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921.
In the common nonparametric regression model the problem of testing for a specific parametric form of the variance function
is considered. Recently Dette and Hetzler [8] proposed a test statistic which is based on an empirical process of pseudo residuals.
The process converges weakly to a Gaussian process with a complicated covariance kernel depending on the data generating process.
In the present paper we consider a standardized version of this process and propose an application of the Khmaladze transformation
to obtain asymptotically distribution-free tests for the corresponding Kolmogorov-Smirnov and Cramér-von Mises functionals.
The finite-sample properties of the proposed tests are investigated by means of a simulation study.
相似文献
922.
We consider a special case of the optimal separation, via a sphere, of two discrete point sets in a finite dimensional Euclidean
space. In fact we assume that the center of the sphere is fixed. In this case the problem reduces to the minimization of a
convex and nonsmooth function of just one variable, which can be solved by means of an “ad hoc” method in O(p
log
p) time, where p is the dataset size. The approach is suitable for use in connection with kernel transformations of the type adopted in the
support vector machine (SVM) approach. Despite of its simplicity the method has provided interesting results on several standard
test problems drawn from the binary classification literature.
This research has been partially supported by the Italian “Ministero dell’Istruzione, dell’Università e della Ricerca Scientifica”,
under PRIN project Numerical Methods for Global Optimization and for some classes of Nonsmooth Optimization Problems (2005017083.002). 相似文献
923.
A new regression method based on independent component analysis 总被引:1,自引:0,他引:1
Based on independent component analysis (ICA), a new regression method, independent component regression (ICR), was developed to build the model of NIR spectra and the routine components of plant samples. It is found that ICR and principal component regression (PCR) are completely equivalent when they are applied in quantitative prediction. However, independent components (ICs) can give more chemical explanation than principal components (PCs) because independence is a high-order statistic that is a much stronger condition than orthogonality. Three ICs are obtained by ICA from the NIR spectra of plant samples; it is found that they are strongly correlated to the NIR spectra of water, hydrocarbons and organonitrogen compounds, respectively. Therefore, ICA may be a promising tool to retrieve both quantitative and qualitative information from complex chemical data sets. 相似文献
924.
A chemometric method for analysis of conductometric titration data was introduced to extend its applicability to lower concentrations and more complex acid-base systems. Auxiliary pH measurements were made during the titration to assist the calculation of the distribution of protonable species on base of known or guessed equilibrium constants. Conductivity values of each ionized or ionizable species possibly present in the sample were introduced in a general equation where the only unknown parameters were the total concentrations of (conjugated) bases and of strong electrolytes not involved in acid-base equilibria. All these concentrations were adjusted by a multiparametric nonlinear regression (NLR) method, based on the Levenberg-Marquardt algorithm. This first conductometric titration method with NLR analysis (CT-NLR) was successfully applied to simulated conductometric titration data and to synthetic samples with multiple components at concentrations as low as those found in rainwater (∼10 μmol L−1). It was possible to resolve and quantify mixtures containing a strong acid, formic acid, acetic acid, ammonium ion, bicarbonate and inert electrolyte with accuracy of 5% or better. 相似文献
925.
Let X be a random variable taking values in a function space
, and let Y be a discrete random label with values 0 and 1. We investigate asymptotic properties of the moving window classification
rule based on independent copies of the pair (X,Y). Contrary to the finite dimensional case, it is shown that the moving window classifier is not universally consistent in
the sense that its probability of error may not converge to the Bayes risk for some distributions of (X,Y). Sufficient conditions both on the space
and the distribution of X are then given to ensure consistency. 相似文献
926.
应用主成分估计方法,对Logistic回归模型进行参数估计,并消除多重共线性影响.首先选取了累计贡献率达到85%以上的6个主成分,对因变量进行主成分估计,然后挑选出冠心病患者发病的主要影响因素,最后得到了因变量(冠心病发病)与6个主要影响因素(血压(sbp)、累计烟草量(tobacco)、低密度脂蛋白胆固醇(ldl)、心脏病家族史(famhist)、型表现(typea)和发病年龄(age))的回归模型.根据结果可知,心脏病家族史是导致心脏病发病最大的一个原因,它是一个不可控因素;在可控因素中,累计烟草量对冠心病发病的影响最大,因此建议患者应该控制烟草摄入量,以保证病情的稳定性. 相似文献
927.
Brian Rickard 《International Journal of Mathematical Education in Science & Technology》2018,49(3):341-354
Tutoring centres are common in universities in the United States, but there are few published studies that statistically examine the effects of tutoring on student success. This study utilizes multiple regression analysis to model the effect of tutoring attendance on final course grades in Calculus I. Our model predicted that every three visits to the tutoring centre is correlated with an increase of a students’ course grade by one per cent, after controlling for prior academic ability. We also found that for lower-achieving students, attending tutoring had a greater impact on final grades. 相似文献
928.
一般的回归模型中认为所有的数据点的重要程度是相同的,但有的实际问题中可能由于种种原因,其中有某个数据特别重要,针对这种情况,提出一种带一个插值点的回归模型,并得到这种回归模型三个参数的最大似然估计. 相似文献
929.
This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method. 相似文献
930.
考虑多元分布的正态性检验问题,用投影寻踪方法,给出了两个检验统计量,模拟计算也表明所提出的检验统计量具有良好的功效. 相似文献