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81.
Miguel Ángel García-MarchFernando Giménez Francisco R. VillatoroJezabel Pérez Pedro Fernández de Córdoba 《Applied mathematics and computation》2011,217(18):7427-7431
A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon-Bézout process. 相似文献
82.
An efficient adaptive analysis procedure for node-based smoothed point interpolation method (NS-PIM)
Qian Tang Zhihua ZhongGuiyong Zhang Xu Xu 《Applied mathematics and computation》2011,217(21):8387-8402
This paper presents an efficient adaptive analysis procedure being able to operate in the framework of the node-based smoothed point interpolation method (NS-PIM). The NS-PIM uses three-node triangular cells and is very easy to be implemented, which make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a new error indicator is devised for NS-PIM settings; two ways are proposed to calculate the local critical value; a simple h-type local refinement scheme is adopted and Delaunay technology is used for regenerating optimal new mesh. A number of typical numerical examples involving stress concentration and solution singularities have been tested. The results demonstrate that the present procedure achieves much higher convergence rate results compared to the uniform refinement, and can obtain upper bound solution in strain energy. 相似文献
83.
Hongchao Kang Shuhuang Xiang 《Applied mathematics and computation》2011,218(7):3553-3564
This paper presents some quadrature methods for a class of highly oscillatory integrals whose integrands may have singularities at the two endpoints of the interval. One is a Filon-type method based on the asymptotic expansion. The other is a Clenshaw-Curtis-Filon-type method which is based on a special Hermite interpolation polynomial and can be evaluated efficiently in O(N log N) operations, where N + 1 is the number of Clenshaw-Curtis points in the interval of integration. In addition, we derive the corresponding error bound in inverse powers of the frequency ω for the Clenshaw-Curtis-Filon-type method for the class of highly oscillatory integrals. The efficiency and the validity of these methods are testified by both the numerical experiments and the theoretical results. 相似文献
84.
Vasiliy Ye. Belozyorov 《Applied mathematics and computation》2011,218(8):4546-4566
The wide class of 3-D autonomous systems of quadratic differential equations, in each of which either there is a couple of coexisting limit cycles or there is a couple of coexisting chaotic attractors, is found. In the second case the couple consists of either Lorentz-type attractor and another attractor of a new type or two Lorentz-type attractors. It is shown that the chaotic behavior of any system of the indicated class can be described by the Ricker discrete population model: zi+1 = zi exp(r − zi), r > 0, zi > 0, i = 0, 1, … . The values of parameters, at which in the 3-D system appears either the couple of limit cycles or the couple of chaotic attractors, or only one limit cycle, or only one sphere-shaped chaotic attractor, are indicated. Examples are given. 相似文献
85.
Osman Ra?it I?ikMehmet Sezer Zekeriya Güney 《Applied mathematics and computation》2011,217(22):9438-9450
We introduce a new method to solve high order linear differential equations with initial and boundary conditions numerically. In this method, the approximate solution is based on rational interpolation and collocation method. Since controlling the occurrence of poles in rational interpolation is difficult, a construction which is found by Floater and Hormann [1] is used with no poles in real numbers. We use the Bernstein series solution instead of the interpolation polynomials in their construction. We find that our approximate solution has better convergence rate than the one found by using collocation method. The error of the approximate solution is given in the case of the exact solution f ∈ Cd+2[a, b]. 相似文献
86.
A boundary element method (BEM) for the analysis of two- and three-dimensional uncoupled transient thermo-elastic problems involving time- and space-dependent heat sources is presented. The domain integrals are efficiently treated using the Cartesian transformation and the radial integration methods without considering any internal cells. Similar to the dual reciprocity method (DRM), some internal points without any connectivity are considered; however, in contrast to the DRM, any arbitrary mesh-free interpolation method can be used in the present formulation. There is no need to find any particular solutions and the shape functions in the mesh-free interpolation method can be arbitrary and sufficiently complicated. Unlike the DRM, the generated system of equations contains the unknowns only on the boundary. After finding the primary unknowns on the boundary, the temperature, displacement, and stress components at all internal points can directly be found without solving any system of equations. Three examples with different forms of heat sources are presented to demonstrate the efficiency and accuracy of the proposed method. Although the proposed BEM is mathematically more complicated than domain methods, such as the finite element method (FEM), it is more efficient from a modelling viewpoint since only the surface mesh has to be generated in the presented method. 相似文献
87.
At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters d1 (0 〈 dl ≤ m) and d2 (0 ≤ d2≤ n), builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower. 相似文献
88.
Zheng Zhang · Xu Han · Chao Jiang State Key Laboratory of Advanced Design Manufacturing for Vehicle Body College of Mechanical Vehicle Engineering Hunan University Changsha China 《Acta Mechanica Sinica》2011,27(5):757-766
In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usage of linear interpolation principle.The original problem is projected onto the reduced basis space by linear interpolation projection,and subsequently an associated interpolation matrix is generated.To ensure the largest nonsingularity,the interpolation matrix needs to go through a timenode choosing process,which is developed by applying the angle of vector spaces.As a part of this technique,error estimation is recommended for achieving the computational error bound.To ensure the successful performance of this technique,the offline-online computational procedures are conducted in practical engineering.Two numerical examples demonstrate the accuracy and efficiency of the presented method. 相似文献
89.
90.
Acceleration of self‐consistent field convergence in ab initio molecular dynamics simulation with multiconfigurational wave function 下载免费PDF全文
The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self‐consistent field iterations in ab initio molecular dynamics simulations with the Hartree–Fock method and the Kohn–Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness. © 2014 Wiley Periodicals, Inc. 相似文献