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Roberto Feola Filippo Giuliani Stefano Pasquali 《Journal of Differential Equations》2019,266(6):3390-3437
We consider the dispersive Degasperis–Procesi equation with . In [15] the authors proved that this equation possesses infinitely many conserved quantities. We prove that there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of the Sobolev space with , both on and . By the analysis of these conserved quantities we deduce a result of global well-posedness for solutions with small initial data and we show that, on the circle, the formal Birkhoff normal form of the Degasperis–Procesi at any order is action-preserving. 相似文献
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Dr. María Jose Capitán Dr. Jesús Álvarez Dr. Yang Wang Dr. Roberto Otero Dr. Manuel Alcamí Prof. Fernando Martín Prof. Rodolfo Miranda 《Chemphyschem》2013,14(14):3294-3302
The structure and stability of adenine crystals and thin layers has been studied by using scanning tunneling microscopy, X‐ray diffraction, and density functional theory calculations. We have found that adenine crystals can be grown in two phases that are energetically quasi‐degenerate, the structure of which can be described as a pile‐up of 2D adenine planes. In each plane, the structure can be described as an aggregation of adenine dimers. Under certain conditions, kinetic effects can favor the growth of the less stable phase. These results have been used to understand the growth of adenine thin films on gold under ultra‐high vacuum conditions. We have found that the grown phase corresponds to the α‐phase, which is composed of stacked prochiral planes. In this way, the adenine nanocrystals exhibit a surface that is enantiopure. These results could open new insight into the applications of adenine in biological, medical, and enantioselective or pharmaceutical fields. 相似文献
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Roberto Centore 《Liquid crystals》2013,40(3):239-245
Four liquid crystalline carbonate dimers DCn containing the dimethylbenzalazine mesogen, bis(oxycarbonyloxy)alkane flexible spacers with three to six methylene units and acetate terminal groups were synthesised and their mesogenic behaviour investigated. As compared with the corresponding ester dimers a strong reduction of odd–even fluctuations of nematic–isotropic (N–I) transition entropy is observed. A theoretical analysis of the dimers within the rotational isomeric states (RIS) mean-field approach is also reported. A satisfying agreement between calculated and observed thermodynamic properties is obtained. In fact, the theoretical analysis correctly predicts a significant reduction of the odd–even fluctuations for the core order parameter S as well as for the nematic to isotropic transition entropy △SNI . The calculated distributions of conformers also show reduced differences between even and odd members. In particular, for even dimers the calculated fraction of linear extended conformers in the nematic phase at the N–I transition is around 27%, which is far below that of the corresponding ester dimers (46%). 相似文献
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The liquid–liquid equilibrium data at 25 °C of the system water–1-pentanol–1-propanol, that present a I type solubility gap, have been used to calculate the spinodal curve of this system through the use of the Wheeler–Widom model. As in the case of the water–chloroform–acetic acid system, analyzed with the same model in the past, a local fitting method has been necessary. A procedure based on the experimental position of the plait point was used to obtain the single spinodal points. The relative positions of binodal and spinodal curves indicate the presence of a large metastable area in the alcoholic-rich region. 相似文献
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Gabriele Oliva Roberto Setola Stefano Panzieri 《The European physical journal. Special topics》2016,225(10):1929-1944
In this paper we develop a data-driven hierarchical clustering methodology to group the economic sectors of a country in order to highlight strongly coupled groups that are weakly coupled with other groups. Specifically, we consider an input-output representation of the coupling among the sectors and we interpret the relation among sectors as a directed graph; then we recursively apply the spectral clustering methodology over the graph, without a priori information on the number of groups that have to be obtained. In order to do this, we resort to the eigengap criterion, where a suitable number of groups is selected automatically based on the intensity and structure of the coupling among the sectors. We validate the proposed methodology considering a case study for Italy, inspecting how the coupling among clusters and sectors changes from the year 1995 to 2011, showing that in the years the Italian structure underwent deep changes, becoming more and more interdependent, i.e., a large part of the economy has become tightly coupled. 相似文献
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Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity. 相似文献
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