Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation,we investigate the polynomial function model in Born-Infeld theory in this...Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation,we investigate the polynomial function model in Born-Infeld theory in this paper with the form of-([10α(φ′)^(2)]φ′)′=λf(φ(x)),whereλ>0 is a real parameter,f∈C 2(0,+∞)is a nonlinear function.We are interested in the exact number of positive solutions of the above nonlinear equation.We specifically develop for the problem combined with a careful analysis of a time-map method.展开更多
A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracki...A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.展开更多
基金Supported by National Natural Science Foundation of He’nan Province of China(Grant No.222300420416)National Natural Science Foundation of China(Grant Nos.11471099,11971148)Graduate Talents Program of Henan University(Grant No.SYLYC2022078).
文摘Based on the Lagrangian action density under Born-Infeld type dynamics and motivated by the one-dimensional prescribed mean curvature equation,we investigate the polynomial function model in Born-Infeld theory in this paper with the form of-([10α(φ′)^(2)]φ′)′=λf(φ(x)),whereλ>0 is a real parameter,f∈C 2(0,+∞)is a nonlinear function.We are interested in the exact number of positive solutions of the above nonlinear equation.We specifically develop for the problem combined with a careful analysis of a time-map method.
文摘A polynomial model, time origin shifting model(TOSM, is used to describe the trajectory of a moving target .Based on TOSM, a recursive laeast squares(RLS) algorithm with varied forgetting factor is derived for tracking of a non-maneuvering target. In order to apply this algorithm to maneuvering targets tracking ,a tracking signal is performed on-line to determine what kind of TOSm will be in effect to track a target with different dynamics. An effective multiple model least squares filtering and forecasting method dadpted to real tracking of a maneuvering target is formulated. The algorithm is computationally more effcient than Kalman filter and the percentage improvement from simulations show both of them are considerably alike to some extent.
