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major axis    
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    Found a kind of internal relation between the center projection and the parallel projection, under the center projection, the circle is changed into ellipse, but it can't decide the relation between the conjugate axis or major axis and minor axis of ellipse, which can be solved by this theorem.
    在中心投影和平行投影之间建立一种对应关系,在中心投影下把圆变成椭圆,但是不能确定椭圆的共轭轴或长轴与短轴的位置和长度,该定理解决了这个问题。
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  长轴
    Found a kind of internal relation between the center projection and the parallel projection, under the center projection, the circle is changed into ellipse, but it can't decide the relation between the conjugate axis or major axis and minor axis of ellipse, which can be solved by this theorem.
    在中心投影和平行投影之间建立一种对应关系,在中心投影下把圆变成椭圆,但是不能确定椭圆的共轭轴或长轴与短轴的位置和长度,该定理解决了这个问题。
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  major axis
At the phase plane "the longitude of the subsatellite point-semi-major axis" the regions of migration of separatrices where the separatrices can move due to the influence of perturbations are isolated.
      
The dimensions of these regions and the distances between them have the same order of magnitude, several kilometers along the semi-major axis.
      
Flow past an oblate ellipsoid of revolution aligned along the major axis
      
We found no evidence of gas rotation around the major axis of NGC 6286, which argues against the assumption that this galaxy has a forming polar ring.
      
We found no significant deviations from the circular rotation of the galactic disk in the velocity field in the regions of brightness excess along the major axis of the galaxy (the putative polar ring).
      
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By using the method of mathematical analysis this article deals with the parti-cular point A,the point with minimum X-cordinate in front view,on the curve ofintersection of a right circular cone and a right circular cylinder with their axesobliqueIy intersecting (Fig.1).In this article the particular points are solved boththeoretically and graphically in comparatively satisfied manner.Through a preliminary research,two regularities have been derived as follows:1.These particular points (Fig.1) are distributed...

By using the method of mathematical analysis this article deals with the parti-cular point A,the point with minimum X-cordinate in front view,on the curve ofintersection of a right circular cone and a right circular cylinder with their axesobliqueIy intersecting (Fig.1).In this article the particular points are solved boththeoretically and graphically in comparatively satisfied manner.Through a preliminary research,two regularities have been derived as follows:1.These particular points (Fig.1) are distributed on a plane(its front view beingan edge view),represented by the following equation of line(sin~2α+sin~2θcos~2α)/(hsin~2α)z-(cos~2αsinθcosθ)/(hsin~2α)x=12.The said particular points are also distributed on the surface of an ellipsoid,whose major axis is the same as the axis of the right circular cylinders.The frontview of the ellipsoid is an ellipse represented by the following equation(1-cos~2θcos~2α)/(h~2sin~2α)X~2+1/(h~2sin~2α)Z~2=1The particular point may be easily located by only drawing straight lines andcircles.

本文应用解析方法,对一组锥-柱斜交相贯线最右点在空间及投影图上所处位置作了初步探讨,得出两个分布规律;文中还以形数结合,研讨了锥-柱斜交相贯线最右点的求作问题,提出了较为简捷的作图方法.

The Euclidean distance, which is most often used in Q-mode cluster analysis, is unable to reflect the influence of eorrelativity between variables on the results of cluster analysis, so it cannot fully reveal the clustering situation of samples. For this reason three techniques are proposed in a lot of literature to solve this problem; they are.1. the oblique distance method,2. the principle component analysis method, and3. the Mahalanobis distance method.But there has been no paper researching on the eharaeteristies...

The Euclidean distance, which is most often used in Q-mode cluster analysis, is unable to reflect the influence of eorrelativity between variables on the results of cluster analysis, so it cannot fully reveal the clustering situation of samples. For this reason three techniques are proposed in a lot of literature to solve this problem; they are.1. the oblique distance method,2. the principle component analysis method, and3. the Mahalanobis distance method.But there has been no paper researching on the eharaeteristies of and the relationship between these methods. In practice, these methods are chosen quite at random and without rules. This paper, in both theory and practice, analyses and compares the three methods, and gives the following conclusions:1. the oblique distanee method functions the same as the principle component analysis method, beeausesum from j=1 to m sum from l=1 to, in the above equation, the left part is the expression for computing oblique distanee, and the right part is the Euclidean distance from the principle component analysis method.2. the Mahalanobis distance is equal to the Euelidean distance computed from factor scores; this is because, after data standardization,in this equation, the first part is the expression for computirg mahalanobis distance, and the last paft is the exprssion for computing Euclidean distance from factor scofes.3. the Mahalanobis distance and the oblique distance deal with correlativity in two opposite ways. Generally speaking, the Mahalanobis distance gives correlated variables smaller weight values, and the oblique distance gives them larger weight values, while the Euclidean distance gives equal weights to all variables. lf any two samples are located along the direction of major axis of the distribution ellipse, the Mahalanobis distance between them is smaller than the Euclidean distance, while the oblique distance is larger than the Euclidean distance, if located along the direction of minor axis, it will be an opposite conclusion.The three conclusions stated above are instructive in choosing statistics for clustering in practical work, and helpful in avoiding blndness, and studying the computational results of cluster analysis.

本文分析了斜交距离法、主成分分析法和马氏距离法等处理原始变量相关性的方法的原理,论述了Q型聚类分析相似性统计量的几种数据处理方法之间的特点及其等价关系,并且用实际算例验证了理论推导的正确性。

This paper describes the solution of the computer aided graphics problem of the orthogonal axonometric projection of the conic section cut on the circular cone. It is a very difficult problem in mathematics and engineering graphics. The author resolves this problem by ingenious mathematical models and a simple and convenient program. The distinguishing features of this paper are as follows: drawing the orthogonal axonometric drawing the cut of an arbitary position circular cone; drawing the major axis...

This paper describes the solution of the computer aided graphics problem of the orthogonal axonometric projection of the conic section cut on the circular cone. It is a very difficult problem in mathematics and engineering graphics. The author resolves this problem by ingenious mathematical models and a simple and convenient program. The distinguishing features of this paper are as follows: drawing the orthogonal axonometric drawing the cut of an arbitary position circular cone; drawing the major axis and minor axis of an ellipse automatically if the ellipse is full. This paper contributes a more applicable solfware to teaching drawing and engineering drawing.

应用本文推导的数学模型及所设计的程序,解决了教学和工程绘图中在圆锥上截切出圆锥曲线的正轴测投影的计算机辅助绘图问题。该法可绘出任意位置任意大小的圆锥截断的正轴测投影图,对完整的椭圆还能自动画出其长短轴,可供教学绘图和工程绘图中应用。

 
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