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1.
Suppose that attached to each site z ∈ ? is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}z∈?, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of ?. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
2.
Miklos Ajtai James Aspnes Moni Naor Yuval Rabani Leonard J Schulman Orli Waarts 《Journal of Algorithms in Cognition, Informatics and Logic》1998,29(2):306-357
On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long-lived processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion ofdesiredload of a process, which is a function of the tasks it participates in. Theunfairnessof a system is the maximum, taken over all processes, of the difference between the desired load and the actual load.An example of such a setting is thecarpool problemsuggested by Fagin and Williams [IBM Journal of Research and Development27(2) (1983), 133–139]. In this problem, a set ofnpeople form a carpool. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a “fair” way.We investigate this problem under various assumptions on the input distribution. We also show that the carpool problems can capture several other problems of fairness in scheduling. 相似文献
3.
Yuval Z. Flicker 《Mathematische Annalen》1993,297(1):199-219
4.
We consider biased random walk on supercritical percolation clusters in ℤ2. We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random
walk has speed zero, while if the bias is small enough, the speed of the random walk is positive.
Received: 20 November 2002 / Revised version: 17 January 2003
Published online: 15 April 2003
Research supported by Microsoft Research graduate fellowship.
Research partially supported by the DFG under grant SPP 1033.
Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley.
Mathematics Subject Classification (2000): 60K37; 60K35; 60G50
Key words or phrases: Percolation – Random walk 相似文献
5.
Summary We prove the fundamental lemma for spherical functions with respect to the natural (induction) lifting fromPGL(2) toPGL(3) which appears as the unstable counterpart of the stable symmetric-square lifting fromSL(2) toPGL(3) (see [IV] for an introduction to this project, and [VI] for the final results). Thus spherical functions onPGL(2) andPGL(3) which correspond to each other by satisfying an elementary representation theoretic relation are shown to have matching orbital integrals. The proof of this local statement is based on an application of the global trace formula.Partially supported by NSF grants 相似文献
6.
Yuval Ne'eman 《Foundations of Physics》1996,26(5):575-583
Since 1961, the experimental exploration at the fundamental level of physical reality has surprised physists by revealing to them a highly geometric scenery. Like Einstein's (classical) theory of gravity, the standard model, describing the strong, weak, and electromagnetic interaction, testifies in favor of Plato's reported allegation. 相似文献
7.
In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented. 相似文献
8.
While flavor symmetries are useful for studying hadronic B decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ decays, where isospin breaking is shown to be negligible. (2) An SU(3) sum rule for pairs of B→Kπ and B→Kη8, generalized to pairs of B→Kπ, B→Kη and B→Kη′. 相似文献
9.
We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure. 相似文献
10.
We consider Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss model. It is well-known that the mixing-time in the high temperature regime (β < 1) has order n log n, whereas the mixing-time in the case β > 1 is exponential in n. Recently, Levin, Luczak and Peres proved that for any fixed β < 1 there is cutoff at time with a window of order n, whereas the mixing-time at the critical temperature β = 1 is Θ(n
3/2). It is natural to ask how the mixing-time transitions from Θ(n log n) to Θ(n
3/2) and finally to exp (Θ(n)). That is, how does the mixing-time behave when β = β(n) is allowed to tend to 1 as n → ∞. In this work, we obtain a complete characterization of the mixing-time of the dynamics as a function of the temperature,
as it approaches its critical point β
c
= 1. In particular, we find a scaling window of order around the critical temperature. In the high temperature regime, β = 1 − δ for some 0 < δ < 1 so that δ
2
n → ∞ with n, the mixing-time has order (n/δ) log(δ
2
n), and exhibits cutoff with constant and window size n/δ. In the critical window, β = 1± δ, where δ
2
n is O(1), there is no cutoff, and the mixing-time has order n
3/2. At low temperature, β = 1 + δ for δ > 0 with δ
2
n → ∞ and δ = o(1), there is no cutoff, and the mixing time has order .
Research of J. Ding and Y. Peres was supported in part by NSF grant DMS-0605166. 相似文献