In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the...In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the critical point of such nonpolynomial planar vector felds to be the focus or center. Then, using Dulac criterion, we establish some sufcient conditions for the nonexistence of limit cycles of this nonpolynomial planar vector felds. And then, according to Hopf bifurcation theory, we analyze some sufcient conditions for bifurcating limit cycles from the origin. Finally, by transforming the nonpolynomial planar vector felds into the generalized Li′enard planar vector felds, we discuss the existence, uniqueness and stability of limit cycles for the former and latter planar vector felds. Some examples are also given to illustrate the efectiveness of our theoretical results.展开更多
In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields w...In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields which generalize the so–called degenerate infinityvector fields are also integrable.展开更多
Background In this study, we aimed to evaluate the impact of abnormal glucose, lipid and Cystatin-C on the virtual P vector characteristics, which haven＇ t been reported in previous studies. Methods 204 of non-diabet...Background In this study, we aimed to evaluate the impact of abnormal glucose, lipid and Cystatin-C on the virtual P vector characteristics, which haven＇ t been reported in previous studies. Methods 204 of non-diabetes mellitus （NDM）, 130 of DM （type 2） and 39 of impaired glucose tolerance （IGT） patients were consecutively and retrospectively recruited. We selected a one-minute length of electrocardiogram at 4AM for analysis. After a series of calculating algorisms, we obtained the virtual planar P vector parameters. Results There were no significant differences in FPV, FPA, RSPV, RSPA, HPV and HPA groups. After adjusting confounding factors, the re- gression coefficients （RC） were estimated as follow： for FPV, female gender （RC -0.21, P = 0.02）, triglyceride （RC -0.09, P 〈 0.01）, RVOT （RC 0.03, P = 0.02）; for RSPV, female gender （RC -0.21, P 〈 0.01）, triglyceride （RC -0.10, P 〈 0.01）, average heart rate （RC 0.01, P = 0.02）; for HPV, triglyceride （RC -0.08, P 〈 0.001）, LDL （RC -0.19, P 〈 0.01）, Apo B （RC 0.67, P 〈 0.01）; for RSPA, B type of blood （RC -22.06, P = 0.02）, Cystatin-C （RC -72.79, P = 0.02）, thickness of interventricular septum （RC 3.70, P = 0.01）. Cystatin-C was suggested as a cure related to RSPA, and the cut-off point was 1.6 mg/L. There were no significant risk factors associated with FPA and HPA. There was no difference in virtual P vector among DM, IGT and NDM groups. Conclusion In- creased levels of lipid and Cystatin-C significantly impact the characteristics of virtual P vector, whereas glucose does not. These changes may come from a higher low voltage atrial area and abnormal orientation of atrial depolarization.展开更多
： This paper deals with the universal serial manipulator on the inverse kinematics problem of plane type, the fast working space solution method, and the obstacle avoidance path planning method. With the vector proje...： This paper deals with the universal serial manipulator on the inverse kinematics problem of plane type, the fast working space solution method, and the obstacle avoidance path planning method. With the vector projection as the main constraint condition of the target, it proposes a general form of the inverse kinematics solution which does not depend on the robot configuration of freedom degree. By identifying the target vector direction maximum and minimum workspace boundary and determining the destination vector by thick search on the workspaee boundary method, an expressing method of the polar coordinate form of work space is then introduced. Finally, according to the form of plane trajectory planning for obstacle avoidance problem, the method of solving the inverse kinematics solution of the concave and convex forms of the safe obstacle avoidance area is improved. The simulation results verify that the proposed method has feasibility and generality.展开更多
基金Supported by the Natural Science Foundation of Anhui Education Committee(KJ2007A003)the"211 Project"for Academic Innovative Teams of Anhui University(KJTD002B)+3 种基金the Doctoral Scientifc Research Project for Anhui Medical University(XJ201022)the Key Project for Hefei Normal University(2010kj04zd)the Provincial Excellent Young Talents Foundation for Colleges and Universities of Anhui Province(2011SQRL126)the Academic Innovative Scientifc Research Project of Postgraduates for Anhui University(yfc100020,yfc100028)
文摘In this paper, the problem of limit cycles for a class of nonpolynomial planar vector felds is investigated. First, based on Liapunov method theory, we obtain some sufcient conditions for determining the origin as the critical point of such nonpolynomial planar vector felds to be the focus or center. Then, using Dulac criterion, we establish some sufcient conditions for the nonexistence of limit cycles of this nonpolynomial planar vector felds. And then, according to Hopf bifurcation theory, we analyze some sufcient conditions for bifurcating limit cycles from the origin. Finally, by transforming the nonpolynomial planar vector felds into the generalized Li′enard planar vector felds, we discuss the existence, uniqueness and stability of limit cycles for the former and latter planar vector felds. Some examples are also given to illustrate the efectiveness of our theoretical results.
