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set of points
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  点集
     An O(nlogn) Algorithm for the Shortest Paths between Two Set of Points in the Plane
     平面上两个点集间距离的O(nlogn)算法
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     Discusses of Teaching Method on Set of Points Topology
     点集拓扑教学方法的几点讨论
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     Let R be a closed rectangle of sides 1 and 2 in the plane,S be a finite set of points in R,f(S) denote the minimum distance between pairs of points of S,and fR(n) = . Inthis paper,the exact values of fR(n) for 2≤n≤6 and the corresponding configurations aregiven.
     设平面上边长为1和2的闭矩形区域为R,S是R上一个有限点集,f(S)是S中任意两点之间的最小距离,fR(n)=maxf(S),本文给出了当2≤n≤6时,fR(n)的精确值以及相应的图形.
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     An analogue of the multi wavelet bases which lie in the space of functions defined on a discrete set of points {x 1,...,x n}×{y 1,...,y n}R 2 is taken into account.
     一种定义在平面离散点集 {x1 ,… ,xn}{y1 ,… ,yn} R2 上的类似于多小波的准小波基被研究 ,它与通常小波基的差别在于不是由 V0 空间的一个函数通过伸缩平移构成而仅仅是类似 .
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     Let G be a double-outer plane graph, V(G), E(G), F(G) be the set of points, edge and face, a plane graph G is k-total colorable, if the elements of V(G) E(G) can be colored with K-colors, any two distinct adjacent or incident elements receive different colors.
     设G是一个双外平面图,V(G),E(G),F(G)分别为双外平面图G的点集,边集和面集。
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  “set of points”译为未确定词的双语例句
     Let A(G) be the set of points in V(G)-D(G) adjacent to at least one point in D(G).
     A(G)表示V(G) -D(G)的一个子集 ,它的每一个点至少和D(G)的一个点相邻 .
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     For any ergodic measure,we considered the set of points which satisfy the Brin-Katok theorem and Birkhoff ergodic theorem with respect to this measure.
     任给一个遍历测度,我们考虑在该测度下Brin-Katok定理和Birkhoff遍历定理成立的点所组成的集合.
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     In this paper, we dissuss teaching methods in different aspects of set of points topology.
     本文从几个方面对点集拓扑的教学方法进行了讨论。
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     In this paper, the writes proves that: Let X be a regular space satisfying axiom A and Y be a topological space, for any y∈Y, is a nonempty subset in X and multivalued mapping F is upper semicontinuous on Y, then the set of points where F is lower semicontinuous is a residual set in Y.
     本文证明了:设X是满足第二可列公理的正则空间,Y是拓扑空间,对任y∈Y,F(y)是X中的非空子集,且多值映射F在Y上是上半连续的,则F的下半连续点所成之集必是y中的一个剩余集。
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     Based on binary image made of image segmentation pretreatment, the recursion marking was assigned to the corresponding target. The algorithm avoids pixel "1" being rescanned in detection of the connected set of points, which realized the requirements of only considering abstracting the target characteristics without obtaining final marked image itself.
     该算法根据图像预处理分割后的二值图像,对目标图像进行递归标记,避免了基于点的连通体检测中“1”像素点可能被重复扫描的现象,实现了只考虑提取目标特征,不用得到最终的标记图像本身的要求。
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  相似匹配句对
     (L) and set
     (L),证明了范畴Set_0(L)与(?)
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     The set
     集合(英文)
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     ON THE DEFINITION OF THE SET
     关于集合的定义
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     The Structure of Measurable Set
     可测集合的结构
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     The creative points:
     本文创新点
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  set of points
Closed orbits are described and a set of points of dense orbit is explicitly given.
      
In particular, the results in this article show that the oscillations of a function at large scale are comparable to the oscillations of its samples on an appropriate discrete set of points.
      
In the application of CAD/CAM, the target form of a curve, which is used for plotting or as the data supplied for CAM, is a set of points on (or near by) the curve.
      
The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein-Uhlenbeck processes is a random fractal, and eval-uates its Hausdorff dimension.
      
At each iterate, by reduplication, crossover and mutation, a finite set of points can be used.
      
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Consider the differential equation =f(t,x) (1)where x and f(t,x) are n-vectors,f(t, x)∈C[I×R~n, R~n], I denotes thekalf line:0≤t<∞, and R~n denotes n-Euclidean space. Let g(t,x) be a h-vector (h≤n) and g(t, x)∈C[I×R~n, R~n]. The set of points (t,x)∈I×R~n satisfying the relation g(t, x)=0 defines an (n-h+1)-manifold St, Suppose thet (t_0, x_0)∈S_(t0) implies (t,x(t; t_0,x_0)∈S_t for t≥t_0, than S_t is a posititively invariant manifold of equation (1). In this paper we consider some new types of stability...

