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81.
Ian H. Sloan 《BIT Numerical Mathematics》1978,18(1):91-102
Product-integration rules of the form
–1
1
k(x)f(x)dx
i
=1n
w
ni
f(x
ni
) are studied, with the points {w
ni
} chosen to be the zeros of certain orthogonal polynomials, and the weights {w
ni
} chosen to make the rule exact iff is any polynomial of degree less thann. If, in particular, the points are the Chebyshev points, and ifk L
p
[–1, 1] for somep>1, then it is shown that the rule converges to the exact result for all continuous functionsf. With this choice of points, the practical application of the rule is shown to be straightforward in many cases, and to yield satisfactory rates of convergence. The casek(x)=|–x|, >–1, is studied in detail. Results of a similar, but weaker, kind are also obtained for other choices of the points {x
ni
}. 相似文献
82.
83.
Erin J. Peterson Wei Qi Ian N. Stanton Peng Zhang Michael J. Therien 《Chemical science》2020,11(31):8095
High quantum yield NIR fluorophores are rare. Factors that drive low emission quantum yields at long wavelength include the facts that radiative rate constants increase proportional to the cube of the emission energy, while nonradiative rate constants increase in an approximately exponentially with decreasing S0–S1 energy gaps (in accordance with the energy gap law). This work demonstrates how the proquinoidal BTD building blocks can be utilized to minimize the extent of excited-state structural relaxation relative to the ground-state conformation in highly conjugated porphyrin oligomers, and shows that 4-ethynylbenzo[c][1,2,5]thiadiazole (E-BTD) units that terminate meso-to-meso ethyne-bridged (porphinato)zinc (PZnn) arrays, and 4,7-diethynylbenzo[c][1,2,5]thiadiazole (E-BTD-E) spacers that are integrated into the backbone of these compositions, elucidate new classes of impressive NIR fluorophores. We report the syntheses, electronic structural properties, and emissive characteristics of neoteric PZn-(BTD-PZn)n, PZn2-(BTD-PZn2)n, and BTD-PZnn-BTD fluorophores. Absolute fluorescence quantum yield (ϕf) measurements, acquired using a calibrated integrating-sphere-based measurement system, demonstrate that these supermolecules display extraordinary ϕf values that range from 10–25% in THF solvent, and between 28–36% in toluene solvent over the 700–900 nm window of the NIR. These studies underscore how the regulation of proquinoidal conjugation motifs can be exploited to drive excited-state dynamical properties important for high quantum yield long-wavelength fluorescence emission.Incorporation of proquinoidal BTD building blocks into conjugated porphyrin oligomers minimizes the extent of excited-state structural relaxation relative to the ground-state conformation, elucidating new classes of impressive NIR fluorophores. 相似文献
84.
Fletcher MT Wood BJ Brereton IM Stok JE De Voss JJ Kitching W 《Journal of the American Chemical Society》2002,124(26):7666-7667
The origins of the oxygen atoms in 1,7-dioxaspiro[5.5]undecane (1) and hydroxyspiroacetal (2) from Bactrocera cacuminata, and in 2,8-dimethyl-1,7-dioxaspiro[5.5]undecane (3) and hydroxyspiroacetal (4) from B. cucumis, have been investigated by incorporation studies from both [(18)O(2)]-dioxygen and [(18)O]-water. Combined GC-MS examination and high-field NMR analysis have demonstrated that all oxygen atoms in 1 and 2 from B. cacuminata are dioxygen derived, but in contrast, the spiroacetals 3 and 4 from B. cucumis incorporate one ring oxygen from water and one ring oxygen (and the hydroxyl oxygen in 4) from [(18)O(2)]-dioxygen. These results reveal not only the generality of monoxygenase mediation of spiroacetal formation in Bactrocera sp., but also an unexpected complexity in their biosynthesis. A general paradigm accommodating these and other observations is presented. 相似文献
85.
Mixtures of [Ph(3)PNPPh(3)](+)Cl(-) with CuBr(2) (or CuBr(2)+CuCl(2)) in ethanol/dichloromethane yield crystals containing three-coordinate copper(II) with mixed chloride and bromide ligands, namely [Ph(3)PNPPh(3)](+)[CuCl(0.9)Br(2.1)](-) (1) and [Ph(3)PNPPh(3)](+)[CuCl(2.4)Br(0.6)](-) (2). The trigonal-planar coordination of copper(II) is angularly distorted but unambiguous, as there is no other halide ligand within 6.7 A of the copper atom. Density functional theory (DFT) calculations on planar [CuClBr(2)](-) show that the energy surface for angle bending is very soft. Crystallisation in the presence of CH(3)CN yields [Ph(3)PNPPh(3)](+)[CuCl(0.7)Br(2.3)(NCCH(3))](-) (3), in which there is additional secondary coordination by NCCH(3) (Cu-N 2.44 A). DFT calculations of the potential energy surface for this secondary coordination show that it is remarkably flat (<3 kcal mol(-1) for a variation of Cu-N by 0.8 A). The crystal packing in 1, 2 and 3, which involves multiple phenyl embraces between [Ph(3)PNPPh(3)](+) ions and numerous C-H...Cl and C-H...Br motifs, is associated with intermolecular energies that are larger than the variations in intramolecular energies. For reference, the crystal structures of [Ph(3)PNPPh(3)(+)](2)[Cu(2)Cl(6)](2-) (4) and [Ph(3)PNPPh(3)(+)](2)[Cu(2)Br(6)](2-) (5) are described. We conclude 1) that three-coordinate copper(II) with monatomic halide ligands, although uncommon, can be regarded as normal, 2) that steric control by ligands is not necessary to enforce three-coordination, 3) that a hydrophobic aryl environment stabilises [Cu(Cl/Br)(3)](-), and 4) that the energy change in the transition from three- to four-coordinate copper(II) is very small (ca 5 kcal mol(-1)). 相似文献
86.
