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排序方式: 共有334条查询结果,搜索用时 15 毫秒
61.
Joel Friedman Antoine Joux Yuval Roichman Jacques Stern Jean-Pierre Tillich 《Random Structures and Algorithms》1998,12(4):335-350
We prove that for every r and d≥2 there is a C such that for most choices of d permutations π1, π2,…,πd of Sn, the following holds: for any two r-tuples of distinct elements in {1,…,n}, there is a product of less than C log n of the πis which map the first r-tuple to the second. Although we came across this problem while studying a rather unrelated cryptographic problem, it belongs to a general context of which random Cayley graph quotients of Sn are good expanders. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12: 335–350, 1998 相似文献
62.
63.
The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous
to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than our
earlier work (Levine and Peres, Indiana Univ Math J 57(1):431–450, 2008). For the shape consisting of sites, where ω
d
is the volume of the unit ball in , we show that the inradius of the set of occupied sites is at least r − O(logr), while the outradius is at most r + O(r
α
) for any α > 1 − 1/d. For a related model, the divisible sandpile, we show that the domain of occupied sites is a Euclidean ball with error in the radius a constant independent of the total
mass. For the classical abelian sandpile model in two dimensions, with n = πr
2 particles, we show that the inradius is at least , and the outradius is at most . This improves on bounds of Le Borgne and Rossin. Similar bounds apply in higher dimensions, improving on bounds of Fey and
Redig.
Yuval Peres is partially supported by NSF grant DMS-0605166. 相似文献
64.
In the heat-bath Glauber dynamics for the Ising model on the lattice, physicists believe that the spectral gap of the continuous-time
chain exhibits the following behavior. For some critical inverse-temperature β
c
, the inverse-gap is O(1) for β < β
c
, polynomial in the surface area for β = β
c
and exponential in it for β > β
c
. This has been proved for
\mathbbZ2{\mathbb{Z}^2} except at criticality. So far, the only underlying geometry where the critical behavior has been confirmed is the complete
graph. Recently, the dynamics for the Ising model on a regular tree, also known as the Bethe lattice, has been intensively
studied. The facts that the inverse-gap is bounded for β < β
c
and exponential for β > β
c
were established, where β
c
is the critical spin-glass parameter, and the tree-height h plays the role of the surface area.
In this work, we complete the picture for the inverse-gap of the Ising model on the b-ary tree, by showing that it is indeed polynomial in h at criticality. The degree of our polynomial bound does not depend on b, and furthermore, this result holds under any boundary condition. We also obtain analogous bounds for the mixing-time of
the chain. In addition, we study the near critical behavior, and show that for β > β
c
, the inverse-gap and mixing-time are both exp[Θ((β − β
c
)h)]. 相似文献
65.
Olefin metathesis catalysed by ruthenium has emerged at the frontier of modern synthetic chemistry. The desire to enhance catalyst stability, gain control over the catalytic process and deepen the understanding of the mechanisms of metathesis has yielded a class of latent ruthenium precatalysts of delayed initiation and with switchable activity. One of the main methodologies developed for this purpose has been the introduction of tethered carbene ligands. Herein we track the evolution of ruthenium based metathesis catalysts bearing chelated alkylidenes, from the early oxygen Hoveyda type benzylidenes to the latent sulphur containing complexes. 相似文献
66.
Denote by µ a the distribution of the random sum \((1 - a)\sum\nolimits_{j = 0}^\infty {{w_j}{a^j}} \), where P(ω j = 0) = P(ω j = 1) = 1/2 and all the choices are independent. For 0 < a < 1/2, the measure µ a is supported on C a , the central Cantor set obtained by starting with the closed united interval, removing an open central interval of length (1 ? 2a), and iterating this process inductively on each of the remaining intervals. We investigate the convolutions µ a * (µ b ° S λ ?1 ), where S λ (x) = λx is a rescaling map. We prove that if the ratio log b/ log a is irrational and λ ≠ 0, then , where D denotes any of correlation, Hausdorff or packing dimension of a measure.
We also show that, perhaps surprisingly, for uncountably many values of λ the convolution µ1/4* (µ1/3 ° S λ ?1 ) is a singular measure, although dim H (C 1/4) + dim H (C 1/3) > 1 and log(1/3)/ log(1/4) is irrational. 相似文献
$D({\mu _a} * ({\mu _b} \circ S_\lambda ^{ - 1})) = \min ({\dim _H}({C_a}) + {\dim _H}({C_b}),1)$
67.
Yuval Freed Leslie Banks-Sills Jacob Aboudi 《Journal of the mechanics and physics of solids》2008,56(10):3003-3020
In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t0 and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t0, as well as the fiber volume fraction are examined. 相似文献
68.
Kinney and Pitcher (1966) determined the dimension of measures on [0, 1] which make the digits in the continued fraction expansion
i.i.d. variables. From their formula it is not clear that these dimensions are less than 1, but this follows from the thermodynamic
formalism for the Gauss map developed by Walters (1978). We prove that, in fact, these dimensions are bounded by 1−10−7. More generally, we considerf-expansions with a corresponding absolutely continuous measureμ under which the digits form a stationary process. Denote byE
δ the set of reals where the asymptotic frequency of some digit in thef-expansion differs by at leastδ from the frequency prescribed byμ. ThenE
δ has Hausdorff dimension less than 1 for anyδ>0. 相似文献
69.
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
70.
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