This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equati...This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.展开更多
Objectives To investigate the causes, theraputic and preventive methods of com- plications associated with transcatheter occlusion of at- rial septal defect ( ASD) using the Amplatzer septal oc- cluder (ASO) in childr...Objectives To investigate the causes, theraputic and preventive methods of com- plications associated with transcatheter occlusion of at- rial septal defect ( ASD) using the Amplatzer septal oc- cluder (ASO) in children. Methods 289 cases un- derwent transcatheter closure of ASD with ASO. Com- plications occurred in 9 cases. The complications in procedure included systemic circulatory systemic air embolism in 2, pulmonary air embolism in 1, pericar- dial tamponade in 1, ASO malposition requiring emer- gency surgical removal in 1, transient atrial extrasysto- les in 1 and sizing balloon rupture in 1 case. 2 cases with postoperative complications were found in the fol- low-up studies. These included perforation of mitral valve and ASO partially dislodged. In this study, 5 children with intraoperative complication received e- mergency therapy including surgical intervention, and others needed only follow-up, as the complications were transient or asymptomatic. Results There were no children death in this study. The 5 cases who re- ceived treatment were completely healing, and the oth- ers with intra - procedure complications were also had no sequela existed. Cases with mitral valve and ASO partially dislodged were still in follow-up studies, as the 2 patients having no symptoms. Conclutions Air embolism were occurred easily in atrial septal defect cases who received ASO therapy. Complications mainly caused by inappropriate operative procedure and some complications needed emergency treatments. Follow-up studies were important to cases with transcatheter oc- clusion therapy.展开更多
文摘This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.
文摘Objectives To investigate the causes, theraputic and preventive methods of com- plications associated with transcatheter occlusion of at- rial septal defect ( ASD) using the Amplatzer septal oc- cluder (ASO) in children. Methods 289 cases un- derwent transcatheter closure of ASD with ASO. Com- plications occurred in 9 cases. The complications in procedure included systemic circulatory systemic air embolism in 2, pulmonary air embolism in 1, pericar- dial tamponade in 1, ASO malposition requiring emer- gency surgical removal in 1, transient atrial extrasysto- les in 1 and sizing balloon rupture in 1 case. 2 cases with postoperative complications were found in the fol- low-up studies. These included perforation of mitral valve and ASO partially dislodged. In this study, 5 children with intraoperative complication received e- mergency therapy including surgical intervention, and others needed only follow-up, as the complications were transient or asymptomatic. Results There were no children death in this study. The 5 cases who re- ceived treatment were completely healing, and the oth- ers with intra - procedure complications were also had no sequela existed. Cases with mitral valve and ASO partially dislodged were still in follow-up studies, as the 2 patients having no symptoms. Conclutions Air embolism were occurred easily in atrial septal defect cases who received ASO therapy. Complications mainly caused by inappropriate operative procedure and some complications needed emergency treatments. Follow-up studies were important to cases with transcatheter oc- clusion therapy.
