震发生于1975年2月4日,它的一个节面走向N70°W,倾向NE,倾角81°;另一个节面走向N23°E,倾向SE,倾角75°。根据余震的空间分布以及地面形变资料选取N70°W的节面为断层面,主震是发生在这个近乎直立的断层面上的左旋走向滑动,略具正的倾向滑动分量。前震及大多数余震的震源机制和主震的相似,有四个Ms≥4.0的余震的震源机制和主震的迥然不同,表现出滑动向量和主震的滑动向量相反的断层错动方式。这种情况的一种可能的解释是主震时在断层的一些地段发生错动过头。 由野外资料及余震的空间分布资料计算了主震的震源参数。主震断层长70公里,宽20公里,平均错距45厘米,地震矩2.1×10~(26)达因·厘米,应力降4.8巴,应变降7.3×10~(-6)。它是发生在不能积累起较高应力的薄弱地带的一次低应力降的地震。 由地震纵波初动的半周期和振幅的资料计算了81个前震和余震的震源尺度、地震矩、应力降和平均错距。结果表明前震和余震的应力降都比较低,一般在0.1—1巴之间。余震区中有两个应力降相对说来比较高(高于0.8巴)的地区,它们恰好对...

由地震纵波初动符号的资料,求得了海城地震系列中Ms≥4.0的24个地震的断层面解。主震发生于1975年2月4日,它的一个节面走向N70°W,倾向NE,倾角81°;另一个节面走向N23°E,倾向SE,倾角75°。根据余震的空间分布以及地面形变资料选取N70°W的节面为断层面,主震是发生在这个近乎直立的断层面上的左旋走向滑动,略具正的倾向滑动分量。前震及大多数余震的震源机制和主震的相似,有四个Ms≥4.0的余震的震源机制和主震的迥然不同,表现出滑动向量和主震的滑动向量相反的断层错动方式。这种情况的一种可能的解释是主震时在断层的一些地段发生错动过头。 由野外资料及余震的空间分布资料计算了主震的震源参数。主震断层长70公里,宽20公里,平均错距45厘米,地震矩2.1×10~(26)达因·厘米,应力降4.8巴,应变降7.3×10~(-6)。它是发生在不能积累起较高应力的薄弱地带的一次低应力降的地震。 由地震纵波初动的半周期和振幅的资料计算了81个前震和余震的震源尺度、地震矩、应力降和平均错距。结果表明前震和余震的应力降都比较低,一般在0.1—1巴之间。余震区中有两个应力降相对说来比较高(高于0.8巴)的地区,它们恰好对应于主破裂错动过头的部位。这些结果意味着震前高应力、错动过头、相对高应力降和震源机制反向四者之间?

In the first part of our paper, we have extended the concepts of the classical convolution and the "convolution scalar product" given by I. Hlavacek and presented the concepts of the "convolution vector" and the "convolution vector scalar product", which enable us to extend the initial value as well as the initial-boundary value problems for the equation with the operator coefficients to those for the system of equations with the operator coefficients.

在本文的第一部份中.我们扩展了经典的卷积和I.Hlavácěk给出的“卷积数积”的概念,提出了“卷积向量”和“卷积向量点积”的概念.从而可使我们把具有算子系数的方程的初值问题和初值——边值问题推广到具有算子系数的方程组的相应问题中去。在本文的第二部份中,以卷积向量和卷积向量点积的概念为基础导出了非均匀的各向异性固体的非局部微极线性弹性动力学的两种基本型式的互易定理。在本文的第三部份中,利用一和二中卷积向量和卷积向量点积的概念和结论及由钱伟长提出的Lagrange乘子法给出了非局部微极线性弹性动力学的四种主要型式的广义变分原理。它们是与经典弹性理论中的胡海昌-鹫津久一郎型的、Hellinger-Reissner型的和Gurtin型的以及局部微极弹性理论和非局部弹性理论中的Hlavácěk型的和Iesan型的广义变分原理相应的各种变分原理。最后还指出了这里提出的后两种主要型式的广义变分原理是等价的。

In this paper, we discuss two kinds of "global dependency" in highly overlapped pipeline computers and propose some solutions. We also discuss their algorithmic similarity to "bit-masks" and "local index registers" in an array processor, and the similarity to "operation control vectors" and "indirect control vectors" in a vector computer. Because of this similarity, some methods from high-speed pipeline SISD computers can be extended to array processors or vector computers, and vice-versa.

本文讨论高度重叠流水线计算机中两种全局性相关及其解决办法。最后,讨论它们与阵列机的“屏蔽位”和“与处理单元有关的局部变址”算法上的相似性,以及它们与向量机的“运算控制向量”和“间接控制向量”的相似性。这一方法使得高速流水线的单指令流-单数据流计算机与阵列机、向量机的一些成果,通过“相似性”可以相互推广。

 
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