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91.
The problem of estimating of the law
(in the space
of the paths) and the common marginal distribution for a strictly stationary ergodic process X is discussed. We show, in particular, that:(1) The empirical measure
with probability 1 converges weakly in
to
.(2) The empirical measure
corresponding to the path
, converges a.s. when T in total variation to the marginal law if and only if the local time for X exists. (3) The L
p-convergence of the empirical densities f
T to the marginal one is studied.(4) A version of the CLT for empirical densities f
T provided both the mixing properties and the local time of the underlying process are good enough is given. 相似文献
92.
Cristian E. Gutié rrez Qingbo Huang 《Transactions of the American Mathematical Society》2000,352(9):4381-4396
In this paper we establish several geometric properties of the cross sections of generalized solutions to the Monge-Ampère equation , when the measure satisfies a doubling property. A main result is a characterization of the doubling measures in terms of a geometric property of the cross sections of . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.
93.
On the Distribution of Long-Term Time Averages on Symbolic Space 总被引:2,自引:0,他引:2
The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in
d
are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results. 相似文献
94.
In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures.
This role has two main aspects, the distinction between which has not always been fully clear: 1) From disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study
of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical
interest. 2) Of disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We
discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version
of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field
non-Gibbsian properties. 相似文献
95.
Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable. 相似文献
96.
Piotr Gwiazda 《Mathematical Methods in the Applied Sciences》2005,28(18):2201-2223
This paper concerns measure‐valued solutions for the two‐dimensional granular avalanche flow model introduced by Savage and Hutter. The system is similar to the isentropic compressible Euler equations, except for a Coulomb–Mohr friction law in the source term. We will partially follow the study of measure‐valued solutions given by DiPerna and Majda. However, due to the multi‐valued nature of the friction law, new more sensitive measures must be introduced. The main idea is to consider the class of x‐dependent maximal monotone graphs of non‐single‐valued operators and their relation with 1‐Lipschitz, Carathéodory functions. This relation allows to introduce generalized Young measures for x‐dependent maximal monotone graph. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
97.
The traditional way of employing operational research in organisational interventions has been the expert mode. In this mode, the problem situation faced by the client is given to the operational research consultant, who then builds a model of the situation, solves the model to arrive at an optimal (or quasi-optimal) solution, and then provides a recommendation to the client based on the obtained solution. An alternative mode of engagement is to conduct the whole intervention together with the client: from structuring and defining the nature of the problem situation of interest, to supporting the evaluation of priorities and development of plans for subsequent implementation. In this latter mode, the operational researcher works throughout the intervention not only as an analyst, but also as a facilitator to the client. This paper discusses this latter mode of engagement with clients, with particular emphasis on the use of facilitated modelling as the intervention tool. Drawing on research scattered across a range of publications and domains, the review presented here provides a formal definition of facilitated modelling, together with a general framework that allows the conceptualisation of a wide variety of facilitated modelling approaches to organisational intervention. Design issues in facilitated modelling and their practical implication are discussed, and directions for future research identified. 相似文献
98.
Marcia Salzano 《Journal of statistical physics》1999,97(3-4):817-826
We continue our study of the ergodic behavior of the contact process on infinite connected graphs of bounded degree. Examples are provided of trees on which, as the infection parameter increases, complete convergence alternates between holding and failing infinitely many times. 相似文献
99.
100.
Wolfgang Kreitmeier 《Mathematische Nachrichten》2008,281(9):1307-1327
For a large class of dyadic homogeneous Cantor distributions in ?, which are not necessarily self‐similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non‐existence of the quantization coefficient. The class contains all self‐similar dyadic Cantor distributions, with contraction factor less than or equal to 1/3. For these distributions we calculate the quantization errors explicitly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献