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81.
Donald I. Cartwright 《Annali di Matematica Pura ed Applicata》1988,151(1):1-15
Summary We consider the random walk (Xn) associated with a probability p on a free product of discrete groups. Knowledge of the resolvent (or Green's function) of p yields theorems about the asymptotic behaviour of the n-step transition probabilities p*n(x)=P(Xn= x¦ X0=e) as n. Woess [15], Cartwright and Soardi [3] and others have shown that under quite general conditions there is behaviour of the type p*n(x)Cx– n n– 3/2. Here we show on the other hand that if G is a free product of m copies ofZ
r and if (Xn) is the « average » of the classical nearest neighbour random walk on each of the factorsZ
r, then while it satisfies an « n–3/2 — law » for r small relative to m, it switches to an n– r/2 -law for large r. Using the same techniques, we give examples of irreducible probabilities (of infinite support) on the free groupZ
*m which satisfyn
– for
. 相似文献
82.
A well-known relativistic action at a distance interaction of two unequal masses is altered so as to yield purely Newtonian radial forces with fixed particle rest masses in the system center-of-momentum inertial frame. Although particle masses experience no kinematic mass increase in this frame, speeds are naturally restricted to less than the speed of light. We derive a relation between the center-of-momentum frame total Newtonian energy and the composite rest mass. In a new proper time quantum formalism, we obtain an L2(R4 R4, C) Hilbert space by varying individual particle rest masses. We propose the use of density operators, recognizing that the auxiliary proper time parameter is not an observable. The quantum formalism is applied to our altered version of the relativistic harmonic oscillator. Our generalized coherent states yield four-dimensional wave packets which follow the correct classical world lines. Appendices contain reviews of classical Hamiltonian reparametrization (incorporating our notion of manifest covariance), and a comparison of this work with the literature. 相似文献
83.
Donald R. Schreiber James Huebner Seyed Rahmani Frank J. Millero 《Journal of solution chemistry》1993,22(3):201-210
Enthalpies of mixing (m
H) aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting m
H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl2 and CuCl2 were in agreement with earlier isomolal results by other workers. 相似文献
84.
Kerry J. Adams Thomas D. McGrath Georgina M. Rosair Andrew S. Weller Alan J. Welch 《Journal of organometallic chemistry》1998,550(1-2)
Analysis of the structures of 8,8-(PPh3)2-8,7-nido-RhSB9H10 and 9,9-(PPh3)2-9,7,8-nido-RhC2B8H11 by RMS misfit calculations has confirmed that these rhodaheteroboranes possess nido 11-vertex cluster geometries in apparent contravention of Wade's rules. However, examination of the molecular structures of both species shows that the {RhP2} planes are inclined by ca. 66° with respect to the metal-bonded SB3 or CB3 faces, and that two weak ortho-CHRh agostic interactions occupy the vacant co-ordination position thereby created. As a consequence of these agostic bonds the Rh atom, and hence the overall cluster, is provided with an additional electron pair, meaning that their nido structures are now fully consistent with Wade's rules. The chelated diphosphine compound 8,8-(dppe)-8,7-nido-RhSB9H10 is similar to the PPh3 compound in showing the same agostic bonding. Attempts to prepare a bis-P(OMe)3 analogue result in ligand scavenging and the formation of 8,8,8-{P(OMe)3}3-8,7-nido-RhSB9H10. Similarly, reaction between Cs[6-arachno-SB9H12] and RhCl(dmpe)CO does not result in CO loss but in formation of 8,8-(dmpe)-8-(CO)-8,7-nido-RhSB9H10, shown to exist as a mixture of two of three possible rotamers. Deprotonation of 8,8-(PPh3)2-8,7-nido-RhSB9H10 and 8,8-(dppe)-8,7-nido-RhSB9H10 with MeLi yields the anions [1,1-(PPh3)2-1,2-closo-RhSB9H9]− and [1,1-dppe-1,2-closo-RhSB9H9]−, respectively, with octadecahedral cage structures. It is argued that anion formation causes the agostic bonding to be `switched-off' and results in the cluster adopting the closo architecture predicted by Wade's rules. This structural change is fully reversible on reprotonation, and if reprotonation of [1,1-(dppe)-1,2-closo-RhSB9H9]− is carried out in MeCN, the product 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB9H10 forms. Interestingly, 8,8-(dppe)-8-(MeCN)-8,7-nido-RhSB9H10 reconverts to 8,8-(dppe)-8,7-nido-RhSB9H10 on standing in CDCl3, suggesting that the agostic bonding is sufficiently strong to displace co-ordinated MeCN. All new compounds are fully characterised by multinuclear NMR spectroscopy and, in many cases, by single crystal X-ray diffraction. 相似文献
85.
Application of stir bar sorptive extraction for wine analysis 总被引:4,自引:0,他引:4
Yoji?Hayasaka Kevin?MacNamara Gayle?A.?Baldock Randell?L.?Taylor Alan?P.?PollnitzEmail author 《Analytical and bioanalytical chemistry》2003,375(7):948-955
Stir bar sorptive extraction (SBSE) coupled with gas chromatography/mass spectrometry (GC/MS) was used to analyse wine samples for three applications: flavour and compositional analysis; 2,4,6-trichloroanisole (TCA), a common off-aroma in wine; and agrochemicals. SBSE was found to be orders of magnitude more sensitive than modern conventional methodology, allowing for lower detection and quantitation levels, and improved confirmation of identity; SBSE often gave better signal to noise in scan mode than other methods in selective ion monitoring (SIM) mode. With the help of their characteristic mass spectra all agrochemicals could be identified unambiguously at concentrations of 10 microg L(-1) in wine and a further 100 constituents were detected in a Cabernet Sauvignon sample. Thus it is now possible to analyse complex samples such as wine by scan mode, with better confirmation of identity, and without sacrificing sensitivity, where previously SIM methodology had to be used. 相似文献
86.
