Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the meth...Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.展开更多
The sparse nature of location finding in the spatial domain makes it possible to exploit the Compressive Sensing (CS) theory for wireless location.CS-based location algorithm can largely reduce the number of online me...The sparse nature of location finding in the spatial domain makes it possible to exploit the Compressive Sensing (CS) theory for wireless location.CS-based location algorithm can largely reduce the number of online measurements while achieving a high level of localization accuracy,which makes the CS-based solution very attractive for indoor positioning.However,CS theory offers exact deterministic recovery of the sparse or compressible signals under two basic restriction conditions of sparsity and incoherence.In order to achieve a good recovery performance of sparse signals,CS-based solution needs to construct an efficient CS model.The model must satisfy the practical application requirements as well as following theoretical restrictions.In this paper,we propose two novel CS-based location solutions based on two different points of view:the CS-based algorithm with raising-dimension pre-processing and the CS-based algorithm with Minor Component Analysis (MCA).Analytical studies and simulations indicate that the proposed novel schemes achieve much higher localization accuracy.展开更多
文摘Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.
基金supported by the National Natural Science Foundation of China under Grant No.61001119the Fund for Creative Research Groups of China under Grant No.61121001
文摘The sparse nature of location finding in the spatial domain makes it possible to exploit the Compressive Sensing (CS) theory for wireless location.CS-based location algorithm can largely reduce the number of online measurements while achieving a high level of localization accuracy,which makes the CS-based solution very attractive for indoor positioning.However,CS theory offers exact deterministic recovery of the sparse or compressible signals under two basic restriction conditions of sparsity and incoherence.In order to achieve a good recovery performance of sparse signals,CS-based solution needs to construct an efficient CS model.The model must satisfy the practical application requirements as well as following theoretical restrictions.In this paper,we propose two novel CS-based location solutions based on two different points of view:the CS-based algorithm with raising-dimension pre-processing and the CS-based algorithm with Minor Component Analysis (MCA).Analytical studies and simulations indicate that the proposed novel schemes achieve much higher localization accuracy.
