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81.
It is shown that the finite linear least-squares predictor of a multivariate stationary process converges to its Kolmogorov-Wiener predictor at an exponential rate, provided that the entries of its spectral density matrix are smooth functions. Also, the same rate of convergence holds for the partial sums of the Kolmogorov-Wiener predictor. 相似文献
82.
Arthur Cohen Harold B. Sackrowitz 《Annals of the Institute of Statistical Mathematics》1990,42(4):623-636
The problem of estimating the probability of unobserved outcomes or, as it is sometimes called, the conditional probability
of a new species, is studied. Good's estimator, which is essentially the same as Robbins' estimator, namely the number of
singleton species observed divided by the sample size, is studied from a decision theory point of view. The results obtained
are as follows: (1) When the total number of different species is assumed bounded by some known number, Good's and Robbins'
estimators are inadmissible for squared error loss. (2) If the number of different species can be infinite, Good's and Robbins'
estimators are admissible for squared error loss. (3) Whereas Robbins' estimator is a UMVUE for theunconditional probability of a new species obtained in one extra sample point, Robbins' estimator is not a uniformly minimum mean squared
error unbiased estimator of the conditional probability of a new species. This answers a question raised by Robbins. (4) It
is shown that for Robbins' model and squared error loss, there are admissible Bayes estimators which do not depend only on
a minimal sufficient statistic. A discussion of interpretations and significance of the results is offered.
Research supported by NSF Grant DMS-88-22622. 相似文献
83.
Yuzo Maruyama William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):157-165
This paper develops necessary conditions for an estimator to dominate the James-Stein estimator and hence the James-Stein
positive-part estimator. The ultimate goal is to find classes of such dominating estimators which are admissible. While there
are a number of results giving classes of estimators dominating the James-Stein estimator, the only admissible estimator known
to dominate the James-Stein estimator is the generalized Bayes estimator relative to the fundamental harmonic function in
three and higher dimension. The prior was suggested by Stein and the domination result is due to Kubokawa. Shao and Strawderman
gave a class of estimators dominating the James-Stein positive-part estimator but were unable to demonstrate admissiblity
of any in their class. Maruyama, following a suggestion of Stein, has studied generalized Bayes estimators which are members
of a point mass at zero and a prior similar to the harmonic prior. He finds a subclass which is minimax and admissible but
is unable to show that any in his class with positive point mass at zero dominate the James-Stein estimator. The results in
this paper show that a subclass of Maruyama's procedures including the class that Stein conjectured might contain members
dominating the James-Stein estimator cannot dominate the James-Stein estimator. We also show that under reasonable conditions,
the “constant” in shrinkage factor must approachp-2 for domination to hold. 相似文献
84.
It is shown that for independent and identically distributed random vectors, for which the components are independent and exponentially distributed with a common shift, we can construct unbiased estimators of their density, derived from the Uniform Minimum Variance Unbiased Estimator (UMVUE) of their distribution function. As direct applications of the UMVUEs of the density functions we present a Chi-square goodness of fit test of the model, and give two tables of the UMVUEs of some commonly used functions of the unknown parameters of the multivariate exponential model considered in this paper. 相似文献
85.
基于 Chen- Mangasarian光滑函数的一个子类 ,针对单调非线性互补问题给出了一种不可行非内点连续方法预估校正算法 ,并在适当的条件下 ,证明了算法具有全局线性收敛性和局部二次收敛性。 相似文献
86.
A Comparison of Restricted and Unrestricted Estimators in Estimating Linear Functions of Ordered Scale Parameters of Two Gamma Distributions 总被引:2,自引:1,他引:1
Yuan-Tsung Chang Nobuo Shinozaki 《Annals of the Institute of Statistical Mathematics》2002,54(4):848-860
The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered. A necessary and sufficient condition on the ratio of two coefficients is given for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) in terms of mean square error. A modified MLE which satisfies the restriction is also suggested, and a necessary and sufficient condition is also given for it to dominate the admissible estimator based solely on one sample. The estimation of linear functions of variances in two sample problem and also of variance components in a one-way random effect model is mentioned. 相似文献
87.
广义区间估计及其最优性(Ⅳ) 总被引:1,自引:0,他引:1
陈乃辉 《数学的实践与认识》2003,33(6):55-62
本文在提出了广义区间估计以及其上的最优性概念之后 ,证明了广义区间估计与假设检验的最优性之间的关系 ,推演了一个重要区间估计的最优性 相似文献
88.
89.
裂区试验设计方法是在正交表的基础上进行的.根据试验设计的数据分析结论要求具有再现性这一原理,将证明这种裂区试验设计法要有条件的使用才是合理的.由于广义正交表是保证设计表具有再现性的基本设计表,根据广义正交表来研究这种裂区试验设计方法的合理性.研究结果显示在裂区试验设计法对应的设计表是广义正交表,并且相应的数据分析方法采用广义正交表的数据分析方法时,才能保证其数据分析结论具有客观一致性和可重复再现性. 相似文献
90.
Zain Ul Abadin Zafar Kashif Rehan M. Mushtaq 《Journal of Difference Equations and Applications》2017,23(7):1298-1315
In this paper a non-linear mathematical model with fractional order ?, 0 < ? ≤ 1 is presented for analyzing and controlling the spread of HIV/AIDS. Both the disease-free equilibrium E0 and the endemic equilibrium E* are found and their stability is discussed using the stability theorem of fractional order differential equations. The basic reproduction number R0 plays an essential role in the stability properties of our system. When R0 < 1 the disease-free equilibrium E0 is attractor, but when R0 > 1, E0 is unstable and the endemic equilibrium (EE) E* exists and it is an attractor. Finally numerical Simulations are also established to investigate the influence of the system parameter on the spread of the disease. 相似文献