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981.
关于非线性波动方程的爆破现象 总被引:4,自引:0,他引:4
通过引入一类“爆破因子K(u,ut)”,讨论了非线性波动方程分别具Newmann边界条件和Dirichlet边界条件时,混合问题对于常见的各种非线性情形及初值条件,解在有限时间内的爆破行为。 相似文献
982.
At the special value of the reduced inverse temperature=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.Laboratory associated with the Centre National de la Recherche Scientifique. 相似文献
983.
Tomislav P. Živković 《Journal of mathematical chemistry》2002,32(1):39-71
Interaction of quantum system S
a
described by the generalised × eigenvalue equation A|
s
=E
s
S
a
|
s
(s=1,...,) with quantum system S
b
described by the generalised n×n eigenvalue equation B|
i
=
i
S
b
|
i
(i=1,...,n) is considered. With the system S
a
is associated -dimensional space X
a
and with the system S
b
is associated an n-dimensional space X
n
b
that is orthogonal to X
a
. Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]|
k
=
k
[S
a
+S
b
+P]|
k
(k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S
a
,S
b
and S=S
a
+S
b
+P are, in addition, positive definite. It is shown that each eigenvalue
k
i
of the combined system is the eigenvalue of the × eigenvalue equation
. Operator
in this equation is expressed in terms of the eigenvalues
i
of the system S
b
and in terms of matrix elements
s
|V|
i
and
s
|P|
i
where vectors |
s
form a base in X
a
. Eigenstate |
k
a
of this equation is the projection of the eigenstate |
k
of the combined system on the space X
a
. Projection |
k
b
of |
k
on the space X
n
b
is given by |
k
b
=(
k
S
b
–B)–1(V–
k
P})|
k
a
where (
k
S
b
–B)–1 is inverse of (
k
S
b
–B) in X
n
b
. Hence, if the solution to the system S
b
is known, one can obtain all eigenvalues
k
i
} and all the corresponding eigenstates |
k
of the combined system as a solution of the above × eigenvalue equation that refers to the system S
a
alone. Slightly more complicated expressions are obtained for the eigenvalues
k
i
} and the corresponding eigenstates, provided such eigenvalues and eigenstates exist. 相似文献
984.
Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures,
have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms.
According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to
be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic
equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most
probable mechanisms.
The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another
method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition.
The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation
coefficient (r
2) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given.
Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the
related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of
the latter for which a first-order model was chosen.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
985.
The properties of fluctuations in space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations in space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail. 相似文献
986.
N. G. van Kampen 《Journal of statistical physics》1981,25(3):431-442
In the presence of internal noise the variables describing a system are intrinsically stochastic. If they constitute a Markov process the expansion enables one to extract a deterministic macroscopic equation and to compute the fluctuations in successive approximations. In the lowest or linear noise approximation the fluctuations can be represented by a Langevin equation, provided it is handled appropriately. Higher orders cannot be described by any white noise Langevin equation. The question whether the equation has to be interpreted according to Itô or Stratonovich concerns these higher orders, for which the equation is not valid anyway. 相似文献
987.
988.
SHEN Yu-Feng WANG Qing-Hai ZHU Dao-Qian ZHOU Liang-Mo Dalian Institute of Chemical Physics Chinese Academy of Sciences Dalian Liaoning China 《中国化学》1994,12(2):129-137
The study on retention behavior in supercritical fluid chromatography (SFC) is necessary to understand the mechanism of the various interactions in SFC. The retention of SFC in carboxylic acid methyl ester/polymethylsiloxane/CO2 system was studied systematically and the retention behavior of this kind of compounds under various typical operation conditions was described using the method of an alternative unified theory of chromatographic retention. The results illustrated that expression: Ink.= a + b/T + cp + dp/T + ep2/T can be used to describe quantitatively the retention behavior of carboxylic acid methyl ester/polymethylsiloxane/CO2 system in the ranges of reduced density from 0.549 to 1.411. It was also found that the entropy of solute in stationary phase is dependent on the density of supercritical fluid (SF) under typical operating conditions of SFC. 相似文献
989.
Yoshisuke Ueda 《Journal of statistical physics》1979,20(2):181-196
This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon. 相似文献
990.
A boundS
l is given for the number of bound statesn
i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given
by
whereV
a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r
2. Extensive comparative study ofS
i and the Bargmann inequality is made. 相似文献