This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept ...This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.展开更多
Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. F...Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. First of all, making use of Peer Group Filtering (PGF) techniques, an unsupervised seed region selection algorithm is presented to construct a seed region. Then based on the constructed seed region a polynomial fitting homogeneity criterion is applied to solve the concrete problem of doorplate segmentation appearing in the robot navigation along a corridor. At last, experiments are performed and the results demonstrate the effectiveness of the proposed algorithm.展开更多
There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jorda...There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.展开更多
In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence accel...In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence acceleration algorithms and Laurent property are discussed in detail.展开更多
Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generatin...Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generating function of Hurwitz numbers satisfies the cut-and-join equation. Therefore, it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula. In this paper, at first, we will review the method introduced in Goulden et al.＇s paper to get the λg conjecture for Hodge integral. Through some variables transformation, the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation. By comparing the coefficients of the lowest degree term of both sides in this equation, we can get the ,λg conjecture. Then, in a similar way, we obtain our main result in this paper： a recursive formula for Hodge integral of type contains only one ,λg-l-class. We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.展开更多
We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for...We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.展开更多
文摘This note shows that when studying geometric pro perties, a polynomial system is defined as a line field on a projective space such that its singular set has co dimension at least 2. By this definition, the concept of the degree of a polynomial system does not coincide with the usual one. The usual degenerate polynomial system of degree n+1 should be regarded as a system of degree n . Note that the definition is independent coordinate system. And, by this definition, some geometric properties concerning polynomial vector fields turn out to be evident.
基金Supported by the National Hi-Tech R&D Program of China (No.2002AA423160)the Na-tional Natural Science Foundation of China (No.60205004)the Henan Natural Science Foundation (No.0411013700).
文摘Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. First of all, making use of Peer Group Filtering (PGF) techniques, an unsupervised seed region selection algorithm is presented to construct a seed region. Then based on the constructed seed region a polynomial fitting homogeneity criterion is applied to solve the concrete problem of doorplate segmentation appearing in the robot navigation along a corridor. At last, experiments are performed and the results demonstrate the effectiveness of the proposed algorithm.
基金Supported by the National Science Foundation of China (19771006)
文摘There have been many elegant results discussing the approximation proper- ties of the Bieberbach polynomials. However, very few papers investigated the approxi- mation properties of the extremal polynomials over Jordan curves. In the present paper, some results on a class of extremal polynomials over C1+αsmooth Jordan curves are obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11331008,11201469,11571358 and 11601237)the China Postdoctoral Science Foundation Funded Project(Grant Nos.2012M510186 and 2013T60761)the Hong Kong Research Grant Council(Grant No.GRF HKBU202512)
文摘In this paper, we show that the coupled modified Kd V equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials,convergence acceleration algorithms and Laurent property are discussed in detail.
文摘Hodge integrals over moduli space of stable curves play an important roles in understanding the topological properties of moduli space. ELSV formula connects the Hodge integrals with Hurwitz numbers, and the generating function of Hurwitz numbers satisfies the cut-and-join equation. Therefore, it is natural to consider how to use the cut-and-join equation for Hurwitz numbers to compute Hodge integrals which appear in ELSV formula. In this paper, at first, we will review the method introduced in Goulden et al.＇s paper to get the λg conjecture for Hodge integral. Through some variables transformation, the generating function of Hurwitz number becomes a symmetric polynomial which satisfies a symmetrized cut-and-join equation. By comparing the coefficients of the lowest degree term of both sides in this equation, we can get the ,λg conjecture. Then, in a similar way, we obtain our main result in this paper： a recursive formula for Hodge integral of type contains only one ,λg-l-class. We also point out that our results are closely related to the degree 0 Virasoro conjecture for a curve.
基金supported by National Natural Science Foundation of China (Grant No. 11101402)
文摘We prove here the smoothness and the irreducibility of the periodic dynatomic curves(c,z)∈C2such that z is n-periodic for zd+c,where d 2.We use the method provided by Buff and Lei where they proved the conclusion for d=2.The proof for smoothness is based on elementary calculations on the pushforwards of specific quadratic differentials,following Thurston and Epstein,while the proof for irreducibility is a simplified version of Lau-Schleicher’s proof by using elementary arithmetic properties of kneading sequence instead of internal addresses.
