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281.
This paper considers constrained and unconstrained parametric global optimization problems in a real Hilbert space. We assume that the gradient of the cost functional is Lipschitz continuous but not smooth. A suitable choice of parameters implies the linear or superlinear (supergeometric) convergence of the iterative method. From the numerical experiments, we conclude that our algorithm is faster than other existing algorithms for continuous but nonsmooth problems, when applied to unconstrained global optimization problems. However, because we solve 2n + 1 subproblems for a large number n of independent variables, our algorithm is somewhat slower than other algorithms, when applied to constrained global optimization.This work was partially supported by the NATO Outreach Fellowship - Mathematics 219.33.We thank Professor Hans D. Mittelmann, Arizona State University, for cooperation and support. 相似文献
282.
283.
Gaussian distributions on infinite-dimensional p-adic spaces are introduced and the corresponding L2-spaces of p-adic-valued square integrable functions are constructed. Representations of the infinite-dimensional Weyl group are realized in p-adic L2-spaces. There is a formal analogy with the usual Segal representation. But there is also a large topological difference: parameters of the p-adic infinite-dimensional Weyl group are defined only on some balls (these balls are additive subgroups). p-adic Hilbert space representations of quantum Hamiltonians for systems with an infinite number of degrees of freedom are constructed. Many Hamiltonians with potentials which are too singular to exist as functions over reals are realized as bounded symmetric operators in L2-spaces with respect to a p-adic Gaussian distribution. 相似文献
284.
Elena Soverchia 《Journal of Number Theory》2002,97(2):199-203
Let K be a number field, H its Hilbert class field and L a Galois extension of K containing H. In this paper, we prove that L|H has a relative integral basis (RIB) if the order of G=Gal(L|H) is odd or if the 2-Sylow subgroups of G are not cyclic. If the order of G is even and the 2-Sylow subgroups are cyclic we reduce the problem of the existence of a RIB to a quadratic extension of H. 相似文献
285.
V. M. Manuilov 《Mathematical Notes》1997,62(6):726-730
The classical Hilbert-Schmidt theorem can be extended to compact operators on HilbertA-modules overW
*-algebras of finite type; i.e., with minor restrictions, compact operators onH*
A
can be diagonalized overA. We show that ifB is a weakly denseC
*-subalgebra ofA with real rank zero and if some additional condition holds, then the natural extension fromH
B
toH*
A
⊃H
B
of a compact operator can be diagonalized so that the diagonal elements belong to the originalC
*-algebraB.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 865–870, December, 1997.
Translated by O. V. Sipacheva 相似文献
286.
In this paper, the numerical treatment of magnetic loss of NiZn, MnZn, Ni2Y, and NiZnCu ferrite and their composites, by using Krameres-Kronig relations, is investigated. The complex magnetic permeability spectra for ferromagnetic materials have been studied. Due to the principle of causality and time independence in the relation between magnetic induction B and magnetic field H, the real and the imaginary part of the complex magnetic permeability are mutually dependent, and the correlation is given by the Krameres-Kronig equations. Through them, it is possible to measure the real component of the complex magnetic permeability, assuming the real component is given, and by the Hilbert transform, the imaginary part of the magnetic permeability can be calculated. Magnetic circuit model has been studied theoretically, focusing on the model's poles in the complex plane to verify the principle of causality and the temporary independence. 相似文献
287.
Ziv Ran 《Geometric And Functional Analysis》2008,18(1):184-221
A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first
algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry,
for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms,
focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology,
which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by
certain Kodaira–Spencer data.
Received: May 2006 Revision: January 2007 Accepted: March 2007 相似文献
288.
289.
A common problem in multivariate analysis is that of minimising or maximising a function f of a positive semidefinite matrix A subject possibly to AX = 0. Typically A is a variance-covariance matrix. Using the theory of nearest point projections in Hilbert spaces, it is shown that the solution satisfies the equation f′(A) + M ? A = 0, where A = P0(M) and P0 is a certain projection operator. 相似文献
290.
Resampling a coverage pattern 总被引:1,自引:0,他引:1
Peter Hall 《Stochastic Processes and their Applications》1985,20(2):231-246
The possibility of resampling (bootstrapping) a spatial pattern is investigated. It is suggested that resampling provides a unified approach to consistemt inference in a wide range of coverage problems. Nevertheless, resampling distorts some of the interactions in the problem, and so introduces biases. The sizes of bias and standard deviation are investigated in the case of estimating sampling variance via resampling. 相似文献