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41.
《Discrete Mathematics》2023,346(1):113213
We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least 2π. The combinatorial information of these surfaces is shown to be identified with that of Euclidean polyhedral surfaces with negative combinatorial curvature everywhere. We prove that there is a gap between areas of non-smooth hyperbolic polyhedral surfaces and the area of smooth hyperbolic surfaces. The numerical result for the gap is obtained for hyperbolic polyhedral surfaces, homeomorphic to the double torus, whose 1-skeletons are cubic graphs. 相似文献
42.
R. V. Ambartzumian 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2009,44(1):25-35
Combinatorial integral geometry possesses some results that can be interpreted as belonging to the field of Geometric Tomography. The main purpose of the present paper is to present a case of parallel X-ray approach to tomography of random convex polygons. However, the Introduction reviews briefly some earlier results by the author that refer to reconstruction of (non-random) convex domains by means of a point X-ray. The main tool in treating the parallel X-rays is disintegrated Pleijel identity, or rather, its averaged version, whose derivation is represented in complete detail. The paper singles out a class of random polygons called tomography models, that offer essential advantages for the analysis. The definition of a tomography model is given in terms of stochastic independence. Fortunately, random translation-invariant Poisson processes of lines in IR 2 suggest a class of examples. We recall that each such line process is determined by its rose of directions ρ(?). For rather general ρ(?), the number weighted typical polygon in the polygonal partition of the plane generated by the corresponding Poisson line process happens to be a tomography model. For general tomography models, a differential equation is derived for the Laplace transform for parallel X-rays, that rises several interesting computational problems. 相似文献
43.
The Dutch introduced trigonometry to Japan in the middle of the 17th century, but the use of trigonometry was rarely seen until the 18th century, and its use was limited to practical purposes such as surveying and astronomy. It was rarely used to solve geometry problems currently called wasan, the reason for which is not yet fully explained. In this paper, I summarize a book by Aida Yasuaki (1747–1817) in which he strongly criticizes the use of trigonometry for wasan, and try to find the origins of his antipathy. 相似文献
44.
Yi Hu 《Compositio Mathematica》1999,118(2):159-187
In this paper, certain natural and elementary polygonal objects in Euclidean space, the stable polygons, are introduced, and the novel moduli spaces
of stable polygons are constructed as complex analytic spaces. Quite unexpectedly, these new moduli spaces are shown to be projective and isomorphic to the moduli space
of the Deligne–Mumford stable curves of genus 0. Further, built into the structures of stable polygons are some natural data giving rise to a family of (classes of) symplectic (Kähler) forms. This, via the link to
, brings up a new tool to study the Kähler topology of
. A wild but precise conjecture on the shape of the Kähler cone of
is given in the end. 相似文献
45.
确定两个任意多边形的并的算法 总被引:1,自引:0,他引:1
周培德 《北京理工大学学报》1998,18(1):87-91
设计并分析求两个任意多边形的并的一种新算法。方法利用分治思想设计算法,即根据P,Q凸壳及P与Q的凸壳的不同位置关系,分6种情况分别求并P∪Q的边界。结论该算法优化逐次判断P的每条边是否与Q的边相交的方法。 相似文献
46.
Cohen—Sutherland算法的改进及其推广 总被引:3,自引:0,他引:3
吴有富 《贵州工业大学学报(自然科学版)》1998,27(4):6-9
本文对Cohen-Sutherland算法进行了分析,指出了存在的问题,提出了改进方法;同时提出了二维多边形有向编码逐边裁剪法和三维多面体的有向编码逐面裁剪方法,而二维多边形编码逐边裁剪法和三维多面体的有向编码逐面裁剪方法可加速计算机视觉中图象识别的速度。 相似文献
47.
设P和Q是平面内任意两个互不相交的凸多边形,目前确定P与Q的可碰撞区域的最佳串行算法时间复杂度为O(n+m),其中n和m分别为凸多边形P和Q的顶点个数.在该算法的基础上构造了一个易于并行化的求支撑点的串行算法,进而给出了在MIMD-CREW模型上确定可碰撞区域的并行算法,其时间复杂度为O((S+log_2(n+m))log_2(n+m)/log_2S),其中S为处理机个数 相似文献
48.
Tom M. Cavalier Whitney A. ConnerEnrique del Castillo Stuart I. Brown 《European Journal of Operational Research》2007
This paper addresses the problem of locating a finite number of sensors to detect an event in a given planar region. The objective is to minimize the maximum probability of non-detection where the underlying region consists of a convex polygon. The sensor location problem has a multitude of applications, including the location of aircraft detection sensors, the placement of sentries along a border to detect enemy penetration, the detection of nuclear tests, and the detection of natural and hazardous man-made events. The problem is a difficult nonlinear nonconvex programming problem even in the case of two sensors. A fast heuristic based on Voronoi polygons is developed in this paper. The algorithm can quickly generate high-quality solutions. Computational experience is provided. 相似文献
49.
Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of non-intersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the triangulation that minimizes the area of the largest area triangle in the triangulation. We present algorithms that construct MaxMin and MinMax area triangulations of a convex polygon in O(n2logn) time and O(n2) space. The algorithms use dynamic programming and a number of geometric properties that are established within the paper. 相似文献
50.