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51.
52.
Based on the generalized variational principle and B-spline wavelet on the interval (BSWI), the multivariable BSWI elements with two kinds of variables (TBSWI) for hyperboloidal shell and open cylindrical shell are constructed in this paper. Different from the traditional method, the present one treats the generalized displacement and stress as independent variables. So differentiation and integration are avoided in calculating generalized stress and thus the precision is improved. Furthermore, compared with commonly used Daubechies wavelet, BSWI has explicit expression and excellent approximation property and thus further guarantee satisfactory results. Finally, the effciency of the constructed multivariable shell elements is validated through several numerical examples. 相似文献
53.
数字体积相关是通过分析具有相关关系的两组三维图像,获得物体变形过程中位移场和应变场的计算方法。了解该算法在实际噪音下的表现,对这种方法的应用具有十分重要的意义。利用爬山法、最小二乘法,结合三次B样条插值,建立了一套数字体积相关计算方法,用两组具有真实噪音的三维X射线CT数据对该算法进行了系统评测。在没有噪音的理想情况下,该算法的位移误差为0.0065voxel;在真实X-CT噪音的情况下,位移误差增加到0.008voxel,应变误差约为100με。结果表明,本方法可对真实物体变形进行三维位移场、应变场分析。 相似文献
54.
In this paper, numerical solution of Burgers-Fisher equation is presented based on the cubic B-spline quasi-interpolation. At first, the generalized Burgers-Fisher equation and the cubic B-spline quasi-interpolation are introduced. Moreover, the numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Moreover, the stability of this method is studied. At last, the numerical results obtained by this way have been compared with the exact solution to show the efficiency of the method. The main advantage of the resulting scheme is that the algorithm is very simple, so it is very easy to implement. 相似文献
55.
In this paper, a finite element collocation approach using cubic B-splines is employed for the numerical solution of a generalized form of the nonlinear Klein-Gordon equation. The efficiency of the method is tested on a number of examples that represent special cases of the extended equation including the sine-Gordon equation. The numerical results are compared with existing numerical and analytic solutions and the outcomes confirm that the scheme yields accurate and reliable results even when few nodes are used at the time levels. 相似文献
56.
In the present paper a numerical method, based on finite differences and spline collocation, is presented for the numerical solution of a generalized Fisher integro-differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed-form difference scheme. A number of test examples are solved to assess the accuracy of the method. The numerical solutions obtained, indicate that the approach is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods. Convergence and stability of the scheme have also been discussed. 相似文献
57.
58.
The newly developed integral function of airfoil profiles based on Trajkovski conformal transform theory could be used to optimize the profiles for the thin thickness airfoil. However, it is hard to adjust the coefficients of the integral function for the medium thickness airfoil. B-spline curve has an advantage of local adjustment, which makes it to effectively control the airfoil profiles at the trailing edge. Therefore, a new direct design method for the medium thickness wind turbine airfoil based on airfoil integral expression and B-spline curve is presented in this paper. An optimal mathematical model of an airfoil is built. Two new airfoils with similar thickness, based on the new designed method and the original integral method, are designed. According to the comparative analysis, the CQU-A25 airfoil designed based on the new method exhibits better results than that of the CQU-I25 airfoil which is designed based on the original method. It is demonstrated that the new method is feasible to design wind turbine airfoils. Meanwhile, the comparison of the aerodynamic performance for the CQU-A25 airfoil and for the DU91-W2-250 airfoil is studied. Results show that the maximum lift coefficient and the maximum lift/drag ratio of the CQU-A25 airfoil are higher than the ones of DU91-W2-250 airfoil in the same condition. This new airfoil design method would make it possible to design other airfoils with different thicknesses. 相似文献
59.
Charles A. Micchelli Yuesheng Xu Haizhang Zhang 《Advances in Computational Mathematics》2008,28(2):157-169
It was observed in [4] that the Hilbert transform of the univariate B-spline preserves the B-spline recurrence. Motivated by this observation,
we characterize translation invariant operators that preserve the multivariate B-spline recurrence and analogous results are
also provided for the multivariate cube spline.
Charles A. Micchelli was supported in part by the US National Science of Foundation under grant CCR-0407476.
Yuesheng Xu was supported in part by the US National Science Foundation under grant CCR-0407476, by the Natural Science Foundation
of China under grant 10371122, by the Chinese Academy of Sciences under the program “One Hundred Distinguished Chinese Scientists”
and by Ministry of Education, People’s Republic of China, under the Changjian Scholarship through Zhongshan University. 相似文献
60.
In this paper, we consider the knot placement problem in B-spline curve approximation. A novel two-stage framework is proposed for addressing this problem. In the first step, the $l_{\infty, 1}$-norm model is introduced for the sparse selection of candidate knots from an initial knot vector. By this step, the knot number is determined. In the second step, knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm — the differential evolution algorithm (DE). The candidate knots selected in the first step are served for initial values of the DE algorithm. Since the candidate knots provide a good guess of knot positions, the DE algorithm can quickly converge. One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically. Compared with the current existing algorithms, the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance. Furthermore, the proposed algorithm is robust to noisy data and can handle with few data points. We illustrate with some examples and applications. 相似文献