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101.
Bernard Bialecki 《Numerical Algorithms》1994,8(2):167-184
Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N
2log2
N) andO(N
2log2log2
N) arithmetic operations, respectively. 相似文献
102.
The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl2 is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl. 相似文献
103.
104.
Boris Andreianov Franck Boyer Florence Hubert 《Numerical Methods for Partial Differential Equations》2007,23(1):145-195
Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W?1,p′(Ω) source term and W1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
105.
106.
运用多种密度泛函理论 (DFT)和从头算 (abinitio)方法研究了草酰胺顺、反异构体的分子几何构型 ,结果表明Beck88交换函数与LYP非局域相关函数形成杂化的DFT方法B3LYP与MP2方法计算结果比较吻合。在此基础上选择B3LYP方法对草酰胺分子电子结构、红外光谱和前线分子轨道组成进行了系统研究 ;与实验事实对比分析了气态草酰胺分子中配位原子的反应活性 相似文献
107.
In a previous paper we gave a new formulation and derived the Euler equations and other necessary conditions to solve strong, pathwise, stochastic variational problems with trajectories driven by Brownian motion. Thus, unlike current methods which minimize the control over deterministic functionals (the expected value), we find the control which gives the critical point solution of random functionals of a Brownian path and then, if we choose, find the expected value.This increase in information is balanced by the fact that our methods are anticipative while current methods are not. However, our methods are more directly connected to the theory and meaningful examples of deterministic variational theory and provide better means of solution for free and constrained problems. In addition, examples indicate that there are methods to obtain nonanticipative solutions from our equations although the anticipative optimal cost function has smaller expected value.In this paper we give new, efficient numerical methods to find the solution of these problems in the quadratic case. Of interest is that our numerical solution has a maximal, a priori, pointwise error of O(h3/2) where h is the node size. We believe our results are unique for any theory of stochastic control and that our methods of proof involve new and sophisticated ideas for strong solutions which extend previous deterministic results by the first author where the error was O(h2).We note that, although our solutions are given in terms of stochastic differential equations, we are not using the now standard numerical methods for stochastic differential equations. Instead we find an approximation to the critical point solution of the variational problem using relations derived from setting to zero the directional derivative of the cost functional in the direction of simple test functions.Our results are even more significant than they first appear because we can reformulate stochastic control problems or constrained calculus of variations problems in the unconstrained, stochastic calculus of variations formulation of this paper. This will allow us to find efficient and accurate numerical solutions for general constrained, stochastic optimization problems. This is not yet being done, even in the deterministic case, except by the first author. 相似文献
108.
G. N. Merrill 《Journal of Physical Organic Chemistry》2007,20(1):19-29
Ab initio molecular orbital calculations were carried out on epibromohydrin (EBH) and epichlorohydrin (ECH) in an attempt to elucidate their reactivity with respect to a hard nucleophile, hydroxide. These systems were modeled in both the gas phase and a polar solvent under basic conditions. In the gas phase, it was determined that a direct displacement mechanism (nucleophilic attack at the C1 position) was operative for EBH, while an indirect pathway (nucleophilic attack at the C3 position and subsequent intramolecular displacement) was followed for ECH. In an acetone solution, only the indirect displacement mechanism was found to occur. An electrostatic argument is advanced to account for this behavior in polar solution. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
109.
D. Boilley A. Marchix B. Jurado K. -H. Schmidt 《The European Physical Journal A - Hadrons and Nuclei》2007,33(1):47-52
We propose a new formula for the saddle-to-scission time that is more general that the one based on Kramers' approach. Its
validity and applicability is then studied in detail. Such a formula is useful for the evaluation of the fission time of very
heavy nuclei. 相似文献
110.
Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme. 相似文献