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1.
Efficient Global Optimization of Expensive Black-Box Functions   总被引:20,自引:0,他引:20  
In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.  相似文献
2.
Helix splines as an example of affine Tchebycheffian splines   总被引:16,自引:0,他引:16  
The present paper summarizes the theory of affine Tchebycheffian splines and presents an interesting affine Tchebycheffian free-form scheme, the “helix scheme”. The curve scheme provides exact representations of straight lines, circles and helix curves in an arc length parameterization. The corresponding tensor product surfaces contain helicoidal surfaces, surfaces of revolution and patches on all types of quadrics. We also show an application to the construction of planarC 2 motions interpolating a given set of positions. Because the spline curve segments are calculated using a subdivision algorithm, many algorithms, which are of fundamental importance in the B-spline technique, can be applied to helix splines as well. This paper should demonstrate how to create an affine free-form scheme fitting to certain special applications.  相似文献
3.
分形插值曲面理论及其应用   总被引:15,自引:0,他引:15  
本文叙述了分形曲面的生成原理,给出了分形插值曲面的计算公式,证明了分形插值曲面迭代函数系唯一性定理,导出了分形插值曲面的维数定理,并应用实际数据进行了分形插值曲面的实例研究·  相似文献
4.
The power crust, unions of balls, and the medial axis transform   总被引:11,自引:0,他引:11  
The medial axis transform (or MAT) is a representation of an object as an infinite union of balls. We consider approximating the MAT of a three-dimensional object, and its complement, with a finite union of balls. Using this approximate MAT we define a new piecewise-linear approximation to the object surface, which we call the power crust.

We assume that we are given as input a sufficiently dense sample of points from the object surface. We select a subset of the Voronoi balls of the sample, the polar balls, as the union of balls representation. We bound the geometric error of the union, and of the corresponding power crust, and show that both representations are topologically correct as well. Thus, our results provide a new algorithm for surface reconstruction from sample points. By construction, the power crust is always the boundary of a polyhedral solid, so we avoid the polygonization, hole-filling or manifold extraction steps used in previous algorithms.

The union of balls representation and the power crust have corresponding piecewise-linear dual representations, which in some sense approximate the medial axis. We show a geometric relationship between these duals and the medial axis by proving that, as the sampling density goes to infinity, the set of poles, the centers of the polar balls, converges to the medial axis.  相似文献

5.
求解渗流自由面的复合单元全域迭代法   总被引:11,自引:0,他引:11  
渗流自由面是岩体水力学研究的重点和难点,也是边坡稳定性综合研究的重要内容· 基于对渗流自由面数值求解方法的分析,提出了复合单元全域迭代法,并编制了有限元计算程序· 计算果表明,该法具有程序处理比较简单、计算结果比较精确等特性,一般迭代5次左右便可收敛  相似文献
6.
Least-Squares Fitting of Algebraic Spline Surfaces   总被引:10,自引:0,他引:10  
We present an algorithm for fitting implicitly defined algebraic spline surfaces to given scattered data. By simultaneously approximating points and associated normal vectors, we obtain a method which is computationally simple, as the result is obtained by solving a system of linear equations. In addition, the result is geometrically invariant, as no artificial normalization is introduced. The potential applications of the algorithm include the reconstruction of free-form surfaces in reverse engineering. The paper also addresses the generation of exact error bounds, directly from the coefficients of the implicit representation.  相似文献
7.
广义Bézier曲线与曲面在连接中的应用   总被引:10,自引:0,他引:10  
通常的贝齐尔(Bezier)曲线、曲面,在其端点或边界只具有GC1阶插值性.本文在保持通常贝齐尔曲线、曲面性质的基础上,定义了一种广义的贝齐尔曲线、曲面,使其在曲线段的端点和曲面片的边界具有高阶光滑插值性,它可方便地光滑连接两条参数型的曲线段和两张以上参数型曲面片,并且连接方式是GCr(r≥1)的.所以广义贝齐尔曲线、曲面在计算机辅助设计应用中更具有独特的意义.  相似文献
8.
Minimal Surfaces in the Heisenberg Group   总被引:9,自引:0,他引:9  
We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot–Carathéodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces and Riemannian constant mean curvature surfaces in H equipped with different Riemannian metrics approximating the Carnot–Carathéodory metric. We generate a large library of examples of minimal surfaces and use these to show that the solution to the Dirichlet problem need not be unique. Moreover, we show that the minimal surfaces we construct are in fact X-minimal surfaces in the sense of Garofalo and Nhieu.  相似文献
9.
一类四阶差分方程边值问题及分形曲面的生成   总被引:8,自引:1,他引:7  
本文研究一个二变元四阶差分方程边值问题,证明了此问题的适定性,揭示了解的结构。经过证明和数值模拟,可以作为分形曲面生成和插值的一种新方法。  相似文献
10.
A Taxonomy of Global Optimization Methods Based on Response Surfaces   总被引:8,自引:0,他引:8  
This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach.  相似文献
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