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41.
42.
Jean-Daniel Boissonnat Leonidas J. Guibas Steve Y. Oudot 《Discrete and Computational Geometry》2009,42(1):37-70
It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low
dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation
on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results
do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the
positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between
restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural
results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm
combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not
require the input point sample to be sparse. Its running time is bounded by c(d)n
2, where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown
that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper.
This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid. 相似文献
43.
In this paper, we shall prove that a projective‐planar (resp., toroidal) triangulation G has K6 as a minor if and only if G has no quadrangulation isomorphic to K4 (resp., K5 ) as a subgraph. As an application of the theorems, we can prove that Hadwiger's conjecture is true for projective‐planar and toroidal triangulations. © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 302‐312, 2009 相似文献
44.
高质量点集的快速局部网格生成算法 总被引:1,自引:0,他引:1
高效及高质量的局部网格生成算法是基于节点有限元并行方法设计的关键。泡泡布点算法能够在复杂区域上不经过人工干预生成高质量的节点集,本文提出了基于该方法所生成的节点集的快速局部网格生成算法。该算法充分利用泡泡布点方法提供的节点集及节点邻接链表信息,避免了桶数据结构的建立以及节点的局部搜索过程,只需应用Delaunay三角剖分的外接圆准则从中心节点的邻接链表中去除极少数的非卫星点,可快速地生成局部网格,比现有的局部网格生成算法更为快捷。算例结果表明,该算法高效可靠,生成网格与Delaunay三角剖分网格一致。 相似文献
45.
Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets
Deok‐Soo Kim Joonghyun Ryu Hayong Shin Youngsong Cho 《Journal of computational chemistry》2012,33(13):1252-1273
Given a set of spherical balls, called atoms, in three‐dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well‐solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta‐decomposition, based on the recent theory of the beta‐complex. Given the beta‐complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta‐complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta‐complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ?3 that m = O(n) on average for biomolecules and m = O(n2) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ?2 and extended to ?3. The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site. © 2012 Wiley Periodicals, Inc. 相似文献
46.
47.
任意平面区域三角形网格的全自动生成算法 总被引:9,自引:1,他引:8
本文基于波前法提出了一种对任意平面区域生成三角形网格自动生成算法。算法具有区域适应性强,边界网格质量高,自动化程度高的优点。算法还包括了网格的拓扑优化,光滑及加密处理。此外,初边值条件的自动给定大大减少了数值计算中数据输入和避免了边界搜索计算。大量算例显示了算法的可靠性和适用性。 相似文献
48.
首次提出了一种判别样条空间S13(Δ)维数不依赖剖分几何性质的协调条件· 依此 ,在一类较一般的三角剖分下 ,获得了S13(Δ)的维数· 相似文献
49.
空间编码与灰度投影相结合实现高效3-D形貌测量的研究 总被引:2,自引:1,他引:1
介绍了一种结合空间编码与灰度投影来实现高效三维形貌测量的方法。用空间编码完成对被测空间的粗略编码,用灰度投影完成精确编码,将它们结合起来得到被测物体表面丰富的编码信息,作为一种基于三角法的三维形貌测量方法,能够在物体表面非常不连续和外部光照造成的背景光强分布不确定的情况下工作良好。同时,与传统的空间编码方法相比,它大大提高了空间编码的效率。实验表明,该方法用5 幅图像取得了与灰度码10幅图像相当的测量结果。 相似文献
50.