In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a ...In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these （1＋1）-dimensional models such as coupled integrable dispersionless （CID） and shallow water wave equations. Moreover, we find that the variable separation solution of the （3＋1）-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in （2＋1）-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.展开更多
With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions ...With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.展开更多
With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based ont...With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions,some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.展开更多
Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then...Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.展开更多
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） ...With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （3＋1）-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.展开更多
We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two...We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni （2014） in an earlier paper.展开更多
This paper proposes a new technique that is used to embed depth maps into corresponding 2-dimensional （2D） images. Since a 2D image and its depth map are integrated into one type of image format, they can be treated...This paper proposes a new technique that is used to embed depth maps into corresponding 2-dimensional （2D） images. Since a 2D image and its depth map are integrated into one type of image format, they can be treated as if they were one 2D image. Thereby, it can reduce the amount of data in 3D images by half and simplify the processes for sending them through networks because the synchronization between images for the left and right eyes becomes unnecessary. We embed depth maps in the quantized discrete cosine transform （DCT） data of 2D images. The key to this technique is whether the depth maps could be embedded into 2D images without perceivably deteriorating their quality. We try to reduce their deterioration by compressing the depth map data by using the differences from the next pixel to the left. We assume that there is only one non-zero pixel at most on one horizontal line in the DCT block because the depth map values change abruptly. We conduct an experiment to evaluate the quality of the 2D images embedded with depth maps and find that satisfactory quality could be achieved.展开更多
Objectives:To explore the feasibility and efficacy of electrophysiology guidance for transcatheter closure of perimembranous ventricular septal defect(PmVSD)in adults.Methods:Adult patients with PmVSD who underwent tr...Objectives:To explore the feasibility and efficacy of electrophysiology guidance for transcatheter closure of perimembranous ventricular septal defect(PmVSD)in adults.Methods:Adult patients with PmVSD who underwent transcatheter in Guangdong Provincial People’s Hospital,Guangdong Cardiovascular Institute from February 2016 to January 2018 were selected.The distribution of the His-Purkinje system(HPS)close to the margins of PmVSD in the left ventricle was identified using three-dimensional(3D)electro-anatomic mapping and near-field HPS was further confirmed by different pacing protocols.The follow-up protocol included electrocardiogram(ECG)and transthoracic echocardiography at 6,24,72 h,1,3,6 months and 1,2,3,5 years after the procedure.Results:Of the 21 patients in the study,with an average age of 28.1 years,61.9%were female and 38.1%were male.Eighteen patients(85.7%)successfully underwent transcatheter intervention.The minimum distance between the margins of the PmVSD and near-field HPS ranged from 2.5±0.7(1.3~3.9)mm.An average follow-up period was 4.1±1.3(0.25~5)years,median of which was 5 years.1,3,5-year follow-up rate was 95.2%,90.4%and 52.4%,respectively.At the end of the follow-up,ECG abnormalities were observed in 5 cases(23.8%),including left anterior hemiblock(LAH)in 3 cases(14.3%),incomplete right bundle branch block and LAH in 1 case(4.8%),premature atrial contraction in 1 case(4.8%).Mild tricuspid regurgitation(TR)and mild TR with mild mitral regurgitation with mild aortic regurgitation was observed in 1 case(4.8%),as well as left ventricular diastolic dysfunction.Conclusions:The study indicates that the results have guiding significance for transcatheter closure of PmVSD guided by 3D electro-anatomic mapping technique.However,this method requires a larger amount of clinical research data to support.展开更多
基金The authors express their sincere thanks to the anonymous referees for their constructive suggestions and kind help.
文摘In this paper, the entangled mapping approach （EMA） is applied to obtain variable separation solutions of （1＋1）-dimensional and （3＋1）-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these （1＋1）-dimensional models such as coupled integrable dispersionless （CID） and shallow water wave equations. Moreover, we find that the variable separation solution of the （3＋1）-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in （2＋1）-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Undergraduate Scientific and Technological Innovation Project of Zhejiang Province of China (Grant No. 2012R412018)the Undergraduate Innovative Base Program of Zhejiang A & F University
文摘With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Province+1 种基金the Scientific Research Foundation of Key Discipline of Zhejiang Provincethe Natural Science Foundation of Zhejiang Lishui University under Grant No KZ06006
文摘With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions,some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Provincethe Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y606128 and Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.FC06001 and QN06009
文摘With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （3＋1）-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.
基金supported by National Science Foundation of USA(Grant No.DMS1252992)an Alfred P.Sloan Research Fellowship
文摘We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S2× S1 or RP3#P3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni （2014） in an earlier paper.
文摘This paper proposes a new technique that is used to embed depth maps into corresponding 2-dimensional （2D） images. Since a 2D image and its depth map are integrated into one type of image format, they can be treated as if they were one 2D image. Thereby, it can reduce the amount of data in 3D images by half and simplify the processes for sending them through networks because the synchronization between images for the left and right eyes becomes unnecessary. We embed depth maps in the quantized discrete cosine transform （DCT） data of 2D images. The key to this technique is whether the depth maps could be embedded into 2D images without perceivably deteriorating their quality. We try to reduce their deterioration by compressing the depth map data by using the differences from the next pixel to the left. We assume that there is only one non-zero pixel at most on one horizontal line in the DCT block because the depth map values change abruptly. We conduct an experiment to evaluate the quality of the 2D images embedded with depth maps and find that satisfactory quality could be achieved.
文摘Objectives:To explore the feasibility and efficacy of electrophysiology guidance for transcatheter closure of perimembranous ventricular septal defect(PmVSD)in adults.Methods:Adult patients with PmVSD who underwent transcatheter in Guangdong Provincial People’s Hospital,Guangdong Cardiovascular Institute from February 2016 to January 2018 were selected.The distribution of the His-Purkinje system(HPS)close to the margins of PmVSD in the left ventricle was identified using three-dimensional(3D)electro-anatomic mapping and near-field HPS was further confirmed by different pacing protocols.The follow-up protocol included electrocardiogram(ECG)and transthoracic echocardiography at 6,24,72 h,1,3,6 months and 1,2,3,5 years after the procedure.Results:Of the 21 patients in the study,with an average age of 28.1 years,61.9%were female and 38.1%were male.Eighteen patients(85.7%)successfully underwent transcatheter intervention.The minimum distance between the margins of the PmVSD and near-field HPS ranged from 2.5±0.7(1.3~3.9)mm.An average follow-up period was 4.1±1.3(0.25~5)years,median of which was 5 years.1,3,5-year follow-up rate was 95.2%,90.4%and 52.4%,respectively.At the end of the follow-up,ECG abnormalities were observed in 5 cases(23.8%),including left anterior hemiblock(LAH)in 3 cases(14.3%),incomplete right bundle branch block and LAH in 1 case(4.8%),premature atrial contraction in 1 case(4.8%).Mild tricuspid regurgitation(TR)and mild TR with mild mitral regurgitation with mild aortic regurgitation was observed in 1 case(4.8%),as well as left ventricular diastolic dysfunction.Conclusions:The study indicates that the results have guiding significance for transcatheter closure of PmVSD guided by 3D electro-anatomic mapping technique.However,this method requires a larger amount of clinical research data to support.
