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121.
We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies 3 = 31, whose wall oscillates at the frequency w = 21, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum n = n1 where the distance between perfect mirrors oscillates at the frequencies 1 and 21. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered. 相似文献
122.
一阶时滞微分方程解的零点分布 总被引:3,自引:0,他引:3
Abstract. The paper gives two estimates of the distance between adjacent zeros of solutions 相似文献
123.
Affine-Invariant Distances, Envelopes and Symmetry Sets 总被引:3,自引:0,他引:3
Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams. 相似文献
124.
Examples are given to show that the closest partition distance measure need not agree with the nearest neighbor interchange distance for unordered labeled binary trees. Proposed algorithms for computing the closest partition distance are shown to be of exponential complexity and hence may not be useful in approximating the nearest neighbor interchange distance. 相似文献
125.
Karol?Horodecki Micha??HorodeckiEmail author Pawel?Horodecki Jonathan?Oppenheim 《Foundations of Physics》2005,35(12):2027-2040
There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and
key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular
case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result
of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the
question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can
create a distribution product with Eve using IM bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that
it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical
distributions.
It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday. 相似文献
126.
C-H. Chu R. V. Hü gli M. Mackey 《Proceedings of the American Mathematical Society》2004,132(11):3305-3308
Let be the Banach algebra of bounded holomorphic functions on the open unit ball of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on . This answers a conjecture of Aron, Galindo and Lindström.
127.
Monika Budzynska 《Proceedings of the American Mathematical Society》2003,131(9):2771-2777
If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some
128.
We study a two-layer neural network made of N and M(N) neurons, producing a two-way association search for a family of p(N) patterns, where each pattern is a pair of two independent sub-categories of information having respectively N and M(N) components. In terms of the ratio =lim
N
M(N)/N, we study the retrieval capability of this network and show that there exists, at least, three regimes of association for which we determine the evolution of the threshold
c
() of the storage capacity =lim
N
p(N)/N. 相似文献
129.
J. Garcí a-Meliá n R. Letelier-Albornoz J. Sabina de Lis 《Proceedings of the American Mathematical Society》2001,129(12):3593-3602
In this paper we prove uniqueness of positive solutions to logistic singular problems , , 1$">, 0$"> in , where the main feature is the fact that . More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near . This expansion involves both the distance function and the mean curvature of .
130.
Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed. 相似文献