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61.
We prove that the-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that the-subgradient mapping is Lipschitz continuous.Research supported in part by the National Science Foundation and the Air Force Office of Scientific Research. 相似文献
62.
Fabio E. Penotti 《International journal of quantum chemistry》2006,106(5):1153-1159
Nonorthogonal single‐configuration and multiconfiguration ab initio calculations are carried out on the BeH2 molecule in its equilibrium (D∞h) geometry, using a highly optimized even‐tempered Slater‐type orbital (STO) basis set. The results are used as a basis for a discussion of the electronic structure of the molecule in modern‐VB terms. A value of Re = 1.329 Å is obtained. Values are also obtained for the symmetric‐stretch harmonic frequency (2053 cm?1), electric quadrupole moment (?5.60 Buckingham), and nuclear quadrupole coupling constants (?3.59 MHz for 9Be and 0.0915 MHz for 2H). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 相似文献
63.
Angelika Baranowska Magdalena Siedlecka Andrzej J. Sadlej 《Theoretical chemistry accounts》2007,118(5-6):959-972
Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size
of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting
(ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method
of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis
sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance
of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2,
and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl4 confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic
calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html. 相似文献
64.
Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L
2-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent. 相似文献
65.
Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the2
P states of Li and Na, and the3
P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size. 相似文献
66.
Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH3 (–0.499 a.u.), PoH2 (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system. 相似文献
67.
J. B. Lasserre 《Journal of Optimization Theory and Applications》1991,70(3):583-595
We consider two-dimensional discrete-time linear systems with constrained controls. We propose a simple polynomial time procedure to give an exact external representation of theN-step reachable set and controllable set. The bounding hyperplanes are explicitly derived in terms of the data of the problem. By using a result in computational geometry, all the calculations are made in polynomial time in contrast to classical methods. The limit case asN is also investigated. 相似文献
68.
Bistatic scattering by arbitrarily shaped objects with rough surface at optical and infrared frequencies 总被引:2,自引:0,他引:2
The scattering cross sections for arbitrarily shaped dielectric objects with rough surface are determined for optical and infrared frequencies using the Kirchhoff approximation. The formula of the coherent scattering cross section is derived, and numerical method of incoherent scattering cross section is given. As a specific example, the infrared laser scattering cross sections of rough spheres are calculated at 1.06 m. 相似文献
69.
70.