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SMOOTHING ESTIMATES OF THE RADIAL SCHRO ¨DINGER PROPAGATOR IN DIMENSIONS n≥2
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作者 李栋 张晓轶 《Acta Mathematica Scientia》 SCIE CSCD 2010年第6期2103-2109,共7页
The usual Kato smoothing estimate for the Schrodinger propagator in 1D takes the form |||δx|1/2eitθxxu0|| Lx∞Lt2〈∽||u0||Lx2. In dimensions n ≥ 2 the smoothing estimate involves certain localization t... The usual Kato smoothing estimate for the Schrodinger propagator in 1D takes the form |||δx|1/2eitθxxu0|| Lx∞Lt2〈∽||u0||Lx2. In dimensions n ≥ 2 the smoothing estimate involves certain localization to cubes in space. In this paper we focus on radial functions and obtain Kato-type sharp smoothing estimates which can be viewed as natural generalizations of the 1D Kato smoothing. These estimates are global in the sense that they do not need localization in space. We also present an interesting counterexample which shows that even though the time-global inhomogeneons Kato smoothing holds true, the corresponding time-local inhomogeneous smoothing estimate cannot hold in general. 展开更多
关键词 SchrSdinger equation smoothing estimate
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EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS
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作者 Thieu Huy NGUYEN Truong Xuan PHAM +1 位作者 Thi Ngoc Ha VU The Sac LE 《Acta Mathematica Scientia》 SCIE CSCD 2022年第5期1875-1901,共27页
In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded ... In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38]. 展开更多
关键词 Boussinesq systems periodic solutions almost periodic solutions unbounded domains smoothing estimates dual estimates interpolation spaces STABILITY
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SMOOTH ESTIMATION OF ROC CURVE IN THE PRESENCE OF AUXILIARY INFORMATION 被引量:1
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作者 Yong ZHOU Haibo ZHOU Yunbei MA 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2011年第5期919-944,共26页
Receiver operating characteristic (ROC) curve is often used to study and compare two- sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of... Receiver operating characteristic (ROC) curve is often used to study and compare two- sample problems in medicine. When more information may be available on one treatment than the other, one can improve estimator of ROC curve if the auxiliary population information is taken into account. The authors show that the empirical likelihood method can be naturally adapted to make efficient use of the auxiliary information to such problems. The authors propose a smoothed empirical likelihood estimator for ROC curve with some auxiliary information in medical studies. The proposed estimates are more efficient than those ROC estimators without any auxiliary information, in the sense of comparing asymptotic variances and mean squared error (MSE). Some asymptotic properties for the empirical likelihood estimation of ROC curve are established. A simulation study is presented to demonstrate the performance of the proposed estimators. 展开更多
关键词 Auxiliary information empirical likelihood ROC curve smooth estimation.
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Distribution Estimation with Smoothed Auxiliary Information
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作者 Xu Liu Ahmad Ishfaq 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2011年第1期167-176,共10页
Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable wi... Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable, A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators. 展开更多
关键词 Auxiliary information Empirical likelihood Estimating equations Smoothed estimating function Symmetric distribution
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Kernel Estimators of the ROC Curve with Censored Data
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作者 Fang-fang Bai Yong Zhou 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第1期43-54,共12页
Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kapla... Receiver operating characteristic (ROC) curves are often used to study the two sample problem in medical studies. However, most data in medical studies are censored. Usually a natural estimator is based on the Kaplan-Meier estimator. In this paper we propose a smoothed estimator based on kernel techniques for the ROC curve with censored data. The large sample properties of the smoothed estimator are established. Moreover, deficiency is considered in order to compare the proposed smoothed estimator of the ROC curve with the empirical one based on Kaplan-Meier estimator. It is shown that the smoothed estimator outperforms the direct empirical estimator based on the Kaplan-Meier estimator under the criterion of deficiency. A simulation study is also conducted and a real data is analyzed. 展开更多
关键词 ROC curve smoothed estimator censored data Kaplan-Meier estimator DEFICIENCY
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