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71.
Aloisio Pessoa de Araujo 《Journal of multivariate analysis》1977,7(1):220-222
We prove that integrability of the norm is the best sufficient condition in terms of integrability of functions of the norm for a positive measure to be a Lévy Measure in C[0, 1]. 相似文献
72.
Peter Reimann 《Journal of statistical physics》1996,85(3-4):403-425
The escape rate for one-dimensional noisy maps near a crisis is investigated. A previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise, including multiplicative white noise as a special case. For single-humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived. It predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order. A simple heuristic explanation of this effect is given. The escape rate is discussed in detail for noise distributions of Lévy, dichotomous, and exponential type. In the latter case, the rate is dominated by an exponentially leading Arrhenius factor in the deep precritical regime. However, the preexponential factor may still depend more strongly than any power law on the noise strength. 相似文献
73.
Two methods for symmetrizing Markov processes are discussed. Letu
a(x, y) be the potential density of a Lévy process on a compact Abelian groupG. A general condition is given that guarantees thatv(x, y)=ua(x, y)+ua(y, x) is the potential density of a symmetric Lévy process onG. The second method arises by considering the linear space of one-potentialsU
1
f, withf inL
2, endowed with the inner product (U
1
f,U
1
g)=fU
1
g+gU
1
f. If the semigroup ofX(t) is normal, then the completionH of this space is the Dirichlet space of a symmetric processY(t). A set that is semipolar forX(t) is polar forY(t). 相似文献
74.
We study asymmetric polling systems where: (i) the incoming workflow processes follow general Lévy-subordinator statistics; and, (ii) the server attends the channels according to the gated service regime, and incurs random inter-dependentswitchover times when moving from one channel to the other. The analysis follows a dynamical-systems approach: a stochastic Poincaré map, governing the one-cycle dynamics of the polling system is introduced, and its statistical characteristics are studied. Explicit formulae regarding the evolution of the mean, covariance, and Laplace transform of the Poincaré map are derived. The forward orbit of the maps transform – a nonlinear deterministic dynamical system in Laplace space – fully characterizes the stochastic dynamics of the polling system. This enables us to explore the long-term behavior of the system: we prove convergence to a (unique) steady-state equilibrium, prove the equilibrium is stationary, and compute its statistical characteristics. 相似文献
75.
S?ren?AsmussenEmail author Mats?Pihlsg?rd 《Methodology and Computing in Applied Probability》2005,7(4):439-457
This paper deals with queues and insurance risk processes where a generic service time, resp. generic claim, has the form
U ∧ K for some r.v. U with distribution B which is heavy-tailed, say Pareto or Weibull, and a typically large K, say much larger than
. We study the compound Poisson ruin probability ψ(u) or, equivalently, the tail
of the M/G/1 steady-state waiting time W. In the first part of the paper, we present numerical values of ψ(u) for different values of K by using the classical Siegmund algorithm as well as a more recent algorithm designed for heavy-tailed claims/service times,
and compare the results to different approximations of ψ(u) in order to figure out the threshold between the light-tailed regime and the heavy-tailed regime. In the second part, we
investigate the asymptotics as K → ∞ of the asymptotic exponential decay rate γ = γ
(K) in a more general truncated Lévy process setting, and give a discussion of some of the implications for the approximations.
AMS 2000 Subject Classification Primary 68M20, Secondary 60K25
†Partially supported by MaPhySto—A Network in Mathematical Physics and Stochastics, founded by the Danish National Research
Foundation.
An erratum to this article is available at . 相似文献
76.
A.M. Reynolds 《Physica A》2010,389(21):4740-4746
Some foragers have movement patterns that can be approximated by Lévy walks whilst others may be better represented as composite Brownian walks. Many attempts have been made to interpret these movement patterns in terms of optimal searching strategies for the location of randomly and sparsely distributed targets. Here it is shown that the relative merits of Lévy walk and composite Brownian walk searches are sensitively dependent upon target encounter dynamics which set the initial conditions for an extensive search. It is suggested these initial conditions are determined, at least in part, by the competing demands of harvesting and safety from predation. In accordance with observations, it is shown that Lévy walks are expected in tritrophic systems and where intraguild predation operates. Composite Brownian walks, on the other hand, are found to be advantageous when the risk of predation is low. Despite having fundamentally different properties, Lévy walks and composite Brownian walks can therefore compete a priori as possible models of animal movements. Throughout, attention is focused on searching for randomly and sparsely distributed resources that are not depleted or rejected once located but instead remain targets for future searches. We re-evaluate and overturn the widely held belief that in numerical simulations this ‘non-destructive’ searching scenario can faithfully and consistently represent destructive searching for patchily distributed resources, i.e. for resources that tend to occur in clusters rather than in isolation. 相似文献
77.
《Mathematische Nachrichten》2018,291(2-3):374-397
Under some mild assumptions on the Lévy measure and the symbol we obtain gradient estimates of Dirichlet heat kernels for pure‐jump isotropic unimodal Lévy processes in . 相似文献
78.
In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic Lévy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise asymptotic behaviors of the tail probability of subordinators when the scaling order is between 0 and 1 including 1.The asymptotic expressions are given in terms of the radial part of characteristic exponent and its derivative. In particular, when varies regularly, as the tail probability is asymptotically equal to a constant times 相似文献
79.
The asymptotic behavior of expectations of some exponential functionals of a Lévy process is studied. The key point is the observation that the asymptotics only depend on the sample paths with slowly decreasing local infimum. We give not only the convergence rate but also the expression of the limiting coefficient. The latter is given in terms of some transformations of the Lévy process based on its renewal function. As an application, we give an exact evaluation of the decay rate of the survival probability of a continuous-state branching process in random environment with stable branching mechanism. 相似文献
80.
This paper considers the martingale problem for a class of weakly coupled Lévy type operators. It is shown that under some mild conditions, the martingale problem is well-posed and uniquely determines a strong Markov process . The process , called a regime-switching jump diffusion with Lévy type jumps, is further shown to possess Feller and strong Feller properties under non-Lipschitz conditions via the coupling method. 相似文献