A method based on dialysis in the presence of histidine, and subsequent copper adsorption and preconcentration using Chelex-100 resin, has been developed for selective extraction of exchangeable copper from blood plasma. The method was verified by comparative analysis using two different instrumental techniques, ICP–MS and AAS. The results obtained were in excellent agreement. Accurate quantification of the exchangeable copper and the firmly bound copper was achieved. The method was further validated by analysis of a lyophilised human serum certified reference material. 相似文献
87.
Marcia I. Dawson Rebecca L.-S. Chan Ian S. Cloudsdale Wesley R. Harris 《Tetrahedron letters》1981,22(29):2739-2742
Tris(catecholcarboxamide) ligands were covalently linked to poly(vinyl amine—vinyl sulfonate sodium salt), and the iron binding capacity of the resultant polymers was found to exceed that of transferrin. 相似文献
88.
In depth, comparative studies on the catalytic dehydrocoupling of the amine-borane adduct Me(2)NH.BH(3) (to form [Me(2)N-BH(2)](2)) and the phosphine-borane adduct Ph(2)PH.BH(3) (to form Ph(2)PH-BH(2)-PPh(2)-BH(3)) with a variety of Rh (pre)catalysts such as [[Rh(1,5-cod)(micro-Cl)](2)], Rh/Al(2)O(3), Rh(colloid)/[Oct(4)N]Cl, and [Rh(1,5-cod)(2)]OTf have been performed in order to determine whether the dehydrocoupling proceeds by a homogeneous or heterogeneous mechanism. The results obtained suggest that the catalytic dehydrocoupling of Me(2)NH.BH(3) is heterogeneous in nature involving Rh(0) colloids, while that of Ph(2)PH.BH(3) proceeds by a homogeneous mechanism even when starting with Rh(0) precursors such as Rh/Al(2)O(3). The catalytic dehydrocoupling reactions are thought to proceed by different mechanisms due to a combination of factors such as (i) the greater reducing strength of amine-borane adducts, (ii) the increased ease of dissociation of phosphine-borane adducts, and (iii) phosphine ligation and/or poisoning of active catalytic sites on metal colloids. 相似文献
89.
Ewa?Cholewa Ian?Burgess Julia?Kunze Jacek?LipkowskiEmail author 《Journal of Solid State Electrochemistry》2004,8(10):693-705
Electrochemical measurements including cyclic voltammetry, differential capacity, and chronocoulometry have been used to characterize the adsorption behaviors of the zwitterionic surfactant
N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (DDAPS) on the Au(111) electrode surface. The thermodynamics of the ideally polarized electrode have been employed to determine the Gibbs excess and the Gibbs energy of adsorption. The results show that the adsorption of DDAPS has a multistate character. The first two states are observed at potentials close to zero charge. At low bulk DDAPS concentrations, it corresponds to the formation of a film of nearly flat adsorbed molecules. At higher concentrations it is converted into a hemimicellar state. The second state is formed at negative potentials and charge densities close to 0 C cm–2. It corresponds to a film of tilted molecules oriented with the hydrocarbon tail towards the metal and the polar head toward the solution.Dedicated to Professor Zbigniew Galus on the occasion of his 70th birthday and in recognition of his many contributions to electrochemistry. 相似文献
90.
Roca M Martí S Andrés J Moliner V Tuñón I Bertrán J Williams IH 《Journal of the American Chemical Society》2003,125(25):7726-7737
A comparative theoretical study of a bimolecular reaction in aqueous solution and catalyzed by the enzyme catechol O-methyltransferase (COMT) has been carried out by a combination of two hybrid QM/MM techniques: statistical simulation methods and internal energy minimizations. In contrast to previous studies by other workers, we have located and characterized transition structures for the reaction in the enzyme active site, in water and in a vacuum, and our potential of mean force calculations are based upon reaction coordinates obtained from features of the potential energy surfaces in the condensed media, not from the gas phase. The AM1/CHARMM calculated free energy of activation for the reaction of S-adenosyl methionine (SAM) with catecholate catalyzed by COMT is 15 kcal mol(-1) lower the AM1/TIP3P free-energy barrier for the reaction of the trimethylsulfonium cation with the catecholate anion in water at 300 K, in agreement with previous estimates. The thermodynamically preferred form of the reactants in the uncatalyzed model reaction in water is a solvent-separated ion pair (SSIP). Conversion of the SSIP into a contact ion pair, with a structure resembling that of the Michaelis complex (MC) for the reaction in the COMT active site, is unfavorable by 7 kcal mol(-1), largely due to reorganization of the solvent. We have considered alternative ways to estimate the so-called "cratic" free energy for bringing the reactant species together in the correct orientation for reaction but conclude that direct evaluation of the free energy of association by means of molecular dynamics simulation with a simple standard-state correction is probably the best approach. The latter correction allows for the fact that the size of the unit cell employed with the periodic boundary simulations does not correspond to the standard state concentration of 1 M. Consideration of MC-like species allows a helpful decomposition of the catalytic effect into preorganization and reorganization phases. In the preorganization phase, the substrates are brought together into the MC-like species, either in water or in the enzyme active site. In the reorganization phase, the roles of the enzymic and aqueous environments may be compared directly because reorganization of the substrate is about the same in both cases. Analysis of the electric field along the reaction coordinate demonstrates that in water the TS is destabilized with respect to the MC-like species because the polarity of the solute diminishes and consequently the reaction field is also decreased. In the enzyme, the electric field is mainly a permanent field and consequently there is only a small reorganization of the environment. Therefore, destabilization of the TS is lower than in solution, and the activation barrier is smaller. 相似文献