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1.
朱俊黎泽 《应用数学》2021,34(2):477-488
本文研究具有随机扰动的哈密顿系统的重现现象,尤其是轨道随机周期变差解和近不变环面解.具体来说,对线性薛定谔方程,我们完整阐述了随机周期变差解何时存在;对随机扰动的近可积哈密顿系统,我们证明了近不变环面的存在性与驱动噪声对应的哈密顿函数的对合性相关.  相似文献   
2.
In the absence of a general theory of diffusions on non-integrable distributions, an important role is played by the investigation of some particular examples. This paper deals with a couple of these type of examples. The first one is the Heisenberg diffusion, which is a degenerate diffusion with non-holonomic constraints living on the horizontal distribution of the Heisenberg group. The paper proves the transience property of the Heisenberg diffusion for small balls. The second example is the Grushin diffusion, also a degenerate diffusion, which moves in the plane along the Grushin distribution. We prove the transience property of this diffusion.  相似文献   
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We classify the possible behaviors of a class of one-dimensional stochastic recurrent growth models. In our main result, we obtain nearly optimal bounds for the tail of hitting times of some compact sets. If the process is an aperiodic irreducible Markov chain, we determine whether it is null recurrent or positive recurrent and in the latter case, we obtain a subgeometric convergence of its transition kernel to its invariant measure. We apply our results in particular to state-dependent Galton–Watson processes and we give precise estimates of the tail of the extinction time.  相似文献   
5.
We consider a dynamically-consistent analytical model of a 3D topographic vortex. The model is governed by equations derived from the classical problem of the axisymmetric Taylor–Couette flow. Using linear expansions, these equations can be reduced to a differential sixth-order equation with variable coefficients. For this differential equation, we formulate a boundary value problem, which has a number of issues for numerical solving. To avoid these issues and find the eigenvalues and eigenfunctions of the boundary value problem, we suggest a modification of the invariant imbedding method (the Riccati equation method). In this paper, we show that such a modification is necessary since the boundary conditions possess singular matrices, which sufficiently complicate the derivation of the Riccati equation. We suggest algebraic manipulations, which permit the initial problem to be reduced to a problem with regular boundary conditions. Also, we propose a method for obtaining a numerical solution of the matrix Riccati equation by means of recurrence relations, which allow us to obtain a matrizer converging to the required eigenfunction. The suggested method is tested by calculating the corresponding eigenvalues and eigenfunctions, and then, by constructing fluid particle trajectories on the basis of the eigenfunctions.  相似文献   
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We show using nonlinear time series analysis that the timing of trades in foreign exchange markets has significant information. We apply a set of methods for analyzing point process data developed in neuroscience and nonlinear science. Our results imply that foreign exchange markets might be chaotic and have short-term predictability.  相似文献   
8.
We analyze the transience, recurrence, and irreducibility properties of general sub-Markovian resolvents of kernels and their duals, with respect to a fixed sub-invariant measure m. We give a unifying characterization of the invariant functions, revealing the fact that an Lp-integrable function is harmonic if and only if it is harmonic with respect to the weak dual resolvent. Our approach is based on potential theoretical techniques for resolvents in weak duality. We prove the equivalence between the m-irreducible recurrence of the resolvent and the extremality of m in the set of all invariant measures, and we apply this result to the extremality of Gibbs states. We also show that our results can be applied to non-symmetric Dirichlet forms, in general and in concrete situations. A second application is the extension of the so called Fukushima ergodic theorem for symmetric Dirichlet forms to the case of sub-Markovian resolvents of kernels.  相似文献   
9.

For a R d -valued sequence of martingale differences { m k } k S 1 , we obtain a moderate deviation principle for the sequence of partial sums { Z n ( t ) 1 ~ k =1 [ nt ] m k / b n , t ] [0,1]}, in the space of càdlàg functions equipped with the Skorohod topology, under the following conditions: a Chen-Ledoux type condition, an exponential convergence in probability of the associated quadratic variation process of the martingale, and a condition of "Lindeberg" type. For the small jumps of Z n (·), we apply the general result of Puhalskii [Puhalskii, A. (1994). "Large deviations of semimartingales via convergence of the predictable characteristics". Stoch. Stoch. Rep. , 49 , pp. 27-85]. Following the method of Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280] and Arcones [Arcones, A. (1999). "The large deviation principle for stochastic processes", Submitted for publication], we prove that the large jumps part of Z n (·) is negligible in the sense of the moderate deviations. One can regard our result as an extension to martingale differences, of the beautiful characterization of moderate deviations for i.i.d.r.v. case due to Chen [Chen, X. (1991). "The moderate deviations of independent vectors in Banach space". Chin. J. Appl. Probab. Stat. , 7 , pp. 124-32] and Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280]. Using the Gordin [Gordin, M.I. (1969). "The central limit theorem for stationary processes". Soviet Math. Dokl. , 10 , pp. 1174-1176] decomposition, the martingale result is applied to prove the moderate deviation principle for a wide class of stationary { -mixing sequences of random variables.  相似文献   
10.
The Debye-series decomposition is of importance for understanding of light scattering features and for the validity of the geometrical optics approximation to light scattering. The numerical stability and accuracy for calculating light scattering with Debye series is studied and an improved algorithm is proposed in this work. The ratios of the Riccati-Bessel functions and the logarithmic derivatives of the Riccati-Bessel functions are employed and calculated with proper recurrences. Exemplifying results are provided to show the improvement of the algorithm.  相似文献   
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