This paper presents the relations between spinors and dual characteristic pairs, and gives a way to get the dual characteristic pairs of Dirac structure associated to a generalized complex structure.
The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 ...The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.展开更多
Most of the Point Pattern Matching (PPM) algorithm performs poorly when the noise of the point's position and outliers exist. This paper presents a novel and robust PPM algorithm which combined Point Pair Topologi...Most of the Point Pattern Matching (PPM) algorithm performs poorly when the noise of the point's position and outliers exist. This paper presents a novel and robust PPM algorithm which combined Point Pair Topological Characteristics (PPTC) and Spectral Matching (SM) together to solve the afore mentioned issues. In which PPTC, a new shape descriptor, is firstly proposed. A new comparability measurement based on PPTC is defined as the matching probability. Finally, the correct matching results are achieved by the spectral matching method. The synthetic data experiments show its robustness by comparing with the other state-of-art algorithms and the real world data experiments show its effectiveness.展开更多
This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, w...This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.展开更多
基金Supported by the Science and Technology Project of Beijing Municipal Commission of Education（SQKM201211232017） Supported by the National Science Foundation of China（Ill26152）
文摘This paper presents the relations between spinors and dual characteristic pairs, and gives a way to get the dual characteristic pairs of Dirac structure associated to a generalized complex structure.
文摘The author gives another linear-algebraic proof of the famous result of Zariski, Delorme,Briancon- Granger- Maisonobe about the moduli number of plane curve singularities with the same topological type as Xa + Yb = 0 (i.e.,with one characteristic pair). Since the original proof depends very much on the division theorem of Briancon, it cannot be generalized to higher dimensions. It is hopeful that the proof here will be applied to the higher dimensional cases.
文摘Most of the Point Pattern Matching (PPM) algorithm performs poorly when the noise of the point's position and outliers exist. This paper presents a novel and robust PPM algorithm which combined Point Pair Topological Characteristics (PPTC) and Spectral Matching (SM) together to solve the afore mentioned issues. In which PPTC, a new shape descriptor, is firstly proposed. A new comparability measurement based on PPTC is defined as the matching probability. Finally, the correct matching results are achieved by the spectral matching method. The synthetic data experiments show its robustness by comparing with the other state-of-art algorithms and the real world data experiments show its effectiveness.
文摘This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.
