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101.
A. Burchard 《Geometric And Functional Analysis》1997,7(5):823-860
We study the continuity, smoothing, and convergence properties of Steiner symmetrization in higher space dimensions. Our
main result is that Steiner symmetrization is continuous in W
1,
p
in all dimensions. This implies that spherical symmetrization cannot be approximated in W
1,
p
by sequences of Steiner symmetrizations. We also give a quantitative version of the standard energy inequalities for spherical
symmetrization.
Submitted: September 1996 相似文献
102.
Sugar-lipid hybrids of the type CnCm were prepared by coupling an alkane chain (Cn) with a maltooligosaccharide (Gm) over an amide linkage. Coupling was performed with maltobionolactone (G2) and n-alkylamine chains Cn withn=8,10,12,14,16, i.e. variation of the hydrophobic part of the molecule, and with hexadecylamine (C16) and different maltooligosaccharides (Gm, m=2,3,4,6). The solution properties of the various products were studied by means of static and dynamic light scattering (LS) and by electron-microscopy (EM).The results may be summarized as follows: If the alkane chain is shorter thann=14, small spherical micelles with a radius of about 3 nm are observed. In time these micelles aggregate further to form increasingly larger spherical clusters which eventually precipitate. Long rod-like micelles form whenn 14. Contour length and chain stiffness were determined by applying theories of semiflexible chains. A qualitative confirmation of the light scattering results, i.e., micelle size and shape, was obtained from electron microscopy. 相似文献
103.
A new small-angle light scattering camera has been developed. In contrast to conventional detection the present system is
based on a recently developed two-dimensional charge-coupled-device chip made by Thomson (France). The advantage of this chip
is its excellent linear response and very low dark signal even at room temperature. The best linearity was obtained by leading
each pixel signal through the same amplifying system. The optical system covered a diffraction angular region from about 1°
to 15° (q = 0.2–2.6 μm−1). The camera was calibrated with grids and pinholes and was tested with polymer latex particles in solution and with spherulites
from polymer films.
Received: 06 December 1999 Accepted: 04 February 2000 相似文献
104.
The so-called quantum Zeno effect is essentially a consequence of the projection postulate for ideal measurements. To test
the effect, Itanoet al. have performed an experiment on an ensemble of atoms where rapidly repeated level measurements were realized by means of
short laser pulses. Using dynamical considerations, we give an explanation why the projection postulate can be applied in
good approximation to such measurements. Corrections to ideal measurements are determined explicitly. This is used to discuss
how far the experiment of Itanoet al. can be considered as a test of the quantum Zeno effect. We also analyze a new possible experiment on a single atom where
stochastic light and dark periods can be interpreted as manifestation of the quantum Zeno effect. We show that the measurement
point of view gives a quick and intuitive understanding of experiments of the above type, although a finer analysis has to
take the corrections into account. 相似文献
105.
106.
High-pressure and/or high-temperature analysis of geo- and material science samples routinely employs diamond anvil cells (DACs) as a research instrument. In particular, DACs allow for various in situ characterizations (e.g. Raman and Fourier transform infra red spectroscopies, X-ray diffraction (XRD), X-ray spectroscopy including fluorescence (XRF) and absorption (XAS)) at elevated pressure and temperature. The measurement of pressure (P) and/or temperature (T) in the sample chamber is crucial, but not always accurate, more specifically in the case of low-pressure applications (a few GPa). The development of modified diamonds (intelligent anvils ‘i-anvils’) adapted to a new generation of DACs (intelligent diamond anvil cells: iDAC) can contribute to solve this problem, as the diamond itself serves as the PT sensor, being prepared, for example, by high-energy ion implantation [H. Bureau, M. Burchard, S. Kubsky et al., This volume (2006).] on a micrometric scale. Several most interesting measurement methods used with DACs are based on X-ray techniques (e.g. XRF, XRD, XAS). We present the first results of X-ray transmission measurements with iDACs, performed at the hard-X-ray microfocus beamline ID22 at the ESRF (European Synchrotron Radiation Facility), Grenoble, France. Sensor response to intense irradiation as a function of X-ray energy (E ph∈10;18.1 keV) was investigated. The values of the sensor were found to be independent of the irradiation in the investigated energy range and thus validate the use of these sensors for precise and reliable measurements on a wide range of applications with high-energy synchrotron radiation. No influence of the sensor on the X-ray transmission properties of the anvil has been found. 相似文献
107.
The degenerate parabolic equation u t + ? x [u 3(u xxx + u x ? sin x)] = 0 models the evolution of a thin liquid film on a stationary horizontal cylinder. It is shown here that for each mass there is a unique steady state, given by a droplet hanging from the bottom of the cylinder that meets the dry region with zero contact angle. The droplet minimizes the associated energy functional and attracts all strong solutions that satisfy certain energy and entropy inequalities, including all positive solutions. The distance of solutions from the steady state cannot decay faster than a power law. 相似文献
108.
Werner Bauer Martin Baumann Leonhard Scheck Almut Gassmann Vincent Heuveline Sarah C. Jones 《Theoretical and Computational Fluid Dynamics》2014,28(1):107-128
We demonstrate how efficient r-adapted grids for the prediction of tropical cyclone (TC) tracks can be constructed with the help of goal-oriented error estimates. The binary interaction of TCs in a barotropic model is used as a test case. We perform a linear sensitivity analysis for this problem to evaluate the contribution of each grid cell to an error measure correlated with the cyclone positions. This information allows us to estimate the local grid resolution required to minimize the TC position error. An algorithm involving the solution of a Poisson problem is employed to compute how grid points should be moved such that the desired local resolution is achieved. A hexagonal shallow-water version of the next-generation numerical weather prediction and climate model ICON is used to perform model runs on these adapted grids. The results show that for adequately chosen grid adaptation parameters, the accuracy of the track prediction can be maintained even when a coarser grid is used in regions for which the estimated error contribution is low. Accurate track predictions are obtained only when a grid with high resolution consisting of cells with nearly constant size and regular shape covers the part of the domain where the estimated error contribution is large. The number of grid points required to achieve a certain accuracy in the track prediction can be decreased substantially with our approach. 相似文献
109.
Burchard Kaup 《manuscripta mathematica》1975,15(4):385-408
A method of Stein [17] is generalized to construct in an explicit way complex bases of open holomorphic mappings, defined on normal complex analytic spaces. Using theorems concerning the existence of pushouts, we can sharpen a theorem of Wolffhardt ([22],§4) and generalize the above construction. As a consequence, we can prove for a big class of complex bases b:X→B, that the induced mapping π1(X)→π1(B) its surjective. We give a characterisation of locally simple and analytically locally simple analytic equivalence relations. 相似文献
110.