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31.
The l-labelled version of the IOS is re-examined in detail. It is shown that recent severe criticism of the method, based on studies of a system with a long-range attractive anisotropy and spherically symmetric hard core and assuming a weak anisotropy and straight-line Trajectories, is unjustified. 相似文献
32.
The response of giant magnetoresistance (GMR) devices depends critically on the film microstructure, with parameters such
as layer thickness and interfacial abruptness being crucial. This paper presents results obtained using high resolution electron
microscopy (HREM), chemical mapping and atom probe microanalysis. Local variations in the magnetic properties are induced
by the microstructure and also when the films are patterned to form small elements. These lead to changes in the magnetization
reversal mechanism. Some results of the studies of the magnetization reversal carried out using in situ in Lorentz transmission electron microscopy (LTEM) magnetizing experiments are also included. 相似文献
33.
Cameron?L.?Williams Bernhard?G.?BodmannEmail author Donald?J.?Kouri 《Journal of Fourier Analysis and Applications》2017,23(3):660-678
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized by an intertwining relation with dilations and by having a Gaussian as an eigenfunction. This broadens the perspective to an entire family of Fourier-like transforms that are uniquely identified by the same dilation-related property and by having Gaussian-like functions as eigenfunctions. We show that these transforms share many properties with the Fourier transform, particularly unitarity, periodicity and eigenvalues. We also establish short-time analogues of these transforms and show a reconstruction property and an orthogonality relation for the short-time transforms. 相似文献
34.
The Volterra inverse scattering series method is developed to obtain the interaction potential for one‐dimensional quantum barrier scattering problems. The Lippmann–Schwinger equation describing quantum barrier scattering is renormalized from a Fredholm to a Volterra integral equation. Employing the Born–Neumann series solution of the Lippmann–Schwinger Volterra equation and a related expansion of the interaction potential in orders of the data, we derive the Volterra inverse scattering series for the reflection and transmission amplitudes. Each term of the interaction potential is computed using the scattering amplitude and the Volterra Green's function. We do not consider the separate issue of extracting scattering amplitudes from quantum cross sections. The triangular nature of the Volterra Green's function significantly reduces computational effort. The Volterra series is then applied to several one‐dimensional quantum barrier scattering problems. Computational results show that the first few terms in the Volterra series can yield accurate interaction barriers. In addition, the potential barriers are calculated using the Born inverse scattering series based on the Lippmann–Schwinger Fredholm equation with the reflection amplitude. The comparison between the Born and Volterra results demonstrates that the Volterra inverse scattering series can provide a more accurate and more efficient method for determining the interaction potential. 相似文献
35.
The first computations suggesting the occurrence of rainbow scattering in the magnetic transitions occurring in molecule-corrugated surface scatteringare presented. The system studied models a Cl2 molecule scattered by a corrugated surface for which the potential is taken to be of the dumbbell type suggested by Gerber, Beard and Kouri (a sum of atom-Surface interactions). The magnetic transition probabilities which likely signal the Δmj rainbow are much larger than those observed in the only previous study of magnetic transitions in molecule-surface scattering 相似文献
36.
37.
We show that the Dirichlet–Gabor waveletdistributed approximating functional (DAF) can be derived from the same variational principle used to obtain noninterpolating waveletDAFs (such as the Hermite DAF). This variational approach for such interpolating DAFs complements the original viewpoint that they are generated by regularizing interpolating shells or through twoparameter Dirac delta sequences. 相似文献
38.
Two families of statistical measures are used for quantitative characterization of nonequilibrium patterns and their evolution. The first quantifies the disorder in labyrinthine patterns, and captures features like the domain size, defect density, variations in wave number, etc. The second class of characteristics can be used to quantify the disorder in more general nonequilibrium structures, including those observed during domain growth. The presence of distinct stages of relaxation in spatiotemporal dynamics under the Swift-Hohenberg equation is analyzed using both classes of measures. 相似文献
39.
A sudden approximation recently derived by Cross using a semiclassical treatment of the orbital motion is recast into a form which permits factorization of differential and integral degeneracy averaged cross sections, opacities as a function of final angular momentum quantum number, the scattering amplitude, and the phenomenological cross section which describes spectral line broadening. Calculations are done using an average of initial and final orbital angular momentum quantum numbers for the partial wave parameter for ArN2, ArTIF, H+H2 and Li+H2. The results indicate that the method is a good approximation for integral cross sections and opacities when the energy sudden approximation is valid and when the coupling of the orbital motion is important. 相似文献
40.
Dragomir Z. DJ Okovic Kaming Zhao 《Transactions of the American Mathematical Society》1998,350(2):643-664
Generalized Witt algebras, over a field of characteristic , were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto's, we give an essentially equivalent definition of generalized Witt algebras over , where the ingredients are an abelian group , a vector space over , and a map which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.