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1.
2.
We provide a detailed investigation of limits of N–soliton solutions of the Toda lattice as N tends to infinity. Our principal results yield new classes of Toda solutions including, in particular, new kinds of soliton–like
(i.e., reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one–dimensional Jacobi operators
and explicitly construct tri–diagonal matrices that yield a purely absolutely continuous spectrum in (-1,1) and give rise
to an eigenvalue spectrum that includes any prescribed countable and bounded subset of .
Received: 16 October 1995/Accepted: 23 July 1996 相似文献
3.
Marcel Oliver 《Theoretical and Computational Fluid Dynamics》1997,9(3-4):311-324
The so-called lake equations arise as the shallow-water limit of the rigid-lid equations—three-dimensional Euler equations
with a rigid-lid upper boundary condition—in a horizontally periodic basin with bottom topography. We prove an a priori estimate in the Sobolev space H
m
for m≥ 3 which shows that a solution to the rigid-lid equations can be approximated by a solution of the lake equations for an
interval of time which can be estimated in terms of the initial deviation from a columnar configuration and the magnitude
of the initial data in H
m
, the gradient of the bottom topography in H
m+1
, and the aspect ratio of the basin. In particular, any solution to the lake equations remains close to some solution of the
rigid-lid equations for an interval of time that can be made arbitrarily large by choosing the aspect ratio of the basin small.
Received 10 October 1996 and accepted 15 May 1997 相似文献
4.
5.
Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface
with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of
the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources
of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated
to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which
the duration of the coalescence process, τ*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ*∼σ-1/2 and τ*∼L
3/2.
Received: 22 December 1995 / Accepted: 15 October 1996 相似文献
6.
7.
We report on the integration of the kinematic dynamo problem in a spherical domain forced by velocity fields that are convective
fluid flows resulting from a bifurcation analysis of the spherical Bénard problem. We derive a code based on generalized spherical
harmonics that ensures a divergence-free magnetic field. We determine the growth or decay of a magnetic field in the kinematic
dynamo equation for various physically relevant velocity fields which are stationary as well as time-periodic and chaotic.
Velocity signals that are produced by heteroclinic cycles are used as an input to an energy-saturated kinematic dynamo equation
that limits the growth of the linearly unstable modes. Preliminary calculations indicate the possibility of reversals of the
magnetic field for this case of forcing.
Received 8 October 1996 and accepted 28 April 1997 相似文献
8.
9.
M.C. Gonzalez-Garcia M. Maltoni 《The European Physical Journal C - Particles and Fields》2003,26(3):417-428
We study the stability of the results of the three-neutrino oscillation analysis of atmospheric and reactor neutrino data
under departures of the one dominant mass scale approximation. In order to do so we perform the analysis of atmospheric and
reactor neutrino data in terms of three-neutrino oscillations where the effect of both mass differences is explicitly considered.
We study the allowed parameter space resulting from this analysis as a function of the mass splitting hierarchy parameter which parameterizes the departure from the one dominant mass scale approximation. We consider schemes with both direct and
inverted mass ordering. Our results show that in the analysis of the atmospheric data the derived range of the largest mass
splitting, , is stable, while the allowed ranges of mixing angles and are wider than those obtained in the one dominant mass scale approximation. Inclusion of the CHOOZ reactor data in the analysis
results in the reduction of the parameter space in particular for the mixing angles. As a consequence the final allowed ranges
of the parameters from the combined analysis are only slightly broader than when obtained in the one dominant mass scale approximation.
Received: 31 May 2002 / Revised version: 10 July 2002 / Published online: 31 October 2002 相似文献
10.
Anstreicher 《Discrete and Computational Geometry》2002,28(1):107-114
Abstract. Let S\subset[-1,1) . A finite set \Ccal=\set x
i
i=1
M
\subset\Re
n
is called a spherical S-code if \norm x
i
=1 for each i , and x
i
\tran x
j
∈ S , i\ne j . For S=[-1, 0.5] maximizing M=|C| is commonly referred to as the kissing number problem. A well-known technique based on harmonic analysis and linear programming can be used to bound M . We consider a modification of the bounding procedure that is applicable to antipodal codes; that is, codes where x∈\Ccal\implies -x∈\Ccal . Such codes correspond to packings of lines in the unit sphere, and include all codes obtained as the collection of minimal
vectors in a lattice. We obtain improvements in upper bounds for kissing numbers attainable by antipodal codes in dimensions
16≤ n≤ 23 . We also show that for n=4 , 6 and 7 the antipodal codes with maximal kissing numbers are essentially unique, and correspond to the minimal vectors
in the laminated lattices \Lam
n
. 相似文献