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991.
We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the Euclidean
algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this allows us to interpret their Bezoutian
as the Christoffel- Darboux kernel for a finite family of orthogonal polynomials, arising from the Euclidean algorithm. We
give orthogonality properties of remainders, and reproducing properties of Bezoutians.
Received December 13, 2004 相似文献
992.
The phenomenon of anharmonicity has been proved to be an effect of coupling between the change of nuclear positions in molecular vibrations ( Q ) and the electronic degrees of freedom as represented by the chemical potential (μ) at constant number of electrons (N). The coupling parameters have well‐founded meaning in the conceptual density functional theory (DFT), first approximations to their numerical values have recently become available. The effect of coupling between normal vibrational modes also appears to be the direct consequence of the electron‐nuclear coupling. To show the pure anharmonic effect, calculations for a collection of diatomic molecules have been presented. The anharmonicity, described in the present work as d3E/d Q 3 ≠ 0, has been proved to be the intrinsic property of every oscillating molecular system. A small anharmonic contribution exists even for the “strong harmonic” oscillator, when for the force constant k both a = (?k/? Q )N = 0 and λ = (?k/?N) Q = 0. The latter derivative of the force constant appears to be primary factor determining the anharmonic property of a molecule. An estimate of its values has been provided from the experimental data on the anharmonicity of diatomic molecules. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 相似文献
993.
Piotr Tekely Pascal Palmas Pierre Mutzenhardt 《Journal of magnetic resonance (San Diego, Calif. : 1997)》1997,127(2):238-240
It is shown that the proton chemical-shift anisotropy of hydrate crystals affect dipolar powder pattern at 7.0 T. This may be clearly observed via an asymmetric envelope of dipolar spinning sidebands in magic-angle spinning proton spectra. 相似文献
994.
Piotr Garbaczewski 《Annals of Physics》1983,150(1):22-47
We present a unification of different and independently investigated aspects of the chiral invariant Gross-Neveu model. Special emphasis is placed on the relevance of classical (c-number, non Grassmann) spinor solutions of the G-N field equations for the construction, and thus understanding of the respective quantized Fermi model. To get an insight into the “quantum meaning of classical field theory” if specialized to the G-N case, we perform the path integral quantization procedure which first leads to the Fermi oscillator problem, and then, after appropriate generalizations, to the quantum Fermi G-N model. Path integrals are carried out with respect to c-number spinor paths only, and in fact no reference is necessary to the Grassmann algebra methods, which are conventionally used to integrate out fermions. 相似文献
995.
The N2 reduction reaction in the system (η-C5H5)2TiCl2-Mg in tetrahydrofuran was examined. The 13C and 1H NMR results as well as the chemical properties of the products formed revealed that the reaction yielded a mixture of compounds in which the titanium atom was bonded both to the μ-(η5: η5-fulvalene) ligand and to the cyclopentadienyl ligands. In this system dinitrogen undergoes reduction to N3?, which then forms M3N bridges (M = Ti, Mg). The nitride nitrogen may readily be oxidized to imide nitride N?1, which may react further, e.g. with carbon monoxide to produce isocyanates, or, with excess oxidizing agent N2. THF in this system undergoes polymerisation. In addition, a ?OC4H9 alkoxy group is formed which makes the substitution of the cyclopentadienyl group bonded to the titanium atoms possible. 相似文献
996.
Piotr Przybylski Rados?aw Pankiewicz Franz Bartl 《Journal of Molecular Structure》2003,658(3):193-205
A Schiff base of gossypol with n-butylamine [GSBN] was shown to be capable of complexation of 2H+, Li+, Ca2+ and Ba2+ cations. This process of complex formation was studied by ESI mass spectrometry, 1H and 13C NMR and FT-IR spectroscopy as well as by PM5 semiempirical method. It was found that gossypol Schiff base can form a 1:2 complex with H+ and 1:1 complexes with Li+, Ca2+ and Ba2+ cations. In all complexes the Schiff base of gossypol with metal cations exists in enamine-enamine tautomer, whereas in the 1:2 complex with H+ the imine-imine tautomer was found. The metal cations are coordinated through oxygen atoms of the O1H(O1,H) hydroxyl groups and a lone pair of an N-atom. The structures of these complexes were calculated by PM5 semiempirical method and discussed. 相似文献
997.
998.
Piotr Mikrut 《Proceedings of the American Mathematical Society》2002,130(2):599-607
We will construct an example of a strongly symplectically fillable contact structure on a torus bundle over the circle with parabolic monodromy.
999.
1000.