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71.
72.
In this paper, theoretical results are described on the maximum norm stability and accuracy of finite difference discretizations of parabolic equations on overset nonmatching space-time grids. We consider parabolic equations containing a linear reaction term on a space-time domain which is decomposed into an overlapping collection of cylindrical subregions of the form , for . Each of the space-time domains are assumed to be independently grided (in parallel) according to the local geometry and space-time regularity of the solution, yielding space-time grids with mesh parameters and . In particular, the different space-time grids need not match on the regions of overlap, and the time steps can differ from one grid to the next. We discretize the parabolic equation on each local grid by employing an explicit or implicit -scheme in time and a finite difference scheme in space satisfying a discrete maximum principle. The local discretizations are coupled together, without the use of Lagrange multipliers, by requiring the boundary values on each space-time grid to match a suitable interpolation of the solution on adjacent grids. The resulting global discretization yields a large system of coupled equations which can be solved by a parallel Schwarz iterative procedure requiring some communication between adjacent subregions. Our analysis employs a contraction mapping argument.
Applications of the results are briefly indicated for reaction-diffusion equations with contractive terms and heterogeneous hyperbolic-parabolic approximations of parabolic equations.
73.
G.K. Surya Prakash Juan C. Colmenares Patrice T. Batamack Thomas Mathew George A. Olah 《Journal of molecular catalysis. A, Chemical》2009,310(1-2):180-183
The hydrolysis of methyl bromide with neutral water is performed in the presence and absence of various amines in a batch reactor at different temperatures (50–125 °C). Screening of poly(4-vinylpyridine) as a potential reusable solid amine catalyst showed maximum efficiency. This significant enhancement in efficiency is due to the capture of HBr by solid PVP and remains phase-separated driving the reaction forward. The major advantage of this process is that the polymer can be easily regenerated and reused without loss of activity making it a very effective catalyst for the conversion of methyl halides to methanol and dimethyl ether. 相似文献
74.
G A Olah T Mathew E R Marinez P M Esteves M Etzkorn G Rasul G K Prakash 《Journal of the American Chemical Society》2001,123(47):11556-11561
Quantitative rearrangement of pivalaldehyde to methyl isopropyl ketone is observed in acids such as trifluoromethanesulfonic acid, anhydrous HF, and trifluoroethyl alcohol-BF3 but not in trifluoroacetic acid. Studies in a mixture of trifluoroacetic acid and trifluoromethanesulfonic acid show that acids with H(o) < or = -11 are able to carry out complete isomerization. These results and density functional theory calculations at the B3LYP/6-31G level suggest that protonated pivalaldehyde undergoes further protosolvation at higher acidities to a reactive superelectrophilic species resulting in rearrangement. A mechanism for the pivalaldehyde rearrangement to methyl isopropyl ketone in strong protic acids involving a reactive protosolvated superelectrophilic intermediate is suggested. Aspects of the related mechanism of the reaction with isobutane with CO in HF/BF3 medium leading to methyl isopropyl ketone are also discussed. 相似文献
75.
Shozo Kawamura Makoto Suzuki Hossain MD. Zahid Hirofumi Minamoto 《Applied Acoustics》2009,70(11-12):1393-1399
Machine condition monitoring and fault diagnosis of rotating machinery are very important because of the wide use of rotating machinery in industry. Couplings and gears are used in many mechanical systems to connect elements and transmit power. The system is usually modeled as a single-degree-of-freedom system with a piecewise linear spring property, where the mass of main machine is only considered. In the present study, the dynamic behavior of a system with an unsymmetrical nonlinearity and a significant mass of the connecting part was investigated both experimentally and by numerical simulation. In the experiment, a 1/3 sub-harmonic oscillation was observed, but this oscillation was not found in the simulation using a single-degree-of-freedom system, in which the mass of the connecting part was ignored. However, when a two-degrees-of-freedom system was used that considered both the mass of the connecting part and the impact property, the 1/3 sub-harmonic oscillation was observed. Thus it is recognized that an adequate mathematical model for diagnosis in the early stage of abnormality must be selected on the basis of the mass ratio between the connecting part and the main body. 相似文献
76.
William R Cullen Mathew Dodd Basil U Nwata Deborah A Reimer Kenneth J Reimer 《应用有机金属化学》1989,3(4):351-353
Inorganic arsenic(III) and arsenic(V), methyl-arsenicals, antimony(III), and antimony(V), and butyltin derivatives are present in the shells of molluscs found in the coastal waters of British Columbia. 相似文献
77.
I.M. KrishnakumarBeena Mathew 《European Polymer Journal》2002,38(9):1745-1752
To correlate the coupling difficulty and nature of the support in solid-phase peptide synthesis, a set of difficult peptides were built under identical conditions on rigid and hydrophobic divinyl benzene-crosslinked polystyrene (DVB-PS) and flexible and polar 1,4-butanediol dimethacrylate-crosslinked polystyrene (BDDMA-PS) resins of same functional capacity (∼2 mmol/g). The difficult coupling stages observed on each support were identified by monitoring the acylation time, coupling yield and deprotection efficiency. The yield and purity of the peptides prepared on BDDMA-PS were higher than when DVB-PS support was used. 相似文献
78.
79.
Mathew D. Penrose 《Communications in Mathematical Physics》2001,218(1):153-176
Identical cars are dropped sequentially from above into a large parking lot. Each car is positioned uniformly at random,
subject to non-overlap with its predecessors, until jamming occurs. There have been many studies of the limiting mean coverage
as the parking lot becomes large, but no complete proof that such a limit exists, until now.
We prove spatial laws of large numbers demonstrating that for various multidimensional random and cooperative sequential adsorption
schemes such as the one above, the jamming limit coverage is well-defined.
Received: 18 August 2000 / Accepted: 13 November 2000 相似文献
80.
Mathew D. Halls Julia Velkovski H. Bernhard Schlegel 《Theoretical chemistry accounts》2001,105(6):413-421
Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most
commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ)
Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were
derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies.
Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional
with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew
and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis
set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the
Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr
fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)),
respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement
between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm−1 and above 1800 cm−1 are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for
Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis
set provides reliable theoretical vibrational spectra in a cost-effective manner.
Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001 相似文献