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191.
Hisayuki Tsukuma 《Annals of the Institute of Statistical Mathematics》2003,55(3):447-466
The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which
can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and give unbiased estimate
of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution.
From the unbiased estimate of risk, it is shown that a shrinkage estimator improves on the classical estimator under the loss
function. Furthermore, from the extended Stein and Stein-Haff identities for our elliptically contoured distribution, the
above result under normal errors is extended to the estimation problem under elliptical errors. We show that the shrinkage
estimator obtained under normal models is better than the classical estimator under elliptical errors with the above loss
function and hence we establish the robustness of the above shrinkage estimator. 相似文献
192.
The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion.
In particular, we investigate the expected Hamming weight of the NAF of an n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the covariance of the Hamming weights of the binary expansion and the NAF is computed.
Asymptotically, these Hamming weights become independent and normally distributed.
Communicated by Attila Pethő 相似文献
193.
Geoffrey S Watson 《Journal of multivariate analysis》1984,14(1):74-82
The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp κμ′x, where x and the modal vector μ are unit vectors in q. κ (≥0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when κ1,…,κm are known but tend to infinity, and are unknown but equal to κ which tends to infinity. The three null hypotheses are H01:μ = μ0(m=1), H02:μ1 = … =μm, H03:μi?V, i=1,…,m In each case a sequence of alternatives is taken tending to the null hypothesis. 相似文献
194.
We give a general result to characterize a multivariate distribution from a relationship between the left truncated mean function
and the hazard gradient function. This result allows us to obtain new characterizations of multivariate distributions. In
particular, we show that, for the multivariate normal distribution, the simple relationship, obtained in standardized form
by McGill (1992,Communications in Statistics. Theory Methods,21(11), 3053–3060), actually characterizes the multivariate normal distribution.
Supported by Ministerio de Ciencia y Tecnologia under grant BFM2000-0362. 相似文献
195.
Piecewise polynomial,positive definite and compactly supported radial functions of minimal degree 总被引:23,自引:0,他引:23
Holger Wendland 《Advances in Computational Mathematics》1995,4(1):389-396
We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind. 相似文献
196.
In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the direct approximationtheorem. 相似文献
197.
Yasunori Fujikoshi Takafumi Noguchi Megu Ohtaki Hirokazu Yanagihara 《Annals of the Institute of Statistical Mathematics》2003,55(3):537-553
This paper is concerned with cross-validation (CV) criteria for choice of models, which can be regarded as approximately unbiased
estimators for two types of risk functions. One is AIC type of risk or equivalently the expected Kullback-Leibler distance
between the distributions of observations under a candidate model and the true model. The other is based on the expected mean
squared error of prediction. In this paper we study asymptotic properties of CV criteria for selecting multivariate regression
models and growth curve models under the assumption that a candidate model includes the true model. Based on the results,
we propose their corrected versions which are more nearly unbiased for their risks. Through numerical experiments, some tendency
of the CV criteria will be also pointed. 相似文献
198.
Thomas Mikosch 《Extremes》2006,9(1):3-20
“But he does not wear any clothes” said the little child in Hans Christian Andersen’s “The Emperor’s New Clothes.”Mikosch’s research is partially supported by the Danish Research Council (SNF) GrantNo 21-04-0400. This is a discussion paper which was initiated at the 4th InternationalConference on Extreme Value Analysis in Gothenburg, 15–19 August, 2005; see. 相似文献
199.
We present the score and Wald test analogues to Srivastava's (1985, Comm. Statist. A—Theory Methods, 14, 775–792) likelihood ratio tests for the multivariate growth curve model with missing data, and illustrate their use with data from an immunotherapy experiment (Fukushima et al. (1982, Int. J. Cancer, 29, 107–112, 113–117)). 相似文献
200.
In P.L.Hsu(1941),the proof of the basic Lemma 3 is basedon Lemma 1 which is wrong.The aim of this note is to correct the proof ofLemma 3,consequently,to ensure the main theorem in P.L.Hsu(1941). 相似文献