Kim HJ Kim W Lough AJ Kim BM Chin J 《Journal of the American Chemical Society》2005,127(48):16776-16777
A cobalt(III)-salen complex (3) with an axial substituent on the diamine backbone has been synthesized. Crystal structure reveals that the axial substituent (p-nitrophenyl group) is positioned in close proximity to the metal binding site. The stereoselectivity of the cobalt complex for binding amino alcohols increases with increasing steric bulk of the amino alcohol from alaninol (2.9) to valinol (6.2) and t-leucinol (36.0). 相似文献
87.
One unit of S(IV) (SO2 or SHO3?) is oxidized per 2 units of [NiIII(cyclam)] species to obtain sulfate. Kinetic analyses have been done by varying the acidities (0.013 ? [H+] ? 1.0 M) and halide concentrations (0.000 ? [X?] ? 0.012 M; X=Cl and Br) at constant ionic strength (μ = 1.0 M). The rate law that incorporates the [X?] and [H+] dependence is ?d[NiIII]T/dt=2k[NiIII]T[S(IV)]T where 2k={ka[H+] + kbK + kK′X[H+] [X?] + kK′XK[X?]} {[H+] + K}?1 {1 + K′X[X?]}?1, here ka=87 ± 7 M?1 s?1, kb=(2.5 ± 0.5)×103 M?1 s?1 and pK = 1.8 ± 0.2. Rate constants ka and kb are attributed to the reactions of [NiIII(cyclam) (H2O)2]3+ with SO2 and SHO3?, respectively. Monohalo species apparent equilibrium constants K′Cl=(1600 ± 400) M?1 and K′Br=(190 ± 20) M?1 and rate constants k=80 ± 8 M?1 s?1 and k = 140 ± 15 M?1 s?1 are ascribed to the protonated pathway, involving the [NiIII(cyclam) (H2O)X]2+ and SO2(aq) reaction pairs. The other two rate constants of k=(5 ± 1)×103 M?1 s?1 and k=(3.1 ± 0.5)×104 M?1 s?1, refer to the deprotonated pathway and are assigned to the [NiIII(cyclam) (H2O)X]2+ /SHO3? redox couple. A deuterium H2O / D2O isotope effect of 2.1–2.8 can be attributed partially to an equilibrium isotope effect at low acidity though a small kinetic isotope (2.5 ± 0.5) effect is evident for the dihydrogen sulfito pathway, ka. The kinetic isotope effect and the absence of sulfite radical scavenging effects are explained by a mechanism entailing migration of a hydride from sulfur to the NiIII center to produce a NiIII—H species, which rapidly comproportionates, and S(VI). © 1993 John Wiley & Sons, Inc. 相似文献
88.
Laurence E. Strong Christopher L. Brummel Robert Ryther John R. Radford Alan D. Pethybridge 《Journal of solution chemistry》1988,17(12):1145-1167
Precision molar conductances of benzoic, o-toluic, 2,6-dimethylbenzoic, 2,3,6-trimethylbenzoic, and, o-fluorobenzoic acids have been determined in aqueous solution as a function of temperature and of concentration up to near saturation (<0.035 M). At the higher concentrations molar conductances are found to be less than anticipated for the simple dissociation of a 1-1 electrolyte. Although the deviations are only 1% or less they have been interpreted to show that these acids are dimerized in solution. The interpretation includes an assumption that the dimer ionizes to produce a triple ion. Increasing numbers of methyl groups lead to increasing dimerization. For those acids with two ortho groups the dimerization increases with increasing temperature while the other three show decreasing dimerization with increasing temperature. Temperature functions have been determined for the dimerization constants and from these functions standard changes in enthalpy, entropy, and heat capacity have been determined. Comparisons are made with dimerization studies in non-aqueous solvents. From these as well as the behavior of benzene in water it is concluded that a major factor driving the dimerization is hydrophobic interaction. To provide a limiting conductance of the triple ion needed in the dimerization calculations a conductance study was also made for o-Phenylbenzoic acid on the assumption that its anion provides an approximate model of the triple ion. 相似文献
89.
Katritzky AR Nair SK Khokhlova T Akhmedov NG 《The Journal of organic chemistry》2003,68(14):5724-5727
Enynes 5a-g were prepared in moderate to good yields from 1-(triphenylphosphoranylideneaminoalkyl)benzotriazoles. Ring-closing metathesis of 5a-f afforded functionalized dienes 6a-f, respectively, which were used in a Diels-Alder cycloaddition reaction in the synthesis of the corresponding hexahydroisoquinoline derivatives 7a-f. 相似文献
90.
James J. Li R. Alan Chrusciel Monica B. Norton David B. Reitz Timothy J. Hagen Sofya Tsymbalov E. Ann Hallinan 《Journal of heterocyclic chemistry》1994,31(6):1689-1696
Lithiation of 8-chlorodibenz[b,f][1,4]oxazepine-10-tert-butylcarbamate ( 1 ) is described. Electrophilic substitution of the resulting N-Boc dibenzoxazepine α- lithioamine 2 with ketones, aldehydes, nitriles, iso-cyanates and imines, followed by an in-situ cyclization, gave fused carbamates 5–26 , fused 2H-imidazol-2-ones 27–29 , fused hydantoins 30–32 , and fused ureas 33–35 , respectively, in 11–66% yield. 相似文献