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1.
Goryunov proved that the space of local invariants of Vassiliev type for generic maps from surfaces to three-space is three-dimensional.
The basic invariants were the number of pinch points, the number of triple points and one linked to a Rokhlin type invariant.
In this paper we show that, by colouring the complement of the image of the map with a chess board pattern, we can produce
a six-dimensional space of local invariants. These are essentially black and white versions of the above. Simple examples
show how these are more effective.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
Kevin Houston 《Inventiones Mathematicae》2002,147(3):471-485
The disentanglement of certain augmentations is shown to be the topological join of a disentanglement and a Milnor fibre.
The kth disentanglement of a finite map is defined and for corank 1 maps from ℂ
n
to ℂ
n
+1 it is shown that they are homotopically equivalent to a wedge of spheres. Applications to the Mond conjecture are given.
Oblatum 24-VII-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
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The photodissociation of O(2) in the region from 120-133 nm has been investigated using product imaging. The spectrum in this region is dominated by transitions from the ground state to the first three vibrational levels of the E (3)Sigma(u) (-) state. The O((1)D)+O((3)P) channel is the only product channel observed by product imaging for dissociation at either 124.4 nm or 120.4 nm. The O((1)D(2)) product is aligned in the molecular frame in such a way that its J vector is perpendicular to the relative velocity vector between the O((1)D) and the O((3)P). The variation in the anisotropy of dissociation is approximately predicted by considering transitions on individual lines and then taking into account the coherent excitation of overlapping resonances. At 132.7 nm, both the O((1)D)+O((3)P) and the O((3)P)+O((3)P) channels are observed with branching ratios of 0.40+/-0.08 and 0.60+/-0.09, respectively. At 130.2 nm, the quantum yield for production of O((1)D) is 0.76+/-0.28. 相似文献
6.
The efficiency of13C isotope separation by multiphoton dissociation using a CO2 laser has been shown to increase by ∼33% upon addition of small amounts of HI to the starting mixture. The reason for this
increase is that the CF3 radicals are scavenged by HI more rapidly than they recombine with free iodine atoms to reform the starting material. For
Torr and for 0.5J/cm2 roughly 65% of the CF3 and I radicals reform the starting material in the absence of HI. The results of this study indicate that at −80°C the rate
constants for CF3+CF3→C2F6 and CF3+I→CF3I are about equal and are roughly 8 times higher than that for CF3+HI→CF3H+I. 相似文献
7.
Toluene diluted in argon subjected to continuous argon discharge radiation during condensation at 21 K revealed absorptions at 310.5 and 449.6 nm due to benzyl radical, and 317 nm due to a C77H9 radical. A photosensitive 430 nm band, in agreement with photodissociation spectra of the toluene parent cation, is assigned to this species. 相似文献
8.
Barron JA Glazier S Bernhard S Takada K Houston PL Abruña HD 《Inorganic chemistry》2003,42(5):1448-1455
The absorption and emission spectra, excited-state lifetimes, quantum yields, and electrochemical measurements have been obtained for a new series of chiral complexes based on three different chiral 2,2':6',2' '-terpyridine ligands, (-)-ctpy, (-)-[ctpy-x-ctpy], and (-)-[ctpy-b-ctpy], with one, two, or multiple Ru metal centers. The room-temperature absorption and emission maxima of [[((-)-ctpy)Ru]-(-)-[ctpy-b-ctpy]-[Ru((-)-ctpy)]](PF(6))(4) and ((-)-[ctpy-b-ctpy])-[[Ru((-)-[ctpy-b-ctpy])](PF(6))(2)](n) were shifted to lower energies and also exhibited significantly longer luminescence lifetimes when compared to [Ru((-)-ctpy)(2)](PF(6))(2), [[((-)-ctpy)Ru]-(-)-[ctpy-x-ctpy]-[Ru((-)-ctpy)]](PF(6))(4), and ((-)-[ctpy-x-ctpy])-[[Ru((-)-[ctpy-x-ctpy])](PF(6))(2)](n). In terms of their electrochemical behavior, all of the complexes studied exhibited one Ru-centered and two ligand-centered redox waves and the [[((-)-ctpy)Ru]-(-)-[ctpy-x-ctpy]-[Ru((-)-ctpy)]](PF(6))(4), ((-)-[ctpy-x-ctpy])-[[Ru((-)-[ctpy-x-ctpy])](PF(6))(2)](n), and ((-)-[ctpy-b-ctpy])-[[Ru((-)-[ctpy-b-ctpy])](PF(6))(2)](n)() complexes were found to electrodeposit upon ligand-based reduction. The difference between the formal potentials of the Ru-centered and the first ligand-centered (least negative) waves corresponded linearly with the changes in the observed emission energies. The shifts in energy are discussed using a particle-in-a-box model, and the luminescence lifetimes are discussed in terms of the structure of the excited-state manifold. 相似文献
9.
Water exchange from the oxo-centered rhodium(III) trimer, [Rh3(mu3-O)(mu-O2CCH3)6(OH2)3]+, was investigated using variable-temperature (272.8-281.6 K) and variable-pressure (0.1-200 MPa) 17O NMR spectroscopy. The exchange reaction was also monitored at three different acidities (pH = 1.8, 2.9, and 5.7) in which the molecule is in the fully protonated form (pKa = 8.3 (+/-0.2), I = 0.1 M, T = 298 K). The temperature dependence of the pseudo-first-order rate coefficient for water exchange yields the following kinetic parameters: k(ex)298 = 5 x 10(-3) s(-1), deltaH(double dagger) = 99 (+/-3) kJ mol(-1), and deltaS(double dagger) = 43 (+/-10) J K(-1) mol(-1). The enhanced reactivity of the terminal waters, some 6 orders of magnitude faster than water exchange from Rh(H2O)6(3+), is likely due to trans-labilization from the central oxide ion. Also, another contributing factor is the low average charge on the metal ions (+0.33/Rh). Variation of reaction rate with pressure results in a deltaV(double dagger) = +5.3 (+/-0.4) cm3 mol(-1), indicative of an interchange-dissociative (I(d)) pathway. These results are consistent with those published by Sasaki et al. who proposed that water substitution from rhodium(III) and ruthenium(III) oxo-centered trimers follows a dissociative mechanism based on highly positive activation parameters (Sasaki, Y.; Nagasawa, A.; Tokiwa-Yamanoto, A.; Ito, T. Inorg. Chim. Acta 1993, 212, 175-182). 相似文献
10.