基金supported by the Spanish MCYT,Grant Number BFM 2002-04236-C01-01
文摘In this work we study Lie symmetries of planar quasihomogeneous polynomialvector fields from different points of view, showing its integrability. Additionally, we show thatcertain perturbations of such vector fields which generalize the so–called degenerate infinityvector fields are also integrable.
文摘Background In this study, we aimed to evaluate the impact of abnormal glucose, lipid and Cystatin-C on the virtual P vector characteristics, which haven＇ t been reported in previous studies. Methods 204 of non-diabetes mellitus （NDM）, 130 of DM （type 2） and 39 of impaired glucose tolerance （IGT） patients were consecutively and retrospectively recruited. We selected a one-minute length of electrocardiogram at 4AM for analysis. After a series of calculating algorisms, we obtained the virtual planar P vector parameters. Results There were no significant differences in FPV, FPA, RSPV, RSPA, HPV and HPA groups. After adjusting confounding factors, the re- gression coefficients （RC） were estimated as follow： for FPV, female gender （RC -0.21, P = 0.02）, triglyceride （RC -0.09, P 〈 0.01）, RVOT （RC 0.03, P = 0.02）; for RSPV, female gender （RC -0.21, P 〈 0.01）, triglyceride （RC -0.10, P 〈 0.01）, average heart rate （RC 0.01, P = 0.02）; for HPV, triglyceride （RC -0.08, P 〈 0.001）, LDL （RC -0.19, P 〈 0.01）, Apo B （RC 0.67, P 〈 0.01）; for RSPA, B type of blood （RC -22.06, P = 0.02）, Cystatin-C （RC -72.79, P = 0.02）, thickness of interventricular septum （RC 3.70, P = 0.01）. Cystatin-C was suggested as a cure related to RSPA, and the cut-off point was 1.6 mg/L. There were no significant risk factors associated with FPA and HPA. There was no difference in virtual P vector among DM, IGT and NDM groups. Conclusion In- creased levels of lipid and Cystatin-C significantly impact the characteristics of virtual P vector, whereas glucose does not. These changes may come from a higher low voltage atrial area and abnormal orientation of atrial depolarization.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51205074)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20112304120007)+2 种基金the Harbin Specialized Research Foundation for Innovation Talents(Grant No.RC2012QN009037)the Fundamental Research Funds for the Central Universities(Grant No.HEUCF041505)the State Commission of Science Technology of China(Grant No.2014DFR10010)
文摘： This paper deals with the universal serial manipulator on the inverse kinematics problem of plane type, the fast working space solution method, and the obstacle avoidance path planning method. With the vector projection as the main constraint condition of the target, it proposes a general form of the inverse kinematics solution which does not depend on the robot configuration of freedom degree. By identifying the target vector direction maximum and minimum workspace boundary and determining the destination vector by thick search on the workspaee boundary method, an expressing method of the polar coordinate form of work space is then introduced. Finally, according to the form of plane trajectory planning for obstacle avoidance problem, the method of solving the inverse kinematics solution of the concave and convex forms of the safe obstacle avoidance area is improved. The simulation results verify that the proposed method has feasibility and generality.
基金Supported by the Natural Science Foundation of Anhui Education Committee(KJ2007A003)the"211 Project"for Academic Innovative Teams of Anhui University(KJTD002B)+4 种基金the Doctoral Scientific Research Project for Anhui Medical University(XJ201022)the Key Project for Hefei Normal University(2010kj04zd)the Provincial Excellent Young Talents Foundation for Colleges and Universities of Anhui Province(2011SQRL126)the Academic Innovative Scientific Research Project of Postgraduates for Anhui University(yfc100020yfc100028)
