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41.
C. Bogani M. G. Gasparo A. Papini 《Journal of Optimization Theory and Applications》2007,134(1):47-59
We propose a pattern search method to solve a classical nonsmooth optimization problem. In a deep analogy with pattern search
methods for linear constrained optimization, the set of search directions at each iteration is defined in such a way that
it conforms to the local geometry of the set of points of nondifferentiability near the current iterate. This is crucial to
ensure convergence. The approach presented here can be extended to wider classes of nonsmooth optimization problems. Numerical
experiments seem to be encouraging.
This work was supported by M.U.R.S.T., Rome, Italy. 相似文献
42.
Gerhard Starke 《Numerische Mathematik》1997,78(1):103-117
Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES
or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of
values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from
the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular,
the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations
of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners
which constitute popular preconditioning strategies for such problems.
Received May 3, 1996 相似文献
43.
44.
45.
P. C. Chen 《中国化学会会志》1995,42(5):755-760
Three ab initio calculations (HF/6-3IG, HF/6-3IG*, and HF/6-3IG**) on 2,4,6-trinitrotoluene were made, The results compare well with xray data, except dihedral angles of NO2 relative to the plane of the benzene ring. The deviations are attributed to packing forces and steric effects in the crystal. The most stable structure was a torsional angle 10° of the methyl top with the benzene ring, unlike toluene. The rotational barriers of the methyl top and the 4-nitro group are small. Hydrogen bonding, dipole moments and total atomic charges arc calculated. 相似文献
46.
The many facets of linear programming 总被引:1,自引:0,他引:1
Michael J. Todd 《Mathematical Programming》2002,91(3):417-436
We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex,
ellipsoid, interior-point, and other methods.
Received: June 22, 2000 / Accepted: April 4, 2001?Published online October 2, 2001 相似文献
47.
Gisella Facchinetti 《Fuzzy Optimization and Decision Making》2002,1(3):313-327
In this paper we present two definitions of possibilistic weighted average of fuzzy numbers, and by them we introduce two different rankings on the set of real fuzzy numbers. The two methods are dependent on several parameters. In the first case, the parameter is constant and the results generalize what Carlsson and Fuller have obtained in (2001). In the second case, the parameter is a function, not fixed a priori by the decision maker, but it depends on the position of the interval on the real axe. In all the two cases we call the parameter degree of risk, which takes into account of a risk-tendency or aversion of the decision maker. 相似文献
48.
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
49.
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
50.
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