Consider the differential equation =f(t,x) (1)where x and f(t,x) are n-vectors,f(t, x)∈C[I×R~n, R~n], I denotes thekalf line:0≤t<∞, and R~n denotes n-Euclidean space. Let g(t,x) be a h-vector (h≤n) and g(t, x)∈C[I×R~n, R~n]. The set of points (t,x)∈I×R~n satisfying the relation g(t, x)=0 defines an (n-h+1)-manifold St, Suppose thet (t_0, x_0)∈S_(t0) implies (t,x(t; t_0,x_0)∈S_t for t≥t_0, than S_t is a posititively invariant manifold of equation (1). In this paper we consider some new types of stability and boundedness of solutions of (1) with respect to S_t, and obtain some theorems more general than that of [3]、[5]、[7].

本文讨论关于积分流形的各类k-有界性与k-稳定性,建立了判定准则,所得结果推广了文献中有关结论.此外还将文献[7]中关于解在sell意义下全局均匀渐近稳定性强于全局等度渐近稳定性的结论推广到积分流形.

In paper(1),a class of geometric inequalities have been constructed on the bounded set of points,and some relations of the invariants for the k-ciimcnsional simplex in the Euclidean space have been given by the algebric methods. The well-known Neuberg-Pcodc inequality concerning two triangles has been extended to any two simplices in the n-dimensional Euclidean space in(2). This paper obtains two inequalities ( Theorem 1 and Theorem 2) concerning any two simplices from another viewpoint. As the special...

In paper(1),a class of geometric inequalities have been constructed on the bounded set of points,and some relations of the invariants for the k-ciimcnsional simplex in the Euclidean space have been given by the algebric methods. The well-known Neuberg-Pcodc inequality concerning two triangles has been extended to any two simplices in the n-dimensional Euclidean space in(2). This paper obtains two inequalities ( Theorem 1 and Theorem 2) concerning any two simplices from another viewpoint. As the special cases of these two inequalities,we may deduce some other relations among the invariants,which differ from that in (1)

文章[1]利用代数方法建立了有限点集的一类几何不等式,给出了n维欧氏空间中k(k≤n)维单形的一些不变量的关系式;该文作者又在文[2]中将著名的涉及到两个三角形的Neubery—Peode不等式推广到n维欧氏空间的任意两个单形。本文将从另一角度给出n维欧氏空间中的两个关于两个任意单形的不等式(定理1及定理2),而且作为这两个不等式的特例,可导出另一些不同于文[1]中的不变量之间的关系式。

Given a set of points in plane:P_i(x_(?),y_i) (i=0, 1, …, n;X_0points P_(i-1), P_i, P_(i+1)~- lie on a minor arc of a circle and any four consecutive points P_(i-1), P_i, P_(i+1) P_(i+2) are not concyclic. A curve is said to be a fine shape curve of the given set of points {P_i}, if it is a curve of class C2 passing through these points, the number v of its Points of inflection is minimum, the number μ of its points of extreme...

Given a set of points in plane:P_i(x_(?),y_i) (i=0, 1, …, n;X_0points P_(i-1), P_i, P_(i+1)~- lie on a minor arc of a circle and any four consecutive points P_(i-1), P_i, P_(i+1) P_(i+2) are not concyclic. A curve is said to be a fine shape curve of the given set of points {P_i}, if it is a curve of class C2 passing through these points, the number v of its Points of inflection is minimum, the number μ of its points of extreme curvature is minimum and it satisfies certain additional conditions which will fix the intervals to which certain points of inflection or points of extreme curvature will belong.How can we interpolate points into the given set of points so that every fine shape curve of the new set of points will always be a fine shape curve of the original set of points? The present paper gives a solution to the case μ =v= 0 and indicates how to get an heuristic algorithm in general to make the new set of points to have a fine shape curve with v' points of inflection and with μ' points of extreme curvature so that v' =v and the difference μ'-μ is small. At the end of this paper some remarks are made to account for why this problem was raised and how it is related to the method of sequence of cicular rates which is applied to the Hudon Hull Construction System.

在平面上给了一列点P_1(x_iy_i),(i=0,1,2,…,n;x_0

 
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