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11.
12.
D. Beigie 《Journal of Nonlinear Science》1995,5(1):57-103
Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem. 相似文献
13.
Akihito Sakakibara Maki Itoh Itaru Mita 《Journal of polymer science. Part A, Polymer chemistry》1995,33(8):1293-1303
Aromatic polybenzobisoxazoles, having polydimethylsiloxane side chains (SCPBOs), were prepared using terephthaloyl chloride-terminated polydimethylsiloxane macromonomers and 3,3′-bis(trimethylsiloxy)-4,4′-bis(trimethylsilylamino)biphenyl for the purpose of dispersing rigid-rod molecules in silicone matrices for molecular reinforcement. The degree of polymerization of the side chain was varied from 7.8 to 45.4, and a small amount of (3-butenyloxy)terephthaloyl chloride was copolymerized to give the polymers a functionality that can be linked to the matrices. For all the SCPBOs, the WAXD pattern showed only diffuse reflections, suggesting limited structural regularity, although the polymers were optically anisotropic. No melting transition was observed below the side chain decomposition temperature, 350°C. A polydimethylsiloxane/polybenzobisoxazole composite elastomer was obtained first curing the polysiloxane matrix containing the prepolymer of the SCPBO, followed by in situ thermal ring closure of the prepolymer. Some reinforcement was observed, but the presence of plasticizing effect by the unbound SCPBO was suggested at the same time. © 1995 John Wiley & Sons, Inc. 相似文献
14.
Exact rotamer optimization for protein design 总被引:1,自引:0,他引:1
Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features. 相似文献
15.
16.
Rigid-rod aromatic polyimdies having polydimethylsiloxane side chains were prepared for the purpose of dispersing rigid-rod molecules in silicone matrices for molecular reinforcement. The polyimides were obtained by imidizing the polyamide-acids bearing the side chains either thermally or chemically, which were synthesized by reacting 4,4′-diaminobiphenyl-terminated polysiloxane macromonomers with pyromellitic dianhydride in THF. The polyamide-acid films obtained by removing the solvent were soluble in THF, but the polyimides were insoluble in any common solvent. The polyimides showed no melting transition below 350°C on DSC analysis, at which temperature the side chain started decomposing. Although all the polyimides were anisotropic as observed by a polarizing microscope, x-ray diffraction analysis suggested the presence of only limited chain organization. Blends with linear polydimethylsiloxanes were prepared by casting the THF solution containing the polyamide-acid and the polydimethylsiloxane, followed by solvent evaporation and thermal imidization. With relatively longer side chains, the polyimides were proved to be compatibilized with polydimethylsiloxanes. © 1994 John Wiley & Sons, Inc. 相似文献
17.
The partial molar isentropic pressure coefficients at infinite dilution, K
S,2
o
, have been determined for a number of dipeptides in aqueous solution at 25°C. For a series of dipeptides of sequence gly-X, where X is an amino acid with a neutral side chain, the K
S,2
o
values are all more negative than that for diglycine. The results are discussed in terms of the hydration of the side chains. There are significant differences in the K
S,2
o
values for sequence isomeric dipeptides. These differences can be rationalized in terms of the mutual interactions between the side chain and the ionic end groups in the dipeptides. Possible relationships between K
S,2
o
and V
2
o
, the partial molar volume at infinite dilution, were investigated. For the dipeptides of sequence gly-X there is an interesting linear relationship between K
S,2
o
/V
2
o
and V
2
o
. 相似文献
18.
Designing proteins with novel protein/protein binding properties can be achieved by combining the tools that have been developed independently for protein docking and protein design. We describe here the sequence-independent generation of protein dimer orientations by protein docking for use as scaffolds in protein sequence design algorithms. To dock monomers into sequence-independent dimer conformations, we use a reduced representation in which the side chains are approximated by spheres with atomic radii derived from known C2 symmetry-related homodimers. The interfaces of C2-related homodimers are usually more hydrophobic and protein core-like than the interfaces of heterodimers; we parameterize the radii for docking against this feature to capture and recreate the spatial characteristics of a hydrophobic interface. A fast Fourier transform-based geometric recognition algorithm is used for docking the reduced representation protein models. The resulting docking algorithm successfully predicted the wild-type homodimer orientations in 65 out of 121 dimer test cases. The success rate increases to approximately 70% for the subset of molecules with large surface area burial in the interface relative to their chain length. Forty-five of the predictions exhibited less than 1 A C(alpha) RMSD compared to the native X-ray structures. The reduced protein representation therefore appears to be a reasonable approximation and can be used to position protein backbones in plausible orientations for homodimer design. 相似文献
19.
20.
Ana Serbanovic Manuel Nunes da Ponte Carlos A.M. Afonso 《Journal of organometallic chemistry》2005,690(15):3600-3608
In this work, osmium-catalyzed asymmetric dihydroxylation (AD) of methyl trans-cinnamate was studied. Osmium and chiral ligand catalysts were immobilized in ionic liquid only, without any other reaction solvents, while the recovery of the product was performed by extraction with supercritical CO2, and compared with results obtained by extractions with organic solvents such as hexane and diethyl ether. In supercritical CO2 extraction experiments, optimal extraction pressure was found and ionic liquid chosen, so that the highest reaction yields coupled with lowest osmium content in the crude product can be achieved. Finally, recycle experiments of the same (ionic liquid + catalytic system) mixture were successfully conducted. Application of ionic liquids and supercritical CO2 in osmium catalyzed AD allows for the isolation of the diol basically without contamination with osmium, in high yield and enantiomeric excess, and it makes possible the efficient reuse of ionic liquid solvent and the catalytic system. 相似文献