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91.
Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes. It is also a generalisation of 1D Drossel–Schwabl forest-fire model. A solution of the set of equations describing stationary state of Random Domino Automaton in inverse-power case is presented. A link with Motzkin numbers allows to present explicit form of asymptotic behaviour of the automaton.  相似文献   
92.
This paper aims to investigate the direct relationship between inflation and inflation uncertainty by employing a dynamic method for the monthly country–region–place United States data for the time period 1976–2007. While the bulk of previous studies has employed GARCH models in investigating the link between inflation and inflation uncertainty, in this study Stochastic Volatility in Mean models are used to capture the shocks to inflation uncertainty within a dynamic framework. These models allow researchers to assess the dynamic effects of innovations in inflation as well as inflation volatility on inflation and inflation volatility over time, by incorporating the unobserved volatility as an explanatory variable in the mean (inflation) equation. Empirical findings suggest that innovations in inflation volatility increases inflation. This evidence is robust across various definitions of inflation and different sub-periods.  相似文献   
93.
Real-world networks are characterized by common features, including among others a scale-free degree distribution, a high clustering coefficient and a short typical distance between nodes. These properties are usually explained by the dynamics of edge and node addition and deletion.  相似文献   
94.
The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.  相似文献   
95.
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold md) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. The triggering efficiency of earthquakes is assumed to vanish below a lower magnitude limit m0, in order to ensure the convergence of the theory and may reflect the physics of state-and-velocity frictional rupture. We show that, to a good approximation, the statistical distribution of seismic rates of events with magnitudes above md generated by an ETAS model with branching ratio n is the same as that of events generated by another ETAS model with effective parameter n(md). Our present analysis thus confirms, for the full statistical (time-independent or large time-window approximation) properties, the results obtained previously by one of us and Werner, based solely on the average seismic rates (the first-order moment of the statistics). Our analysis also demonstrates that this correspondence is not exact, as there are small corrections which can be systematically calculated, in terms of additional contributions that can be mapped onto a different branching model. We also show that this approximate correspondence of the ETAS model onto itself obtained by changing m0 into md, and n into n(md) holds only with respect to its statistical properties and not for all its space-time properties.  相似文献   
96.
I. Mazilu  G. Zamora  J. Gonzalez 《Physica A》2010,389(3):251-427
In this paper, we use random walk theory to describe the length dynamics of microtubules, one of the principal components of the cytoskeleton. We present a simple two-state model (growing and shrinking) of microtubule length evolution that incorporates a variable rate of switching between the states. Using the generating function technique, we calculate the mean length of microtubule, its variance and diffusion coefficient. We also report analytical and computer simulation results for the mean number of positive monomers in microtubule, and find good qualitative agreement with experimental data.  相似文献   
97.
We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.  相似文献   
98.
We consider the problem of option pricing when the underlying asset follows a general semimartingale process. After reviewing the foundations of arbitrage pricing theory for semimartingales and the link with Lévy processes, we introduce a general method to price options in this framework based on Fourier and Wavelet analysis. Received 4 September 2000  相似文献   
99.
Motivated by the probabilistic methods for nonlinear differential equations introduced by McKean (1975) for the Kolmogorov-Petrovski-Piskunov (KPP) equation, and by Le Jan and Sznitman (1997) for the incompressible Navier-Stokes equations (NSE), we identify a new class of stochastic cascade models, referred to as doubly stochastic Yule cascades. We establish non-explosion criteria under the assumption that the randomization of Yule intensities from generation to generation is by an ergodic time-reversible Markov process. In addition to the cascade models that arise in the analysis of certain deterministic nonlinear differential equations, this model includes the multiplicative branching random walks, the branching Markov processes, and the stochastic generalizations of the percolation and/or cell ageing models introduced by Aldous and Shields (1988) and independently by Athreya (1985).  相似文献   
100.
In this paper, we discuss an application of the Stochastic Dual Dynamic Programming (SDDP) type algorithm to nested risk-averse formulations of Stochastic Optimal Control (SOC) problems. We propose a construction of a statistical upper bound for the optimal value of risk-averse SOC problems. This outlines an approach to a solution of a long standing problem in that area of research. The bound holds for a large class of convex and monotone conditional risk mappings. Finally, we show the validity of the statistical upper bound to solve a real-life stochastic hydro-thermal planning problem.  相似文献   
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