In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore...In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.展开更多
Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding co...Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.展开更多
This paper thoroughly studies the＇. process of obtaining sulfur nanoparticles in aqueous medium from sodium polysulfide. Nanosize sulfur particles with orthorhombic structure were obtained at room temperature by mixi...This paper thoroughly studies the＇. process of obtaining sulfur nanoparticles in aqueous medium from sodium polysulfide. Nanosize sulfur particles with orthorhombic structure were obtained at room temperature by mixing sodium polysulfide aqueous solution with various inorganic and organic acids. Sulfur nanoparticles were characterized by laser particle-size analyzer, X-ray diffraction, electron probe microscopy. Size of sulfur nanoparticles in aqueous dispersion is affected ;trongly by acid concentration, as well as nature of alcohols, used as wetting agents when measuring sulfur particles size iin aqueous medium. Availability of obtaining sulfur nanoparticles of 22-25 nm average si;,e in aqueous medium was revealed. High biological activity of sulfur nanoparticles and ethylalcohol composition on wheat grain couching was established.展开更多
Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis...Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.展开更多
基金Supported by the NSF of China(69971016)Supported by the Shanghai Higher Learning Science and Technology Development Foundation(04DB24)
文摘In present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.
文摘Let P n be a set of n points in the unit square S,l(P n) denoe the length of the minimum spanning tree of P n, andC n= max P nSl(P n), n=2,3,… In this paper,the exact value of C n for n=2,3,4 and the corresponding configurations are given. Additionally,the conjectures of the configuration for n=5,6,7,8,9 are proposed.
文摘This paper thoroughly studies the＇. process of obtaining sulfur nanoparticles in aqueous medium from sodium polysulfide. Nanosize sulfur particles with orthorhombic structure were obtained at room temperature by mixing sodium polysulfide aqueous solution with various inorganic and organic acids. Sulfur nanoparticles were characterized by laser particle-size analyzer, X-ray diffraction, electron probe microscopy. Size of sulfur nanoparticles in aqueous dispersion is affected ;trongly by acid concentration, as well as nature of alcohols, used as wetting agents when measuring sulfur particles size iin aqueous medium. Availability of obtaining sulfur nanoparticles of 22-25 nm average si;,e in aqueous medium was revealed. High biological activity of sulfur nanoparticles and ethylalcohol composition on wheat grain couching was established.
基金supported in part by a grant of Research Grants Council of Hong Kong,and National Natural Science Foundation of China (Grant No. 11101157)
文摘Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.
