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41.
We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function with . More precisely, for any we construct -bi-Sobolev maps with identity boundary conditions; for , we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide. 相似文献
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《Journal of Polymer Science.Polymer Physics》2018,56(4):297-307
The elasticity of polypeptide chains is usually characterized by the worm‐like chain model that was proposed first to describe the elasticity of double‐stranded DNA. However, the molecular dynamics simulation data on the elasticity of the polypeptide chains are deviated significantly away from the theoretical data obtained based on the worm‐like chain model. Here, we provide a revised worm‐like chain model by considering entropic, enthalpic, and hydrophobic effects and the effect of the compressing force applied to the polypeptide chains. The theoretical data obtained based on the revised model are in good agreement with the molecular dynamics simulation data. Additionally, we reveal that, besides the positive‐force regime in the elasticity of polypeptide chains, the negative‐force regime also plays important roles in the biological functions of proteins. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 297–307 相似文献
45.
Nanoparticles are increasingly being used for treatment and diagnostic purposes, but their effects on cells is not fully understood. Here, the interaction of fluorescent up-conversion nanoparticles (UpC-NPs) with neutrophils was investigated by imaging and measurement of membrane-cytosceletal elasticity by atomic force microscopy. It was found that UpC-NPs induce the death of neutrophils mainly by necrosis, and to a smaller extent by a novel process called ‘mummification'. Necrosis occurs by gradual loss of intracellular contents and nuclei, 45–110 min after exposure to UpC-NPs. Mummification is apparent as an increase in the rigidity of the neutrophils' membrane and acquisition of a characteristic bumpy shape with numerous protrusions; this structure does not change during atomic force microscopy scanning. Coating UpC-NPs with protein by incubation with serum leads to (1) formation of nanoparticle aggregates in the nm and μm size range, (2) a reduction in toxicity, (3) reduced mummification of neutrophils, and (4) no significant reduction of the elasticity of the membrane-cytoskeletal complex of neutrophils 30 min after exposure to coated UpC-NPs. The study shows that serum proteins greatly curb the toxicity of nanoparticles and reveals mummification as a novel mechanism of UpC-NP-induced cell death. 相似文献
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Andrea Giuntoli Nicola Calonaci Sebastiano Bernini Dino Leporini 《Journal of Polymer Science.Polymer Physics》2017,55(23):1760-1769
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τY/G between the shear yield strength τY and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τY/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769 相似文献
47.
V. V. Tereshatov 《Journal of Macromolecular Science: Physics》2015,54(4):365-380
The stress–strain dependences of segmented elastomers based on polyetherurethanes, polyesterurethane ureas, and polybutadieneurethane ureas were investigated. These dependences were adequately described using the generalized approach proposed earlier by the authors for amorphous elastomers. The experimental data obtained for four series of samples with chemical cross-linking confirmed an applicability of this approach for segmented elastomers. Unlike amorphous elastomers, the effective network density value was affected not only by the density of the chemical network, but the contribution of the network formed by the hard domains also needs be taken into account. 相似文献
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Brent D. Viers 《高分子科学杂志,A辑:纯化学与应用化学》2013,50(2):131-138
End‐linking poly(dimethylsiloxane) was used to prepare bimodal elastomers networks so as to have inhomogeneous nanostructures, and also to prepare others having very broadly multimodal chain‐length distributions. Macroscopic phase separation, probably high crosslink density clusters, was observed to occur in some of the bimodal networks. The mechanical properties in simple extension and in equilibrium swelling were measured. The bimodal elastomers that were not obviously inhomogeneous showed very good mechanical properties, but the macroscopically phase‐separated networks, and the broadly multimodal network were weak. Analysis of the Mooney‐Rivlin profiles suggests that the reinforcing mechanism could have a structural component in addition to that from the limited extensibilities of the short chains. The mechanical properties and the extents of swelling support the cluster conjecture, in accord with previous morphological studies on spatially‐inhomogeneous polysiloxane elastomers. 相似文献
50.
The dynamic surface elasticity of the solution of carboxymethylchitosan (CMCH) and cetyltrimethylammonium bromide (C16TAB) was measured as a function of the surfactant concentration and the surface age by the oscillating drop method. The results showed that the surface layer of the CMCH/C16TAB solution transformed from loose to structured with the increase in the surfactant concentration. The surface elasticity versus the surface pressure curve during the adsorption showed different features at different surfactant concentration ranges, which was connected with the structural transformation of the surface layer. Our results show that the measurement of dynamic surface dilational properties is a powerful tool for studying the surface kinetics, which is helpful for dealing non-equilibrium systems in industry. 相似文献