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21.
Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. By using a streamfunction formulation instead of a velocity potential one, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact linear theory compared to other MS-type equations. The main goal of this work is to extend the CMSE model for solving two-layer flow with a free-surface. In order to allow for an exact reference, an analytical solution for a two-layer fluid over a sloping plane beach is derived. This analytical solution is used for validating the results of the approximated MS-type models. It is found that the two-layer CMSE model performs better than the potential based one. In addition, the new model is used for investigating the scattering of linear surface water waves and interfacial ones over variable bathymetry. 相似文献
22.
Yehuda Pinchover 《Journal d'Analyse Mathématique》1995,66(1):57-83
In this paper we study the asymptotic behavior of the ground state energyE(R) of the Schrödinger operatorP R=?Δ+V 1(x)+V 2(x-R),x,R ∈?n, where the potentialsV i are small perturbations of the Laplacian in ?n,n≥3. The methods presented here apply also in the investigation of the ground state energyE(g) of the operatorPg=P+V 1(x)+V 2(gx), x ∈X,g ∈G, whereP g is an elliptic operator which is defined on a noncompact manifoldX, G is a discrete group acting onX by diffeomorphismsG×X∈(g, x)→gx∈X, andP is aG-invariant elliptic operator which is subcritical inX. 相似文献
23.
24.
Microwave discharge of O2 produces O(3P) atoms which form O3 on florisil surface. Reaction with adsorbed naphthalene results in -formylcinnamaldehydes as the main product. 相似文献
25.
The recently developed Classical Stochastic Diffusion Theory is applied to obtain the coverage dependence of desorption rates for Xe on W(111). Using the attractive Xe-Xe potential from gas phase experiments, we find a strong coverage dependence in the desorption rates and calculate Temperature Programmed Desorption Spectra (for a potential with reduced attractiveness) that are in excellent qualitative agreement with experimental results. We also investigated the effect of purely repulsive adsorbate-adsorbate interactions where we find, for some coverage ranges, that two different adsorption configurations can be stable (at different temperatures) leading to a marked change in the corresponding desorption rates and to distinct non-Arrhenius behavior. 相似文献
26.
Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elástic-perfectly plastic relation, and a special elastic-viscoplastic, strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times. 相似文献
27.
28.
Let a be a quadratic form associated with a Schrödinger operator L=-∇·(A∇)+V on a domain Ω⊂Rd. If a is nonnegative on , then either there is W>0 such that for all , or there is a sequence and a function ?>0 satisfying L?=0 such that a[?k]→0, ?k→? locally uniformly in Ω?{x0}. This dichotomy is equivalent to the dichotomy between L being subcritical resp. critical in Ω. In the latter case, one has an inequality of Poincaré type: there exists W>0 such that for every satisfying there exists a constant C>0 such that for all . 相似文献
29.
We show that for some absolute (explicit) constant C, the following holds for every finitely generated group G, and all d > 0: If there is some
R
0 > exp(exp(Cd
C
)) for which the number of elements in a ball of radius R
0 in a Cayley graph of G is bounded by R0d{R_0^d} , then G has a finite-index subgroup which is nilpotent (of step < C
d
). An effective bound on the finite index is provided if “nilpotent” is replaced by “polycyclic”, thus yielding a non-trivial
result for finite groups as well. 相似文献
30.
Moshe Marcus Victor J. Mizel Yehuda Pinchover 《Transactions of the American Mathematical Society》1998,350(8):3237-3255
Let be a domain in and . We consider the (generalized) Hardy inequality , where . The inequality is valid for a large family of domains, including all bounded domains with Lipschitz boundary. We here explore the connection between the value of the Hardy constant and the existence of a minimizer for this Rayleigh quotient. It is shown that for all smooth -dimensional domains, , where is the one-dimensional Hardy constant. Moreover it is shown that for all those domains not possessing a minimizer for the above Rayleigh quotient. Finally, for , it is proved that if and only if the Rayleigh quotient possesses a minimizer. Examples show that strict inequality may occur even for bounded smooth domains, but for convex domains.