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991.
Summary.
In this paper we determine all iseomorphic pairs (isomorphic
pairs with monotonic, thus continuous isomorphisms) of
continuous, strictly increasing, linearly homogeneous functions defined on
cartesian squares
I
2 and
J
2 of
intervals of positive numbers or on their restrictions
or
and
or
We prove that, if the iseomorphy is nontrivial, then each
homogeneous function is a (weighted) geometric or power mean or a
joint pair of such means.
In functional equations terminology this means that all nontrivial
continuous strictly increasing linearly homogeneous solutions
G, H
(with the continuous strictly monotonic
F also unknown) of the
equation
on D
< or
D
>
are weighted geometric or power means, while on
I
2
they are joint pairs of weighted geometric means or of weighted
power means. 相似文献
992.
We study the Howe dualities involving the reductive dual pairs (O(d),spo(2m|2n)) and (Sp(d),osp(2m|2n)) on the (super)symmetric tensor of . We obtain complete decompositions of this space with respect to their respective joint actions. We also use these dualities to derive a character formula for these irreducible representations of spo(2m|2n) and osp(2m|2n) that appear in these decompositions. 相似文献
993.
《Advances in Mathematics》2004,182(2):278-306
Let Tα be the translation operator by α in the space of entire functions defined by . We prove that there is a residual set G of entire functions such that for every f∈G and every the sequence is dense in , that is, G is a residual set of common hypercyclic vectors ( functions) for the family . Also, we prove similar results for many families of operators as: multiples of differential operator, multiples of backward shift, weighted backward shifts. 相似文献
994.
In this paper we aim to investigate different questions concerning the stability of the set of all intersections of closed balls in a normed space. We are mainly concerned with: (i) the stability of under the closure of the vector sums; (ii) the stability under the addition of balls. We prove that (i) and (ii) are different properties which have strong connections with the geometry of the space. They have interest both in finite and infinite dimension. In the former case, there is a link with linear programming theory. We also study two more stability properties related to the well-known binary intersection property. Mazur sets and Mazur spaces are introduced, as a natural family satisfying (i). We prove that every two-dimensional normed space is a Mazur space, a result which distinguishes dimension d?2 from dimension d?3. We also discuss the connections between Mazur spaces and porosity. 相似文献
995.
Janusz Matkowski 《Indagationes Mathematicae》2004,15(1):73-83
Let (Ω, Σ, μ) be a measure space and ?, ψ : (0, ∞) → (0, ∞) some bijective functions. Suppose that the functional ?,ψ defined on class of μ-integrable simple functions χ : Ω → [0, ∞), μ({? : χ(?) > 0} > 0, by the formula
996.
Sandra Spiroff 《Journal of Pure and Applied Algebra》2004,186(1):77-89
Let A be an excellent local normal domain and {fn}n=1∞ a sequence of elements lying in successively higher powers of the maximal ideal, such that each hypersurface A/fnA satisfies R1. We investigate the injectivity of the maps Cl(A)→Cl((A/fnA)′), where (A/fnA)′ represents the integral closure. The first result shows that no non-trivial divisor class can lie in every kernel. Secondly, when A is, in addition, an isolated singularity containing a field of characteristic zero, dim A?4, and A has a small Cohen-Macaulay module, then we show that there is an integer N>0 such that if , then Cl(A)→Cl((A/fnA)′) is injective. We substantiate these results with a general construction that provides a large collection of examples. 相似文献
997.
Projective metrics were first introduced by A. Cayley and F. Klein who constructed analytical models over the field of complex numbers. The aim of this paper is to give for the first time a purely synthetic definition of all projective spaces with Cayley-Klein metrics and to develop the synthetic foundation of projective-metric geometry to a level of generality including metrics over arbitrary fields of characteristic 2. 相似文献
998.
Béla?BollobásEmail author David?Gamarnik Oliver?Riordan Benny?Sudakov? 《Combinatorica》2004,24(2):187-207
Consider a complete graph on n vertices with edge weights chosen randomly and independently from an exponential distribution with parameter 1. Fix k vertices and consider the minimum weight Steiner tree which contains these vertices. We prove that with high probability the weight of this tree is (1+o(1))(k-1)(log n-log k)/n when k =o(n) and n.* Research supported in part by NSF grant DSM9971788 Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Part of this research was done while visiting IBM T. J. Watson Research Center. 相似文献
999.
The Diameter of a Scale-Free Random
Graph 总被引:1,自引:0,他引:1
We consider a random graph process in which vertices are
added to the graph one at a time and joined to a fixed number
m of earlier vertices, where
each earlier vertex is chosen with probability proportional to
its degree. This process was introduced by Barabási and Albert
[3], as a simple model of the growth of real-world graphs such
as the world-wide web. Computer experiments presented by
Barabási, Albert and Jeong [1,5] and heuristic arguments given
by Newman, Strogatz and Watts [23] suggest that after
n steps the resulting graph
should have diameter approximately logn. We show that while this holds for
m=1, for
m2 the diameter is
asymptotically log n/log
logn.* Research supported in part by NSF grant no.
DSM9971788 相似文献
1000.
The goal of the paper is to initiate research towards a general, Blow-up Lemma type embedding statement for pseudo-random graphs with sublinear degrees. In particular, we show that if the second eigenvalue of a d-regular graph G on 3n vertices is at most cd
3/n
2 log n, for some sufficiently small constant c > 0, then G contains a triangle factor. We also show that a fractional triangle factor already exists if < 0.1d
2/n. The latter result is seen to be best possible up to a constant factor, for various values of the degree d = d(n).* Supported by a USA-Israeli BSF grant, by a grant from the Israel Science Foundation and by a Bergmann Memorial Award. Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey. Research supported in part by NSF grant DMS 99-70270 and by the joint Berlin/Zurich graduate program Combinatorics, Geometry, Computation, financed by the German Science Foundation (DFG) and ETH Zürich. 相似文献