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21.
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Oscillations of first-order neutral delay differential equations 总被引:1,自引:0,他引:1
M. K. Grammatikopoulos E. A. Grove G. Ladas 《Journal of Mathematical Analysis and Applications》1986,120(2)
Consider the neutral delay differential equation (*) (d/dt)[y(t) + py(t − τ)] + qy(t − σ) = 0, t t0, where τ, q, and σ are positive constants, while p ε (−∞, −1) (0, + ∞). (For the case p ε [−1, 0] see Ladas and Sficas, Oscillations of neutral delay differential equations (to appear)). The following results are then proved. Theorem 1. Assume p < − 1. Then every nonoscillatory solution y(t) of Eq. (*) tends to ± ∞ as t → ∞. Theorem 2. Assume p < − 1, τ > σ, and q(σ − τ)/(1 + p) > (1/e). Then every solution of Eq. (*) oscillates. Theorems 3. Assume p > 0. Then every nonoscillatory solution y(t) of Eq. (*) tends to zero as t → ∞. Theorem 4. Assume p > 0. Then a necessary condition for all solutions of Eq. (*) to oscillate is that σ > τ. Theorem 5. Assume p > 0, σ > τ, andq(σ − τ)/(1 + p) > (1/e). Then every solution of Eq. (*) oscillates. Extensions of these results to equations with variable coefficients are also obtained. 相似文献
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We obtain an algebraic rate of convergence for monotone and consistent finite difference approximations to Lipschitz‐continuous viscosity solutions of uniformly elliptic partial differential equations. © 2007 Wiley Periodicals, Inc. 相似文献
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Panagiotis D. Vellis John A. Mikroyannidis Chih‐Nan Lo Chain‐Shu Hsu 《Journal of polymer science. Part A, Polymer chemistry》2008,46(23):7702-7712
A series of soluble conjugated ligands TT , FT , PT , and NT that contained terpyridyl terminal units were synthesized by Heck coupling. These ligands absorbed at 341–434 nm and emitted blue–green light, with maximum at 440–522 nm and photoluminescence quantum yields of 0.15–0.71 in solution. The double‐layer electroluminescent devices with the configuration of ITO/PEDOT/ligand FT , PT , or NT /Ca/Al exhibited a brightness of 43–63 cd/m2. These ligands were further reacted with zinc(II) and ruthenium(II) ions and subsequent anion exchange to afford linear and supramolecular complexes. The photophysics of these complexes were investigated. A significant redshift of the emission maximum of the Zn complexes relative to the corresponding ligands was observed. The Ru complexes were used to fabricate photovoltaic devices with the structure ITO/PEDOT/Ru complex/P3HT:PCBM (1:1 wt/wt)/Ca/Al. The power conversion efficiency of these polymer–fullerene bulk heterojunction photovoltaic devices was up to 0.71%. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 7702–7712, 2008 相似文献
25.
Panagiotis Misaelides David Fellhauer Xavier Gaona Marcus Altmaier Horst Geckeis 《Journal of Radioanalytical and Nuclear Chemistry》2017,311(3):1665-1671
The 232Th-uptake ([Th(IV)]° = 9.7 × 10?5 M) from carbonate solutions ([CO 3 2 ]tot = 0.25 M, 9.0 < pHc < 10.8) by raw and HDTMA-modified HEU-type zeolitic-, chabazitic- and phillipsitic-tuffs was investigated. The strong uptake by the HDTMA-tuffs at pHc≈9 was assigned to the Th(CO3) 5 6? and ThOH(CO3) 4 5? predominance. The sorption coefficients (R d) decreased with increasing pHc indicating carbonate competition. Enhanced R d values for pHc > 10.5 are likely due to ThO2(am)-precipitation. The 237Np-uptake ([Np(V)]° = 2.6 × 10?5 M) from carbonate solutions ([CO 3 2 ]tot = 0.25 and 3.0 × 10?4 M) by raw and HDTMA-modified HEU-type zeolitic tuff and pulverized pure heulandite crystals was studied under Ar-atmosphere at 6 < pHc < 11. The R d values for both elements indicated the modified tuffs potential to remove tetravalent- and pentavalent actinides from environmental matrices. 相似文献
26.
Eric S. Simon Panagiotis G. Papoulias Philip C. Andrews 《Journal of the American Society for Mass Spectrometry》2010,21(9):1624-1632
The fragmentation characteristics of peptides derivatized at the side-chain ε-amino group of lysyl residues via reductive
amination with benzaldehyde have been examined using collision-induced dissociation (CID) tandem mass spectrometry. The resulting
MS/MS spectra exhibit peaks representing product ions formed from two independent fragmentation pathways. One pathway results
in backbone fragmentation and commonly observed sequence ion peaks. The other pathway corresponds to the unsymmetrical, heterolytic
cleavage of the Cζ-Nε bond that links the benzyl derivative to the side-chain lysyl residue. This results in the elimination of the derivative
as a benzylic or tropylium carbocation and a (n − l)+-charged peptide product (where n is the precursor ion charge state). The frequency of occurrence of the elimination pathway
increases with increasing charge of the precursor ion. For the benzylmodified tryptic peptides analyzed in this study, peaks
representing products from both of these pathways are observed in the MS/MS spectra of doubly-charged precursor ions, but
the carbocation elimination pathway occurs almost exclusively for triply-charged precursor ions. The experimental evidence
presented herein, combined with molecular orbital calculations, suggests that the elimination pathway is a charge-directed
reaction contingent upon protonation of the secondary ε-amino group of the benzyl-derivatized lysyl side chain. If the secondary
ε-amine is protonated, the elimination of the carbocation is observed. If the precursor is not protonated at the secondary
ε-amine, backbone fragmentation persists. The application of appropriately substituted benzyl analogs may allow for selective
control over the relative abundance of product ions generated from the two pathways. 相似文献
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A straightforward size exclusion chromatography (SEC) method was developed and validated for the determination of total polivinylpyrrolidone (PVP) in ophthalmic solutions using the unusual combination of size exclusion chromatography (SEC), ultraviolet-visible detection and quantitation of an analyte peak that elutes in the total exclusion volume of the column. Samples of opthalmic solutions are diluted with water and injected onto a TSKgel G1000PW, 7.5 mm i.d. × 30 cm, 12 μm column at 50°C, with 80:20 0.1M sodium acetate-methanol mobile phase and UV detection at 220 nm. Validation was successful for a stability indicating pharmaceutical method, with parameters including specificity, accuracy, linearity, and precision within typical pharmaceutical acceptance criteria. A stress study with acid, base, peroxide, heat, and light indicates that there is no interference from drug, product, or excipients. 相似文献