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961.
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:
is considered, where Θ is a bounded domain in R
n
(n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem
has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if
.
Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation
(011606). 相似文献
962.
A daunting challenge in the area of computational biology has been to develop a method to theoretically predict the correct three-dimensional structure of a protein given its linear amino acid sequence. The ability to surmount this challenge, which is known as the protein folding problem, has tremendous implications. We introduce a novel ab initio approach for the protein folding problem. The accurate prediction of the three-dimensional structure of a protein relies on both the mathematical model used to mimic the protein system and the technique used to identify the correct structure. The models employed are based solely on first principles, as opposed to the myriad of techniques relying on information from statistical databases. The framework integrates our recently proposed methods for the prediction of secondary structural features including helices and strands, as well as -sheet and disulfide bridge formation. The final stage of the approach, which culminates in the tertiary structure prediction of a protein, utilizes search techniques grounded on the foundations of deterministic global optimization, powerful methods which can potentially guarantee the correct identification of a protein's structure. The performance of the approach is illustrated with bovine pancreatic trypsin inhibitor protein and the immunoglobulin binding domain of protein G. 相似文献
963.
We determine the Lie superalgebras that are graded by the
root system B(m,n) of the
orthosymplectic Lie superalgebra osp(2m +
1,2n).
Mathematics Subject Classification (2000) Primary 17B70, Secondary 17A70 相似文献
964.
Existence of solution for semilinear problem with the Laplace-Beltrami operator on non-compact Riemannian manifolds with rich
symmetries is proved by concentration compactness based on actions of the manifold's isometry group. 相似文献
965.
We compare and contrast various length vs Laplace spectra of compact flat Riemannian manifolds. As a major consequence we
produce the first examples of pairs of closed manifolds that are isospectral on p-forms for some p ≠ 0, but have different
weak length spectrum. For instance, we give a pair of 4-dimensional manifolds that are isospectral on p-forms for p = 1, 3and we exhibit a length of a closed geodesic that occurs in one manifold but cannot occur in the other. We also exhibit examples
of this kind having different injectivity radius and different first eigenvalue of the Laplace spectrum on functions. These
results follow from a method that uses integral roots of the Krawtchouk polynomials.
We prove a Poisson summation formula relating the p-eigenvalue spectrum with the lengths of closed geodesics. As a consequence
we show that the Laplace spectrum on functions determines the lengths of closed geodesics and, by an example, that it does
not determine the complex lengths. Furthermore we show that orientability is an audible property for closed flat manifolds.
We give a variety of examples, for instance, a pair of manifolds isospectral on functions (resp. Sunada isospectral) with
different multiplicities of length of closed geodesies and a pair with the same multiplicities of complex lengths of closed
geodesies and not isospectral on p-forms for any p, or else isospectral on p-forms for only one value of p ≠ 0. 相似文献
966.
John?J.?BenedettoEmail author Wojciech?Czaja Przemystaw?Gadziński Alexander?M.?Powell 《Journal of Geometric Analysis》2003,13(2):239-254
For any positive real numbers A, B, and d satisfying the conditions
, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|
A
)/log
d
(2+|x|)dx < ∞ and
. 相似文献
967.
Nous ramenons l'existence d'estimations optimales pour la métrique de Kobayashi dans les domaines pseudoconvexes de type fini
deC
2 à un principe de Bloch asymptotique. Nous établissons ce principe en combinant la méthode de renormalisation utilisée par
Gromov dans le contexte des applications harmoniques aux techniques de dilatation des coordonnées. Cecifournit une preuve
totalement élémentaire d'un résultat de Catlin particulièrement utile dans l'étude des questions de prolongement et de rigidité
d'applications holomorphes.
相似文献
968.
Moxun Tang 《Journal of Differential Equations》2003,189(1):148-160
We prove uniqueness of positive radial solutions to the semilinear elliptic equation , subject to the Dirichlet boundary condition on an annulus in . As a by-product, our argument also provides a much simpler, if not the simplest, new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space . 相似文献
969.
Tai-Peng Tsai 《Journal of Differential Equations》2003,192(1):225-282
We consider a nonlinear Schrödinger equation with a bounded localized potential in . The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H1, and that its ground state component is larger than n3−ε with ε>0 small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity. 相似文献
970.
Michael Winkler 《Journal of Differential Equations》2003,192(2):445-474
We study nonglobal positive solutions to the Dirichlet problem for ut=up(Δu+u) in bounded domains, where 0<p<2. It is proved that the set of points at which u blows up has positive measure and the blow-up rate is exactly . If either the space dimension is one or p<1, the ω-limit set of consists of continuous functions solving . In one space dimension it is shown that actually as t→T, where w coincides with an element of a one-parameter family of functions inside each component of its positivity set; furthermore, we study the size of the components of {w>0} with the result that this size is uniquely determined by Ω in the case p<1, while for p>1, the positivity set can have the maximum possible size for certain initial data, but it may also be arbitrarily close to the minimal length π. 相似文献