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121.
122.
The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c1N?1/3+c2N?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 相似文献
123.
We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
124.
Kazuhiro Matsuo 《Journal of statistical physics》1978,18(6):535-555
A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624. 相似文献
125.
Even systems in which strong electron correlation effects are present, such as the large near-degeneracy correlation in a
dissociating electron pair bond exemplified by stretched H2, are represented in the Kohn–Sham (KS) model of non-interacting electrons by a determinantal wavefunction built from the
KS molecular orbitals. As a contribution to the discussion on the status and meaning of the KS orbitals we investigate, for
the prototype system of H2 at large bond distance, and also for a one-dimensional molecular model, how the electron correlation effects show up in the
shape of the KS σ
g
orbital. KS orbitals φHL and φFCI obtained from the correlated Heitler-London and full configuration interaction wavefunctions are compared to the orbital
φLCAO, the traditional linear combination of atomic orbitals (LCAO) form of the (approximate) Hartree-Fock orbital. Electron correlation
manifests itself in an essentially non-LCAO structure of the KS orbitals φHL and φFCI around the bond midpoint, which shows up particularly clearly in the Laplacian of the KS orbital. There are corresponding
features in the kinetic energy density t
s
of the KS system (a well around the bond midpoint) and in the one-electron KS potential v
s
(a peak). The KS features are lacking in the Hartree-Fock orbital, in a minimal LCAO approximation as well as in the exact
one.
Received: 11 December 1996 / Accepted: 10 January 1997 相似文献
126.
Carl M. Bender Fred Cooper Gerald Guralnik Harvey A. Rose David H. Sharp 《Journal of statistical physics》1980,22(6):647-660
We discuss the simple, randomly driven systemdx/dt = –x –x3 +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)n, whereR is the internal Reynolds number ()1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp
2/2 +m
2
x
2/2 +vx
4 +x
6/2, we evaluate the path integral on a lattice by assuming that thex
6 term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy. 相似文献
127.
Qing Z Wen-Chen Z Xiao-Xuan W Yang M 《Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy》2005,62(4-5):769-772
From the high-order perturbation formulas of EPR parameters (zero-field splitting D, g factors gparallel, gperpendicular and hyperfine structure constants Aparallel, Aperpendicular) based on the two spin-orbit coupling parameter model for 3d3 ions in trigonal symmetry, the EPR parameters of Cr3+ and V2+ ions in HfS2 crystals are calculated. From the calculations, it is found that the local trigonal distortion angle theta of impurity center in HfS2:Cr3+ is smaller than that in HfS2:V2+. The dominant cause of the small zero-field splitting |D| and g-anisotropy |Deltag|=|gparallel-gperpendicular| in HfS2:Cr3+ (compound to HfS2:V2+) is due to the small local trigonal distortion angle theta rather than to the small impurity-ligand distance R in HfS2:Cr3+. 相似文献
128.
Hermann Stoll Gerhard Wagenblast Heinzwerner Preuβ 《Theoretical chemistry accounts》1980,57(2):169-178
Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li2, HF, H2O, NH3, CH4 and C2H6. 相似文献
129.
130.
ubica Adam
íková Daniel Miicák Peter ev
ík 《Reaction Kinetics and Catalysis Letters》2005,85(2):215-221
Summary The experimental behavior of the uncatalyzed Belousov - Zhabotinsky reaction between aspirin and bromate in acidic media in the batch reactor has been studied for the first time. Aspirin is an interesting substrate because it is one of the most used medicines. The medical aspirin behaves also in an oscillatory manner with bromate. The oscillating process was investigated under aerobic and anaerobic conditions. The complex dynamic behavior has been observed in the mixed aspirin - vitamin C - BrO3 - H2SO4 system. 相似文献