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251.
Algebraic geometry of Gaussian Bayesian networks 总被引:1,自引:0,他引:1
Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. In the case when the underlying graph is a tree, we show that the vanishing ideal of the model is generated by the conditional independence statements implied by graph. We also show that the ideal of any Bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables. This has a number of important consequences for hidden variable models. Finally, we relate the ideals of Bayesian networks to a number of classical constructions in algebraic geometry including toric degenerations of the Grassmannian, matrix Schubert varieties, and secant varieties. 相似文献
252.
In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration
relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks
against wide cointegrating alternatives including monotonic nonlinearities and certain types of level shifts in the cointegration
relationship. We call our testing device the induced-order Kolmogorov–Smirnov cointegration test (KS), since it is constructed
from the induced-order statistics of the series, and we derive its limiting distribution. This non-parametric statistic endows
the test with a number of desirable properties: invariance to monotonic transformations of the series, and robustness for
the presence of important parameter shifts. By Monte Carlo simulations we analyze the small sample properties of this test.
Our simulation results show the robustness of the induced order cointegration test against departures from linear and constant
parameter models.
This paper is an extension of the work of Aparicio and Granger (1995) and Aparicio and Escribano (1998). 相似文献
253.
In this article, the effect of the space dimensions on the generalized hydrogen-atom specific heat in the generalized Boltzmann-Gibbs
statistics is studied. The temperature dependence of the specific heat for a few different values of q and for different low space dimensions using Tsallis statistics is numerically calculated. The results indicate that for
a fixed value of q, as the space dimension increases the temperature range where the specific heat has a nonzero value, decreases, while the
general behavior of the specific heat does not show any change. Also, there exits a q-independent quantity related to two specific temperatures of the system which is almost linearly dependent on the space dimensions. 相似文献
254.
V. Korepin N. Slavnov 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):555-557
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional
Bose gas and XXZ Heisenberg quantum spin chain.
Received: 4 December 1997 / Accepted: 17 March 1998 相似文献
255.
In this paper a polynomial algorithm called the Minram algorithm is presented which finds a Hamiltonian Path in an undirected graph with high frequency of success for graphs up to 1000 nodes. It first reintroduces the concept described in [13] and then explains the algorithm. Computational comparison with the algorithm by Posa [10] is given.It is shown that a Hamiltonian Path is a spanning arborescence with zero ramification index. Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence. By suitable pivots it locates a locally minimal value of the ramification index. If this local minima corresponds to zero ramification index then the algorithm is considered to have ended successfully, else a failure is reported.Computational performance of the algorithm on randomly generated Hamiltonian graphs is given. The random graphs used as test problems were generated using the procedure explained in Section 6.1. Comparison with our version of the Posa algorithm which we call Posa-ran algorithm [10] is also made. 相似文献
256.
It is proved that the correlation coefficient between the elements of the order statistics is maximal for a rectangularly (uniformly) distributed population. 相似文献
257.
Kenneth S. Kaminsky Lennart S. Rhodin 《Annals of the Institute of Statistical Mathematics》1985,37(1):507-517
The principle of maximum likelihood is applied to the joint prediction and estimation of a future random variable and an unknown
parameter. We assume dependence between present and future, and the approach is non-Bayesian. Our principal application is
to the prediction of higher order statistics from lower ones in Type II censored random samples. Some simple criteria for
existence and uniqueness of the predictor are given for this situation and the methods are illustrated with several examples. 相似文献
258.
Nonparametric global optimization methods have been developed that determine the location of their next guess based on the rank-transformed objective function evaluations rather than the actual function values themselves. Another commonly-used transformation in nonparametric statistics is the normal score transformation. This paper applies the normal score transformation to the multi-univariate method of global optimization. The benefits of the new method are shown by its performance on a standard set of global optimization test problems. The normal score transformation yields a method that gives equivalent searches for any monotonic transformation of the objective function. 相似文献
259.
Eitan Zemel 《Annals of Operations Research》1984,1(3):215-238
We analyze the behaviour of thek center and median problems forn points randomly distributed in an arbitrary regionA ofR d . Under a mild assumption on the regionA, we show that fork≦k(n)=o(n/logn), the objective function values of the discrete and continuous versions of these problems are equal to each otheralmost surely. For the two-dimensional case, both these problems can be solved by placing the centers or medians in an especially simple regular hexagonal pattern (the ‘honeycomb heuristic’ of Papadimitriou). This yields the exact asymptotic values for thek center and median problem, namely, α(|A|/k)1/2 and β(|A|/k)1/2, where |A| denotes the volume ofA, α and β are known constants, and the objective of the median problem is given in terms of the average, rather than the usual total, distance. For the 3- and 4-dimensional case, similar results can be obtained for the center problem to within an accuracy of roughly one percent. As a by-product, we also get asymptotically optimal algorithms for the 2-dimensionalp-normk median problem and for the twin problems of minimizing the maximum number of vertices served by any center and similarly for maximizing the minimum. 相似文献
260.
Murray D. Burke 《Journal of multivariate analysis》1977,7(4):491-511
The recently developed strong approximation methods are discussed and applied to the problem of testing whether two independent multivariate samples come from the same population and whether the components of the observations are independent. The usual Cramér-von Mises statistic, as well as one based on the difference between the sum of the two multivariate EDF's and twice the product of the marginal EDF's of one, are studied. A fairly sensitive integral statistic is also discussed. Consistency and some asymptotic power properties are explored. Emphasis is placed on explication of the strong approximation methodology. 相似文献