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141.
Werner Kutzelnigg 《Theoretical chemistry accounts》1988,73(2-3):173-200
The Fermi-contact interaction (FCI) can easily be derived from 1st order perturbation theory applied to the non-relativistic wave equation for a spin-(1/2) particle of Lévy-Leblond, with the nuclear spin described by the field of an external magnetic dipole, and it results from the fact that the turn-over-rule for the operator
is only valid if the derivatives implicit in
are taken in the distribution sense. If one avoids to apply the turn-over-rule, the FCI is obtained without the need to introduce a -function. It is also shown that the formulation of a magnetic point dipole as the limit of an extended nucleus directly leads to the FCI. Traditional methods of the derivation of the FCI are analyzed in the light of this new interpretation. It is then explained why the perturbation expansions in powers of the magnetic moment of the nucleus necessarily diverges, but that the expression for the 1st order energy on which the concept of the FCI is based, can nevertheless be justified by means of the Hellmann-Feynman theorem with a correction term if singular wave functions are involved. Finally some comments on a theory beyond first order are made.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday 相似文献
142.
Thomas Merakis Annette Murphy Leone Spiccia Alan Beguin Werner Marty 《Helvetica chimica acta》1989,72(5):993-995
Crystalline salts of the hydrolytic dimer of Cr(III), [Cr2(μ-OH)2(H2O)8]X4·n H2O (X = p-toluenesulfonate (tos) or mesitylene-2-sulfonate (dmtos)) have been prepared in good yields via a simple two-step procedure: H+ oxidation of Cr metal to give Cr2+ (T ≈? 70°) followed by O2 oxidation, of Cr2+ to give the dimer (T ≈? 25°). The mechanism of conversion of Cr2+ into the dimer is discussed. 相似文献
143.
Elisabeth Eriksrud 《Journal of Electroanalytical Chemistry》1977,76(1):27-49
The title subject has been studied by galvanostatic single-pulse, chronopotentiometric and equilibrium measurements on the Zn(Hg)/Zn(II) electrode in x M KI+(1?x) M KCl (x from 0 to 1), 1 M KBr and 1 M MeCl (Me=Li, Na, K and Cs) solutions of pH 3 at 25°C. Quantitative information about the effect of specifically adsorbed halides on the rates of the Zn(II)/Zn(I) and the Zn(I)/Zn(Hg) steps is obtained separately (for the latter step mainly at potentials near ?1.0 V(SCE)), and the latter step seems to be more influenced than the former by the adsorption. An attempt is made to correlate the adsorption effect on the rate of the Zn(II)/Zn(I) step to double-layer parameters according to recent models for such effects. The extra current observed at potentials where the halides are adsorbed, seems to vary with the surface activity of the specifically adsorbed ion. The lack of any observed kinetic effect of Cs+, which is specifically adsorbed at these potentials, is possibly due to the Cs+ specific adsorption enhancing the Cl? specific adsorption and vice versa, so that the decelerating and accelerating effects by these ions may cancel each other. 相似文献
144.
Summary We study some features concerning the occupation timeA
t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A1u0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf
t
A
t/(tf(t))=0 or for a decreasing functionf. 相似文献
145.
Karin Krüger Natalia V. Shakhlevich Yuri N. Sotskov Frank Werner 《The Journal of the Operational Research Society》1995,46(12):1481-1497
We consider a scheduling problem where a set of n jobs has to be processed on a set of m machines and arbitrary precedence constraints between operations are given. Moreover, for any two operations i and j values a ij >0 and a ji >0 may be given where a ij is the minimal difference between the starting times of operations i and j when operation i is processed first. Often, the objective is to minimize the makespan but we consider also arbitrary regular criteria. Even the special cases of the classical job shop problem J//Cmax belong to the set of NP-hard problems. Therefore, approximation or heuristic algorithms are necessary to handle large-dimension problems. Based on the mixed graph model we give a heuristic decomposition algorithm for such a problem, i.e. the initial problem is partitioned into subproblems that can be solved exactly or approximately with a small error bound. These subproblems are obtained by a relaxation of a subset of the set of undirected edges of the mixed graph. The subproblems are successively solved and a proportion of the results obtained for one subproblem is kept for further subproblem definitions. Numerical results of the algorithm presented here are given. 相似文献
146.
147.
Dietmar Krämer Erwin Rosenberg Achim Krug Robert Kellner Wolfgang Hutter Werner Hampel 《Mikrochimica acta》1994,116(4):183-189
Chloride is determined indirectly by Spectrophotometric flow injection analysis. Two systems are compared, both based on the principle of ion exchange of easily detectable anions versus chloride from suitable mercury salts. The first method is based on the exchange of chloride with chloranilate which is detected at 332 nm or at 306 nm in neutral or in acidic medium respectively. In the second case, chloride reacts with Hg(SCN)2. The liberated thiocyanate forms a strongly coloured complex with Fe(III) in acidic solution with an absorption maximum at 460 nm. Both methods have a detection limit of about 5 mol Cl–/l (175 ng/ml). In the case of the thiocyanate method, the relative standard deviation is about 2% (7 measurements) in the range of 5 to 150 mol/l and decreases significantly to a value of approximately 0.2% at higher concentrations; for the chloranilate method it is 10% for lower and about 1% for higher concentrations respectively. 相似文献
148.
Werner Hoffmann 《Annals of Global Analysis and Geometry》1994,12(1):19-63
Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered. 相似文献
149.
In the present paper, we discuss spectral properties of a periodic Schrödinger operator which is perturbed by randomly distributed impurities; such operators occur as simple models for crystals (or semi-conductors) with impurities. While the spectrum itself is independent of the concentrationp of impurities, for 0<p<1, we focus our attention on the limiting behavior of the integrated density of states
p
of the random Schrödinger operator, inside a spectral gap of the periodic operator, asp0. Denoting byU
0 the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located at the origin, say), we show that the integrated density of states concentrates around the points ofU
0, in the sense that
p
(U
) is of orderp, for any fixed -neighborhoodU
ofU
0, while
p
(K)C·p
2, for any compact subsetK of the gap which does not intersectU
.Research partially supported by Deutsche Forschungsgemeinschaft 相似文献
150.