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61.
62.
63.
Nonlinear Galerkin methods and mixed finite elements:
two-grid algorithms for the Navier-Stokes equations 总被引:14,自引:0,他引:14
Summary.
A nonlinear Galerkin method using mixed finite
elements is presented for the two-dimensional
incompressible Navier-Stokes equations. The
scheme is based on two finite element spaces
and for the approximation of the velocity,
defined respectively on one coarse grid with grid
size and one fine grid with grid size and
one finite element space for the approximation
of the pressure. Nonlinearity and time
dependence are both treated on the coarse space.
We prove that the difference between the new
nonlinear Galerkin method and the standard
Galerkin solution is of the order of $H^2$, both in
velocity ( and pressure norm).
We also discuss a penalized version of our algorithm
which enjoys similar properties.
Received October 5, 1993 / Revised version received November
29, 1993 相似文献
64.
65.
Approximate inertial manifolds for reaction-diffusion equations in high space dimension 总被引:4,自引:0,他引:4
Martine Marion 《Journal of Dynamics and Differential Equations》1989,1(3):245-267
The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4. 相似文献
66.
Katrin?ThümmlerEmail author Steffen?Fischer Alexander?Feldner Viktoria?Weber Marion?Ettenauer Fritz?Loth Dieter?Falkenhagen 《Cellulose (London, England)》2011,18(1):135-142
The aim of this work was to synthesize and characterize cellulose microspheres with a particle size below 5 μm and narrow
size distribution. After activation and functionalization with antibodies, these particles shall be applied as adsorbents
in suspension-based extracorporeal blood purification systems, such as the Microspheres-Based Detoxification System. In the
frame of this work such microspheres were developed and synthesized with reproducible properties. Besides using well-established
methods for characterization of this kind of bead cellulose, additional procedures for the examination of its properties were
developed and applied. 相似文献
67.
Schebb NH Huby M Morisseau C Hwang SH Hammock BD 《Analytical and bioanalytical chemistry》2011,400(5):1359-1366
Soluble epoxide hydrolase (sEH) is a promising therapeutic target for the treatment of hypertension, pain, and inflammation-related diseases. In order to enable the development of sEH inhibitors (sEHIs), assays are needed for determination of their potency. Therefore, we developed a new method utilizing an epoxide of arachidonic acid (14(15)-EpETrE) as substrate. Incubation samples were directly injected without purification into an online solid phase extraction (SPE) liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS-MS) setup allowing a total run time of only 108 s for a full gradient separation. Analytes were extracted from the matrix within 30 s by turbulent flow chromatography. Subsequently, a full gradient separation was carried out on a 50X2.1 mm RP-18 column filled with 1.7 μm core-shell particles. The analytes were detected with high sensitivity by ESI-MS-MS in SRM mode. The substrate 14(15)-EpETrE eluted at a stable retention time of 96 ± 1 s and its sEH hydrolysis product 14,15-DiHETrE at 63 ± 1 s with narrow peak width (full width at half maximum height: 1.5 ± 0.1 s). The analytical performance of the method was excellent, with a limit of detection of 2 fmol on column, a linear range of over three orders of magnitude, and a negligible carry-over of 0.1% for 14,15-DiHETrE. The enzyme assay was carried out in a 96-well plate format, and near perfect sigmoidal dose-response curves were obtained for 12 concentrations of each inhibitor in only 22 min, enabling precise determination of IC(50) values. In contrast with other approaches, this method enables quantitative evaluation of potent sEHIs with picomolar potencies because only 33 pmol L(-1) sEH were used in the reaction vessel. This was demonstrated by ranking ten compounds by their activity; in the fluorescence method all yielded IC(50) ≤ 1 nmol L(-1). Comparison of 13 inhibitors with IC(50) values >1 nmol L(-1) showed a good correlation with the fluorescence method (linear correlation coefficient 0.9, slope 0.95, Spearman's rho 0.9). For individual compounds, however, up to eightfold differences in potencies between this and the fluorescence method were obtained. Therefore, enzyme assays using natural substrate, as described here, are indispensable for reliable determination of structure-activity relationships for sEH inhibition. 相似文献
68.
Hedberg C Dekker FJ Rusch M Renner S Wetzel S Vartak N Gerding-Reimers C Bon RS Bastiaens PI Waldmann H 《Angewandte Chemie (International ed. in English)》2011,50(42):9832-9837
A matter of common sense: A common recognition motif consisting of a negatively charged group five to six bonds away (red) from the (thio)ester functionality (green) and a positively charged tail group ten to twelve bonds away (blue) was identified in two native acyl protein thioesterase?1 (APT1) substrates. This similarity led to the design of potent inhibitors of the Ras-depalmitoylating enzyme APT1. 相似文献
69.
70.
Bauer M Többens DM Mayer E Loerting T 《Physical chemistry chemical physics : PCCP》2011,13(6):2167-2171
A range of techniques has so far been employed for producing amorphous aqueous solutions. In case of aqueous tetrahydrofuran (THF) this comprises hyperquenching of liquid droplets, vapour co-deposition and pressure-induced amorphization of the crystalline cubic structure II clathrate. All of these samples are thermally labile and crystallize at temperatures above 110 K. We here outline a variant of the pressure-amorphization protocol developed by Suzuki [Phys. Rev. B, 2004, 70, 172108], which results in a highly crystallization resistant amorphous THF hydrate. The hydrate produced according to our protocol (annealing to 180 K at 1.8 GPa rather than to 150 K at 1.5 GPa) does not transform to the cubic structure II THF clathrate even at 150 K. We track the reason for this higher stability to the presence of crystalline remnants when following the Suzuki protocol, which are removed when using our protocol involving higher pressures and an annealing step. These crystalline remnants later serve as crystallization seeds lowering the thermal stability of the amorphous sample. Our protocol thus makes a purely amorphous THF hydrate available to the research community. We use powder X-ray diffraction to study the process of nucleation and slow crystal growth in the temperature range 160-200 K and find that the local cage structure and periodicity of the fully crystalline hydrate develops even at the earliest stages of crystallization, when the "clathrate crystal" has a size of about two unit cells. 相似文献