Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p...Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.展开更多
In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge betwe...In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.展开更多
文摘Abstract Denote by z（p） （resp. Zp） the p localization （resp. p completion） of z. Then we have the canonical inclusion Z（p）→ zp. Let S2n-1（p） be the p-local （2n- 1）-sphere and let B2n（p） be a connected p-local space satisfying S2n-l（p）≌ΩB2n（p）, then H＊B2n（p）,Z（p）） = Z（p）[U] with ｜u｜ = 2n. Define the degree of a self-map f of B2n（p） to be k E Z（p） such that f＊（u） = ku. Using the theory of integer-valued polynomials we show that there exists a self-map of B2n（p） of degree k if and only if k is an n-th power in Zp.
基金supported by National Natural Science Foundation of China(Grant Nos.11031007,11171322,61222206 and 11371341)One Hundred Talent Project of the Chinese Academy of Sciencesthe Program for New Century Excellent Talents in University(Grant No.NCET-11-0881)
文摘In this paper we present a new representation of curve, named parametric curve with an implicit domain(PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.
