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81.
Dikran Dikranjan 《Topology and its Applications》2007,154(7):1321-1340
We study CLP-compact spaces (every cover consisting of clopen sets has a finite subcover) and CLP-compact topological groups. In particular, we extend a theorem on CLP-compactness of products from [J. Steprāns, A. Šostak, Restricted compactness properties and their preservation under products, Topology Appl. 101 (3) (2000) 213-229] and we offer various criteria for CLP-compactness for spaces and topological groups, that work particularly well for precompact groups. This allows us to show that arbitrary products of CLP-compact pseudocompact groups are CLP-compact. For every natural n we construct:
- (i)
- a totally disconnected, n-dimensional, pseudocompact CLP-compact group; and
- (ii)
- a hereditarily disconnected, n-dimensional, totally minimal, CLP-compact group that can be chosen to be either separable metrizable or pseudocompact (a Hausdorff group G is totally minimal when all continuous surjective homomorphisms G→H, with a Hausdorff group H, are open).
82.
Florin Nicolae 《Journal of Number Theory》2007,124(1):26-30
Let K/Q be a finite Galois extension with the Galois group G, let χ1,…,χr be the irreducible non-trivial characters of G, and let A be the C-algebra generated by the Artin L-functions L(s,χ1),…,L(s,χr). Let B be the subalgebra of A generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) B is of Krull dimension r and has the same quotient field as A; (2) B=A iff G is M-group; (3) the integral closure of B in A equals A iff G is quasi-M-group. 相似文献
83.
84.
85.
N. I. Chernov 《Probability Theory and Related Fields》1995,101(3):321-362
Summary We prove the central limit theorem and weak invariance principle for abstract dynamical systems based on bounds on their mixing coefficients. We also develop techniques of Markov approximations for dynamical systems. We apply our results to expanding interval maps, Axiom A diffeomorphisms, chaotic billiards and hyperbolic attractors. 相似文献
86.
The number of compositionsC(n) of a positive integern into distinct parts can be considered as a natural analogue of the numberq(n) of distinct partitions ofn. We obtain an asymptotic estimate forC(n) and in addition show that the sequence {C(n, k)} of distinct compositions ofn withk distinct parts is unimodal. Our analysis is more complicated than is usual for composition problems. The results imply however that the behaviour of these functions is of comparable complexity to partition problems. 相似文献
87.
Walter M. Miller 《Set-Valued Analysis》1995,3(2):181-194
A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of . 相似文献
88.
In this work we investigate a class of string, compact Jacobi matrices with very rapidly decreasing weights. In particular, we have found Hellinger-Weyls function representation as ratio of two entire functions with known Taylor series representation. The asymptotical estimations of zeroes of this entire functions and of eigenvalues of a corresponding operator are found. The application of this theory to Rogers-Ramanujans functions is considered.Submitted: November 18, 2002 Revised: October 30, 2003 相似文献
89.
Michel Balazard 《Advances in Mathematics》2004,188(1):69-86
Opération fondamentale de l'arithmétique, familière depuis des millénaires, la division euclidienne n'a pas livré tous ses secrets. Ainsi, notons pour k et a entiers positifs, le reste de la division euclidienne de k par a, et imaginons un instant que, par un choix convenable d'un entier n et de réels c2,…,cn, nous sachions rendre arbitrairement petite la quantité
90.
We proceed with our study of increasing self-described sequences F, beginning with 1 and defined by a functional equation
In [1] we exhibited the simple solution f (t)=Ct, for some (0,1), of the associated functional-differential equation
and we proved that provided <2/(2+d()), where
we have the asymtotic equivalence F(m)~ Cm.In the present paper we show that this last result is optimal, in the sense that the self-described sequence defined by |F–1(m)|=F(m)2, that is
for which the boundary case =2/(2+d())(=1/2) holds, does not satisfy F(m) ~ Cm. We also show that the m-th term F(m) of a sequence F for which the boundary case holds is nevertheless of asymptotic order m.Then we investigate the behaviour of self-described sequences F when lies beyond the boundary case. In [1] we established the estimates
when is the unique fixed point of a certain associated function. We were only able to prove in general that the latter holds when does not lie beyond the boundary case, however. In the present paper we prove that whenever
is the unique fixed point of this function, and in addition we obtain estimates more precise than (*). This applies for instance to the sequence defined by
that is
相似文献