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971.
We first give an example of a rigid structure of computable dimension 2 such that the unique isomorphism between two non-computably isomorphic computable copies has Turing degree strictly below , and not above . This gives a first example of a computable structure with a degree of categoricity that does not belong to an interval of the form for any computable ordinal α. We then extend the technique to produce a rigid structure of computable dimension 3 such that if , , and are the degrees of isomorphisms between distinct representatives of the three computable equivalence classes, then each . The resulting structure is an example of a structure that has a degree of categoricity, but not strongly. 相似文献
972.
Matthias Ruf 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(4):887-937
We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a non-convex potential. In this setting the geometry of the lattice strongly influences the anisotropy of the limit functional. Thus we can use statistically isotropic lattices and stochastic homogenization techniques to approximate the vectorial Mumford–Shah functional in any dimension. 相似文献
973.
We solve a certain differential equation and system of integral equations. As applications, we characterize holomorphic symbols of commuting Toeplitz operators on the pluriharmonic Bergman space. In addition, pluriharmonic symbols of normal Toeplitz operators are characterized. Also, zero semi-commutators for certain classes of Toeplitz operators are characterized.This research is partially supported by KOSEF(98-0701-03-01-5). 相似文献
974.
Dmitry Roytenberg 《Letters in Mathematical Physics》2007,79(2):143-159
We give a detailed exposition of the Alexandrov–Kontsevich–Schwarz– Zaboronsky superfield formalism using the language of
graded manifolds. As a main illustrating example, to every Courant algebroid structure we associate canonically a three-dimensional
topological sigma-model. Using the AKSZ formalism, we construct the Batalin–Vilkovisky master action for the model.
相似文献
975.
Multi-Scale Gaussian Processes: a Novel Model for Chaotic Time Series Prediction 总被引:1,自引:0,他引:1 下载免费PDF全文
Based on the classical Gaussian process (GP) model, we propose a multi-scale Gaussian process (MGP) model to predict the existence of chaotic time series. The MGP employs a covariance function that is constructed by a scaling function with its different dilations and translations, ensuring that the optimal hyperparameter is easy to determine. Moreover, the scaling function with its different dilations and translations can form a set of complete bases, resulting in the fact that the MGP can acquire better prediction performance than the GP. The experiments can lead to the following conclusions: (i) The MGP gives a relatively better prediction performance in comparison with the classical GP model. (ii) The prediction performance of the MGP is competitive with support vector machine (SVM). They give better performance as compared to the radial basis function networks. 相似文献
976.
We use variational methods to study problems in nonlinear 3-dimensional elasticity where the deformation of the elastic body
is restricted by a rigid obstacle. For an assigned variational problem we first verify the existence of constrained minimizers
whereby we extend previous results. Then we rigorously derive the Euler-Lagrange equation as necessary condition for minimizers,
which was possible before only under strong smoothness assumptions on the solution. The Lagrange multiplier corresponding
to the obstacle constraint provides structural information about the nature of frictionless contact. In the case of contact
with, e.g., a corner of the obstacle, we derive a qualitatively new contact condition taking into account the deformed shape
of the elastic body. By our analysis it is shown here for the first time rigorously that energy minimizers really solve the
mechanical contact problem.
Received: 20 October 2000 / Accepted: 7 June 2001 / Published online: 5 September 2002 相似文献
977.
Floris Takens 《Topology and its Applications》2005,152(3):219-225
The solenoid was first introduced by Vietoris, motivated by questions from algebraic topology. It later appeared in the study of dynamical systems. This paper discusses the history of solenoids and settles an isomorphism problem. 相似文献
978.
979.
980.
A.G. Smirnov 《Advances in Mathematics》2005,196(2):310-345
A new generalized function space in which all Gelfand-Shilov classes (α>1) of analytic functionals are embedded is introduced. This space of ultrafunctionals does not possess a natural nontrivial topology and cannot be obtained via duality from any test function space. A canonical isomorphism between the spaces of hyperfunctions and ultrafunctionals on Rk is constructed that extends the Fourier transformation of Roumieu-type ultradistributions and is naturally interpreted as the Fourier transformation of hyperfunctions. The notion of carrier cone that replaces the notion of support of a generalized function for ultrafunctionals is proposed. A Paley-Wiener-Schwartz-type theorem describing the Laplace transformation of ultrafunctionals carried by proper convex closed cones is obtained and the connection between the Laplace and Fourier transformations is established. 相似文献