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221.
Hamparsum Bozdogan Stanley L. Sclove 《Annals of the Institute of Statistical Mathematics》1984,36(1):163-180
Summary Multi-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaike's
Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used
in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC
is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors
and variance-covariance matrices. Numerical examples are presented for AIC and another criterion calledw-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives.
This research was supported by Office of Naval Research Contract N00014-80-C-0408, Task NR042-443 and Army Research Office
Contract DAAG 29-82-K-0155, at the University of Illinois at Chicago. 相似文献
222.
Representation theorem and local asymptotic minimax theorem are derived for nonparametric estimators of the distribution function on the basis of randomly truncated data. The convolution-type representation theorem asserts that the limiting process of any regular estimator of the distribution function is at least as dispersed as the limiting process of the product-limit estimator. The theorems are similar to those results for the complete data case due to Beran (1977, Ann. Statist., 5, 400–404) and for the censored data case due to Wellner (1982, Ann. Statist., 10, 595–602). Both likelihood and functional approaches are considered and the proofs rely on the method of Begun et al. (1983, Ann. Statist., 11, 432–452) with slight modifications.Division of Biostatistics, School of Public Health, Columbia Univ. 相似文献
223.
To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown meansμi's and unknown variancesσ2i's, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates ofμi's andσ2i's under the restriction and proposes an algorithm for obtaining the estimates. 相似文献
224.
An algorithm is presented for the design of optimal detection filters in radar and communications systems, subject to inequality constraints on the maximum output sidelobe levels. This problem was reduced in an earlier paper (Ref. 1) to an unconstrained one in the dual space of regular Borel measures, with a nondifferentiable cost functional. Here, the dual problem is solved via steepest descent, using the directional Gateaux differential. The algorithm is shown to be convergent, and numerical results are presented.This research was supported by the Australian Research Grants Committee. 相似文献
225.
The catenary form of loss function is considered in the framework of Bayesian decision theory. The mathematical tractability of this form seems to be unrecognized; it contains quadratic loss as a limiting case. For various probability distributions expressions are given for posterior analysis, and limiting properties are investigated. 相似文献
226.
For a simple multivariate regression model, nonparametric estimation of the (vector of) intercept following a preliminary test on the regression vector is considered. Along with the asymptotic distribution of these estimators, their asymptotic bias and dispersion matrices are studied and allied efficiency results are presented. 相似文献
227.
228.
考虑随机系数自回归模型Yt =Φtyt-1+ ut,其中 Φt为随机系数,ut为随机误差。在允许Φt与ut相依以及Eut无穷的条件下,构造了误差方差的自加权估计,并证明了该估计的渐近正态性。最后通过数值模拟,说明
自加权估计的稳健和有效性。 相似文献
229.
The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed. 相似文献
230.
J Kleffe 《Journal of multivariate analysis》1979,9(3):442-451
The paper deals with optimal quadratic unbiased estimation of the unknown dispersion matrix in multivariate regression models without assuming normality of the errors. We show that Hsu's theorem for univariate regression models continues to multivariate models with no additional assumptions. Furthermore optimal quadratic plus linear estimating functions for regression coefficients are considered, and we investigate whether the ordinary linear estimates are the best. This leads to a new theorem which is similar to that of Hsu. 相似文献