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61.
Coulomb Sturmians are obtained in prolate spheroidal coordinates by separation of variables in the Schrödinger equation and direct solution of the appropriate one-dimensional equations. Molecular orbitals are expressed as linear combinations of the introduced Coulomb Sturmians and some low-lying energy terms and corresponding wave functions are calculated for one-electron diatomic molecules. It is shown that similarity of the one- and two-centre orbitals in spheroidal coordinates, combined with completeness and good convergence properties of Coulomb Sturmians, substantially speeds up convergence and makes the calculated results closer to the exact ones. Application of the elaborated calculating scheme for diatomic many-electron molecules is discussed. 相似文献
62.
63.
René Michel 《Extremes》2007,10(3):83-107
The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with
these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with
an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the
simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented
simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A
method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application
of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms
are available on the author’s home page .
相似文献
64.
N. V. Baidakova 《Mathematical Notes》2005,77(5-6):751-766
For interpolation processes by algebraic polynomials of degree n from values at uniform nodes of an m-simplex, where m ≥ 2, we obtain the order of growth in n of the Lebesgue constants, which coincides with that in the one-dimensional case for which Turetskii obtained an asymptotics earlier.__________Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 814–831.Original Russian Text Copyright ©2005 by N. V. Baidakova. 相似文献
65.
66.
The non‐reflective boundary conditions (NRBC) for Navier–Stokes equations originally suggested by Poinsot and Lele (J. Comput. Phys. 1992; 101 :104–129) in Cartesian coordinates are extended to generalized coordinates. The characteristic form Navier–Stokes equations in conservative variables are given. In this characteristic‐based method, the NRBC is implicitly coupled with the Navier–Stokes flow solver and are solved simultaneously with the flow solver. The calculations are conducted for a subsonic vortex propagating flow and the steady and unsteady transonic inlet‐diffuser flows. The results indicate that the present method is accurate and robust, and the NRBC are essential for unsteady flow calculations. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
67.
68.
Treating the symmetry operations as transformations in higher dimensional space, it is shown that Wigner’s method can be straightaway
extended to study the vibrations of nonrigid molecules exhibiting free or nearly free internal rotations. The molecule B(CH3)3 is illustrated. 相似文献
69.
On the use of linear graph theory in multibody system dynamics 总被引:8,自引:0,他引:8
J. J. McPhee 《Nonlinear dynamics》1996,9(1-2):73-90
Multibody dynamics involves the generation and solution of the equations of motion for a system of connected material bodies. The subject of this paper is the use of graph-theoretical methods to represent multibody system topologies and to formulate the desired set of motion equations; a discussion of the methods available for solving these differential-algebraic equations is beyond the scope of this work. After a brief introduction to the topic, a review of linear graphs and their associated topological arrays is presented, followed in turn by the use of these matrices in generating various graph-theoretic equations. The appearance of linear graph theory in a number of existing multibody formulations is then discussed, distinguishing between approaches that use absolute (Cartesian) coordinates and those that employ relative (joint) coordinates. These formulations are then contrasted with formal graph-theoretic approaches, in which both the kinematic and dynamic equations are automatically generated from a single linear graph representation of the system. The paper concludes with a summary of results and suggestions for further research on the graph-theoretical modelling of mechanical systems. 相似文献
70.
Spectral radial basis functions for full sphere computations 总被引:1,自引:1,他引:0
Philip W. Livermore Chris A. Jones Steven J. Worland 《Journal of computational physics》2007,227(2):1209-1224
The singularity of cylindrical or spherical coordinate systems at the origin imposes certain regularity conditions on the spectral expansion of any infinitely differentiable function. There are two efficient choices of a set of radial basis functions suitable for discretising the solution of a partial differential equation posed in either such geometry. One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed. The second is the so-called one-sided Jacobi polynomials that explicitly satisfy the required behavioural conditions. In this paper, we compare these two approaches in their accuracy, differentiability and computational speed. We find that the most accurate and concise representation is in terms of one-sided Jacobi polynomials. However, due to the lack of a competitive fast transform, Chebyshev methods may be a better choice for some computationally intensive timestepping problems and indeed will yield sufficiently (although not infinitely) differentiable solutions provided they are adequately converged. 相似文献