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61.
Given a precompact subset of a type Banach space , where , we prove that for every and all
holds, where is the absolutely convex hull of and denotes the dyadic entropy number. With this inequality we show in particular that for given and with for all the inequality holds true for all . We also prove that this estimate is asymptotically optimal whenever has no better type than . For this answers a question raised by Carl, Kyrezi, and Pajor which has been solved up to now only for the Hilbert space case by F. Gao.
holds, where is the absolutely convex hull of and denotes the dyadic entropy number. With this inequality we show in particular that for given and with for all the inequality holds true for all . We also prove that this estimate is asymptotically optimal whenever has no better type than . For this answers a question raised by Carl, Kyrezi, and Pajor which has been solved up to now only for the Hilbert space case by F. Gao.
62.
Johan Samuelsson Mats Jonsson Tore Brinck Mats Johansson 《Journal of polymer science. Part A, Polymer chemistry》2004,42(24):6346-6352
The reactivities and reaction rates of the thiol–ene coupling reaction of 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto acetate and 2‐ethyl‐(hydroxymethyl)‐1,3‐propanediol trimercapto propionate with two common unsaturated fatty acid methyl esters (methyl oleate and methyl linoleate) were evaluated. The reactions were monitored with real‐time IR and 1H NMR, which both showed that the mercapto acetate was more reactive than the mercapto propionate. Both thiols were more prone to add to the monounsaturated methyl oleate than to methyl linoleate, which contained two unconjugated double bonds. According to bond energy calculations, the thiol hydrogen of mercapto acetate was somewhat more difficult to abstract than the hydrogen of mercapto propionate. Consequently, the formed S? C bond in the acetate case was stronger than in the propionate case, and so the equilibrium was more shifted toward the addition products. The real‐time IR measurements also showed that the cis unsaturation in methyl oleate isomerized much more quickly than that in methyl linoleate, and this also had an impact on the overall addition rate of the thiols because a trans unsaturation was more reactive than a cis unsaturation. The higher isomerization rates in the oleate systems, compared with those of the linoleate systems, was suggested to be due to a more restricted rotation along the C? C bond of the reacted unsaturation in linoleate. This study showed the importance of trans unsaturations in obtaining reasonable reaction rates in thiol–ene reactions with fatty acid derivatives. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 6346–6352, 2004 相似文献
63.
Jakob J. Keller 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1996,47(6):821-836
Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method. 相似文献
64.
Thordur Jonsson 《Communications in Mathematical Physics》1983,90(2):175-186
We study a continuum version of a classical anisotropic spin model in three dimensions with three component spins. We prove the existence of topological defects, called hedgehogs, which are analogous to the vortices in the two-dimensionalxy-model and have a logarithmically divergent action. Bounds for the interaction energy of a hedgehog and an antihedgehog are derived. 相似文献
65.
The yields and isomeric yield ratios in the photoproduction of44Sc from 45Sc, 55Mn, Fe, 59Co and 75As have been measured by activation methods in the energy region 100–800 MeV. Mean cross sections and isomeric cross-section ratios in the energy region 250–800 MeV have been deduced and the number of valence neutrons available for the (γ, n) reaction estimated. The experimental cross sections are compared both to cascade-evaporation calculations based upon the free-nucleon photopion cross sections and to cross sections calculated with a semi-empirical formula. The isomeric cross-section ratios are compared to calculations based on the statistical formalism by Huizenga and Vandenbosch together with cascade-evaporation theory. 相似文献
66.
We derive constraints on the asymptotic behaviour of total cross sections which follow from dispersion relations and measured real parts of the forward scattering amplitudes. For πN and pp scattering, these constraints are calculated using recent results from FNAL and Serpukhov. The relation to other methods is discussed. 相似文献
67.
Jakob Yngvason 《Communications in Mathematical Physics》1973,34(4):315-333
It is shown that every continuous linear functional on the field algebra can be defined by a vector in the Hilbert space of some representation of the algebra. The functionals which can be written as a difference of positive ones are characterized. By an example it is shown that a positive functional on a subalgebra does not always have an extension to a positive functional on the whole algebra. 相似文献
68.
A. Bäcklin N.G. Jonsson R. Julin J. Kantele M. Luontama A. Passoja T. Poikolainen 《Nuclear Physics A》1981,351(3):490-508
0+ states and their depopulating E0 and E2 transitions have been studied in 112–124Sn. Several methods of γ-ray and electron spectrometry have been employed, including special coincidence techniques for lifetime, conversion electron and double Coulomb excitation measurements. For 114–118Sn the E2 transition probabilities from the first excited 0+states (02+) are about 20 W.u., which is compatible with a vibrational two-phonon character. Also the E0 transition probabilities from these states are within a factor of two from the vibrational values. For the second excited 0+ states (03+) the corresponding E2 and E0 transition probabilities are considerably smaller. A total of 12 E0 transitions have been observed. The 03+ → 02+ transition is observed in 114–120Sn and has in 116Sn a reduced transition probability 1–2 orders of magnitude larger than those of the groundstate E0 transitions, which indicates that the 03+ and 02+ states are strong mixtures of components with different 〈r2〉. The 0+ states in 116Sn are discussed as possible rotational band heads associated with a deformation β2 ≈ 0.2. The Coulomb excitation cross section of the 02+ state is found to be sensitive to an interference term including matrix elements with the 22+ state. The relative sign of this term has been determined. 相似文献
69.
70.