The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions a...The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.展开更多
This study proposes a novel dual S-shaped logistic model for automatically quantifying the characteristic kinetic curves of breast lesions and for distinguishing malignant from benign breast tumors on dynamic contrast...This study proposes a novel dual S-shaped logistic model for automatically quantifying the characteristic kinetic curves of breast lesions and for distinguishing malignant from benign breast tumors on dynamic contrast enhanced (DCE) magnetic resonance (MR) images.D(,) is the diagnostic parameter derived from the logistic model.Significant differences were found in D(,) between the malignant benign groups.Fisher's Linear Discriminant analysis correctly classified more than 90% of the benign and malignant kinetic breast data using the derived diagnostic parameter (D(,)).Receiver operating characteristic curve analysis of the derived diagnostic parameter (D(,)) indicated high sensitivity and specificity to differentiate malignancy from benignancy.The dual S-shaped logistic model was effectively used to fit the kinetic curves of breast lesions in DCE-MR.Separation between benign and malignant breast lesions was achieved with sufficient accuracy by using the derived diagnostic parameter D(,) as the lesion's feature.The proposed method therefore has the potential for computer-aided diagnosis in breast tumors.展开更多
This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. ...This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. The climate variables and daily pan evaporation data measured at two weather stations located near Elephant Butte Reservoir, New Mexico, USA and a weather station located in Shanshan County, Xinjiang, China were used in the study. The nonlinear relationship between climate variables and daily pan evaporation was successfully modeled using PLSR approach by solving collinearity that exists in the climate variables. The modeling results were compared to artificial neural networks （ANN） models with the same input variables. The resuits showed that the nonlinear equations developed using PLSR has similar performance with complex ANN approach for the study sites. The modeling process was straightforward and the equations were simpler and more explicit than the ANN black-box models.展开更多
基金The National Natural Science Foundation of China(No.10771032)
文摘The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.
文摘This study proposes a novel dual S-shaped logistic model for automatically quantifying the characteristic kinetic curves of breast lesions and for distinguishing malignant from benign breast tumors on dynamic contrast enhanced (DCE) magnetic resonance (MR) images.D(,) is the diagnostic parameter derived from the logistic model.Significant differences were found in D(,) between the malignant benign groups.Fisher's Linear Discriminant analysis correctly classified more than 90% of the benign and malignant kinetic breast data using the derived diagnostic parameter (D(,)).Receiver operating characteristic curve analysis of the derived diagnostic parameter (D(,)) indicated high sensitivity and specificity to differentiate malignancy from benignancy.The dual S-shaped logistic model was effectively used to fit the kinetic curves of breast lesions in DCE-MR.Separation between benign and malignant breast lesions was achieved with sufficient accuracy by using the derived diagnostic parameter D(,) as the lesion's feature.The proposed method therefore has the potential for computer-aided diagnosis in breast tumors.
基金supported in part by the National Natural Science Founda-tion of China (Grant Nos.51069017,41071026)their sincere appreciation of the reviewers’ valuable suggestions and comments in improving the quality of this paper
文摘This study presented the application of partial least squares regression （PLSR） in estimating daily pan evaporation by utilizing the unique feature of PLSR in eliminating collinearity issues in predictor variables. The climate variables and daily pan evaporation data measured at two weather stations located near Elephant Butte Reservoir, New Mexico, USA and a weather station located in Shanshan County, Xinjiang, China were used in the study. The nonlinear relationship between climate variables and daily pan evaporation was successfully modeled using PLSR approach by solving collinearity that exists in the climate variables. The modeling results were compared to artificial neural networks （ANN） models with the same input variables. The resuits showed that the nonlinear equations developed using PLSR has similar performance with complex ANN approach for the study sites. The modeling process was straightforward and the equations were simpler and more explicit than the ANN black-box models.
