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61.
Yuval Z. Flicker 《Israel Journal of Mathematics》2001,122(1):61-77
The torsorP
δ=Hom⊗ (H
DR,H
σ) under the motivic Galois groupG
σ=Aut⊗
H
δ of the Tannakian category
generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP
σ→P
σ/G
σ
0
to a Gal(
)-torsor, and by its localizationsP
σ⊕k
k
ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is
an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1. 相似文献
62.
We prove that for every n ∈ ? there exists a metric space (X, d X), an n-point subset S ? X, a Banach space (Z, \({\left\| \right\|_Z}\)) and a 1-Lipschitz function f: S → Z such that the Lipschitz constant of every function F: X → Z that extends f is at least a constant multiple of \(\sqrt {\log n} \). This improves a bound of Johnson and Lindenstrauss [JL84]. We also obtain the following quantitative counterpart to a classical extension theorem of Minty [Min70]. For every α ∈ (1/2, 1] and n ∈ ? there exists a metric space (X, d X), an n-point subset S ? X and a function f: S → ?2 that is α-Hölder with constant 1, yet the α-Hölder constant of any F: X → ?2 that extends f satisfies \({\left\| F \right\|_{Lip\left( \alpha \right)}} > {\left( {\log n} \right)^{\frac{{2\alpha - 1}}{{4\alpha }}}} + {\left( {\frac{{\log n}}{{\log \log n}}} \right)^{{\alpha ^2} - \frac{1}{2}}}\). We formulate a conjecture whose positive solution would strengthen Ball’s nonlinear Maurey extension theorem [Bal92], serving as a far-reaching nonlinear version of a theorem of König, Retherford and Tomczak-Jaegermann [KRTJ80]. We explain how this conjecture would imply as special cases answers to longstanding open questions of Johnson and Lindenstrauss [JL84] and Kalton [Kal04]. 相似文献
63.
Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that in a digraph without parallel edges, the number of pairs of vertices having a common in-neighbor or a common out-neighbor is at least the number of edges. We deduce that for any simple group-grading, the dimension of the trivial component is maximal. 相似文献
64.
Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as well as inapproximability results, for some classic network design problems under the power minimization criteria. Our main result is for the problem of finding a min-power subgraph that contains k internally-disjoint vs-paths from every node v to a given node s: we give a polynomial algorithm for directed graphs and a logarithmic approximation algorithm for undirected graphs. In contrast, we will show that the corresponding edge-connectivity problems are unlikely to admit even a polylogarithmic approximation. 相似文献
65.
Yuval Freed Leslie Banks-Sills 《Journal of the mechanics and physics of solids》2007,55(10):2157-2180
Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an SMA under plane strain conditions and mode I deformation is numerically investigated. A small-scale transformation zone is assumed. A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength t0 has a great influence on the toughening behavior of the material. Moreover, the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined. The effect of the Young's moduli ratio of the martensite and austenite phases is examined. 相似文献
66.
Stability of a two-dimensional (2-D) discrete system depends on whether a bivariate polynomial does not vanish in the closed exterior of the unit bi-circle. The paper shows a procedure that tests this 2-D stability condition by testing the stability of a finite collection of real univariate polynomials by a certain modified form of the author's one-dimensional (1-D) stability test. The new procedure is obtained by telepolation (interpolation) of a 2-D tabular test whose derivation was confined to using a real form of the underlying 1-D stability test. Consequently, unlike previous telepolation-based tests, the procedure requires the testing of real instead of complex univariate polynomials. The proposed test is the least-cost procedure to test 2-D stability with real polynomial 1-D stability tests and real arithmetic only. 相似文献
67.
The number of infinite clusters in dynamical percolation 总被引:2,自引:2,他引:0
Summary. Dynamical percolation is a Markov process on the space of subgraphs of a given graph, that has the usual percolation measure
as its stationary distribution. In previous work with O. H?ggstr?m, we found conditions for existence of infinite clusters
at exceptional times. Here we show that for ℤ
d
, with p>p
c
, a.s. simultaneously for all times there is a unique infinite cluster, and the density of this cluster is θ(p). For dynamical percolation on a general tree Γ, we show that for p>p
c
, a.s. there are infinitely many infinite clusters at all times. At the critical value p=p
c
, the number of infinite clusters may vary, and exhibits surprisingly rich behaviour. For spherically symmetric trees, we
find the Hausdorff dimension of the set T
k
of times where the number of infinite clusters is k, and obtain sharp capacity criteria for a given time set to intersect T
k
. The proof of this capacity criterion is based on a new kernel truncation technique.
Received: 5 May 1997 / In revised form: 24 November 1997 相似文献
68.
It is well known that there are planar sets of Hausdorff dimension greater than 1 which are graphs of functions, i.e., all
their vertical fibres consist of 1 point. We show this phenomenon does not occur for sets constructed in a certain “regular”
fashion. Specifically, we consider sets obtained by partitioning a square into 4 subsquares, discarding 1 of them and repeating
this on each of the 3 remaining squares, etc.; then almost all vertical fibres of a set so obtained have Hausdorff dimension
at least 1/2. Sharp bounds on the dimensions of sets of exceptional fibres are presented.
Partially supported by a grant from the Landau Centre for Mathematical Analysis. 相似文献
69.
Yuval Peres 《Israel Journal of Mathematics》1996,95(1):341-347
Say that a sequenceS
0, ..., Sn has a (global) point of increase atk ifS
k is maximal amongS
0, ..., Sk and minimal amongS
k, ..., Sn. We give an elementary proof that ann-step symmetric random walk on the line has a (global) point of increase with probability comparable to 1/logn. (No moment assumptions are needed.) This implies the classical fact, due to Dvoretzky, Erdős and Kakutani (1961), that Brownian
motion has no points of increase.
Research partially supported by NSF grant # DMS-9404391. 相似文献
70.
Critical stability constraints are a small set of conditions that are enough to maintain the stability of a system when some parameters are perturbed from a nominal stable setting. The paper uses a recently introduced efficient integer-preserving (IP) form of the Bistritz test to derive critical constraints for stability of discrete-time linear systems. The new procedure produces polynomial (rather than rational) constraints of particularly low degree whose variates are the free parameters (or the literal coefficients) of the system's characteristic polynomial. Comparison with the modified Jury test, also an efficient IP stability test, shows that the constraints are obtained with less computation and, more contributing to simplicity, the constraints appear as polynomials with degrees lower by a factor of two. 相似文献