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Twin Paradox and the Logical Foundation of Relativity Theory 总被引:3,自引:0,他引:3
We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. 相似文献
3.
A. Loidl A. Krimmel K. Knorr G. Sparn M. Lang C. Geibel S. Horn A. Grauel F. Steglich B. Welslau N. Grewe H. Nakotte F. R. de Boer A. P. Murani 《Annalen der Physik》1992,504(2):78-91
Elastic and inelastic neutron-scattering studies on the system Ce(Cu1?xNix)2Ge2 are reported. These measurements are complemented by measurements of the magnetic susceptibility, high-field magnetization, heat capacity, thermal expansion, electrical resistivity and thermopower. The results reveal an interesting T-x phase diagram consisting of two different antiferromagnetic phases for x < 0.2 and 0.2 < x < 0.75, respectively, and a heavy-Fermi-liquid regime at higher Ni concentrations. The experimental results are interpreted in terms of an alloying-induced transition from local-moment to itinerant heavy-fermion magnetism. Fingerprints of this latter phase are a strongly reduced ordered moment and a short incommensurate ordering wave vector, in accord with theoretical predictions. A surprisingly good agreement between theory and experiment is found for x > 0.5. Further experimental evidence for different types of antiferromagnetic ordering derives from a line-shape analysis of the quasielastic neutron-scattering intensity, from magnetization and thermopower experiments. 相似文献
4.
Dávid Szegvári Romána Zelkó Péter Horváth András Gergely 《Journal of inclusion phenomena and macrocyclic chemistry》2007,57(1-4):169-172
Enantioselective solubility of rac-norgestrel was found in the presence of γ-cyclodextrin or hydroxypropyl-γ-cyclodextrin.
In both cases the efficacious enantiomer was dissolved in greater extent. Calculating the molar absorptivity and molar ellipticity
spectra of the γ- and hydroxypropyl-γ-cyclodextrin aqueous complexes, a simple and rapid direct circular dichroism (CD) spectrometric
method was obtained for the determination of the enantiomer ratio in aqueous solutions. 相似文献
5.
Gergely Harcos 《Mathematische Annalen》2003,326(2):347-365
We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms
of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively.
As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for
L-functions associated to character twists of these cusp forms.
Received: 2 October 2001 / Revised version: 9 September 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): Primary 11F30, 11F37; Secondary 11M41. 相似文献
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Fadila Balegroune Pierre Braunstein Laurent Douce Yves Dusausoy Daniel Grandjean Michael Knorr Martin Strampfer 《Journal of Cluster Science》1992,3(3):275-296
The reactions of K[Fe{Si(OMe)3}(CO)3(PY)][PY=Ph2PCH2C(O)Ph, Ph2PCH2C(O)[(-C5H4)FeCp] (Cp=5-C5H5), Ph2P(CH2)2CN] with CdCl2·2.5H2O, ZnX
2 (X=Cl, I) or InCl3 afforded Fe-Cd-Fe or Fe-M(-X)2
M-Fe (M=Cd, Zn, In;X=Cl, I) and Fe-InCl2 complexes. Some of them contain an unusual and labile -2-SiO alkoxysilyl bridge which may be associated with a bridging mode for the ketophosphine ligand (first such example structurally established), thus providing original results in bimetallic chemistry on the intramolecular coordination of oxygendonor functions ofchemically different hemilabile ligands firmly attached to a neighboring metal center. The structures of the trinuclear complex (3), of the chlorobenzene solvate of the tetranuclear complex (4a·C6H5Cl) and of [mer-(OC)3{(EtO)3Si} (4e) have been determined by X-ray diffraction. Crystals of 3 are orthorhombic, space groupPbcn, witha=19.010(4),b=11.766(5),c=26.998(7)Å, andZ=4. Crystals of4a·C6H5Cl are monoclinic, space groupC2/c witha=22.455(3),b=17.680(2),c=16.627(4)Å, =90.80(4)°, andZ=4. Crystals of4e are monoclinic, space groupC2/c witha=25.392(5),b=18.554(6),c=16.28(1)Å, =120.73(3)°, andZ=4. The structures were solved using direct methods and Fourier difference techniques and refined by blocked full-matrix least squares toR=0.035 (R
w
=0.049) for 2719 observed reflections, toR=0.042 (R
w
=0.056) for 3082 observed reflections, and toR=0.057 (R
w
=0.075) for 1850 observed reflections for3, 4a·C6H5Cl and4e, respectively. The Fe-Zn complexes (9a), (9b) and (9c) were prepared and characterized by spectroscopic methods.Part 21 in the Series: Complexes with Functional Phosphines. Part 20: P. Braunstein, S. Coco Cea, A. DeCian, and J. Fischer (1992).Inorg. Chem.
31, 4203. 相似文献
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