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991.
设$\varphi$为群${\rm Aut}(N)$的同态,记$H_\varphi\times N$为群$N$借助于群$H$的半直积.设$G$为有限不可解群,本文证明: 若$G$中最高阶元素个数为40, 则$G$同构于下列群之一:(1)~$Z_{4\varphi}\times A_5$,\,${\rm ker}\varphi=Z_2$; (2)~$D_{8\varphi}\times A_5,\,{\rm ker}\varphi=Z_2\times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2\times Z_2,\,N\cap Z(G)=Z_2$. 相似文献
992.
We prove that any mapping class on a compact oriented surface with non-empty boundary can be made pseudo-Anosov and right-veering
after a sequence of positive stabilizations.
相似文献
993.
S. Tazhetdinov 《Siberian Mathematical Journal》2008,49(1):175-179
We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible. 相似文献
994.
Let f : U → X be a map from a connected nilpotent space U to a connected rational space X. The evaluation subgroup G
*(U, X; f), which is a generalization of the Gottlieb group of X, is investigated. The key device for the study is an explicit Sullivan model for the connected component containing f of the function space of maps from U to X, which is derived from the general theory of such a model due to Brown and Szczarba (Trans Am Math Soc 349, 4931–4951, 1997).
In particular, we show that non Gottlieb elements are detected by analyzing a Sullivan model for the map f and by looking at non-triviality of higher order Whitehead products in the homotopy group of X. The Gottlieb triviality of a fibration in the sense of Lupton and Smith (The evaluation subgroup of a fibre inclusion, 2006)
is also discussed from the function space model point of view. Moreover, we proceed to consideration of the evaluation subgroup
of the fundamental group of a nilpotent space. In consequence, the first Gottlieb group of the total space of each S
1-bundle over the n-dimensional torus is determined explicitly in the non-rational case.
相似文献
995.
We generalize some identities and q-identities previously known for the symmetric group to Coxeter groups of type B and D. The extended results include theorems of Foata and Schützenberger, Gessel, and Roselle on various distributions of statistics, like inversion number, major index, and descent number. In order to show our results we provide explicit characterizations of the systems of minimal coset representatives of Coxeter groups of type B and D. 相似文献
996.
We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel measures, {νt}t>0, are also studied. We show that these heat kernel measures admit: (1) Gaussian like upper bounds, (2) Cameron-Martin type quasi-invariance results, (3) good Lp-bounds on the corresponding Radon-Nikodym derivatives, (4) integration by parts formulas, and (5) logarithmic Sobolev inequalities. The last three results heavily rely on the boundedness of the Ricci tensor. 相似文献
997.
N. S. Romanovskii 《Algebra and Logic》2008,47(6):426-434
A soluble group G is rigid if it contains a normal series of the form G = G1 > G2 > … > Gp > Gp+1 = 1, whose quotients Gi/Gi+1 are Abelian and are torsion-free as right ℤ[G/Gi]-modules. The concept of a rigid group appeared in studying algebraic geometry over groups that are close to free soluble.
In the class of all rigid groups, we distinguish divisible groups the elements of whose quotients Gi/Gi+1 are divisible by any elements of respective groups rings Z[G/Gi]. It is reasonable to suppose that algebraic geometry over divisible rigid groups is rather well structured. Abstract properties
of such groups are investigated. It is proved that in every divisible rigid group H that contains G as a subgroup, there is
a minimal divisible subgroup including G, which we call a divisible closure of G in H. Among divisible closures of G are divisible
completions of G that are distinguished by some natural condition. It is shown that a divisible completion is defined uniquely
up to G-isomorphism.
Supported by the Council for Grants (under RF President) and State Aid of Leading Scientific Schools (grant NSh-344.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 762–776, November–December, 2008. 相似文献
998.
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic
groups can have. In two previous papers, D. Bochiş and the second author studied the problem for noncubic groups. This paper
deals with “full” cubic groups, while “quarter” cubic groups are left for a subsequent paper. Here, “full” and “quarter” refers
to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston.
This paper’s main result is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also
find stereohedra with 17 facets for one of these groups.
Research partially supported by the Spanish Ministry of Education and Science, grant number MTM2005-08618-C02-02. 相似文献
999.
The isovariant version of Borsuk–Ulam type theorems has been studied by Wasserman and the first author. In this paper, first we consider the relation between the existence of Cn-isovariant maps from free Cn-manifolds to representation spheres and Borsuk–Ulam type inequalities for their dimensions. Our main result classifies the Cn-isovariant maps by Cn-isovariant homotopy types when a Borsuk–Ulam type inequality holds. For proving it, we use the multidegree of a Cn-equivariant map developed by the first author. 相似文献
1000.
用群的共轭类个数刻画了交换群,同时用一个很简洁的方法重新证明了Frobenius G提出的一个著名问题:对于一个固定的数自然数n,共轭类数为n的有限群,在同构的意义下是有限的. 相似文献