Emergent Geometry of KP Hierarchy Jian ZHOU Abstract We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontse...Emergent Geometry of KP Hierarchy Jian ZHOU Abstract We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich taufunction to give a natural explanation of some earlier work.We also apply it to higher WeilPetersson volumes and Witten’s r-spin intersection numbers.展开更多
Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of contin...Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.展开更多
Correlations of active and passive random intersection graphs are studied in this paper. We present the joint probability generating function for degrees of GactVe（n, re, p） and GPaSSiW（n, re, p）, which are genera...Correlations of active and passive random intersection graphs are studied in this paper. We present the joint probability generating function for degrees of GactVe（n, re, p） and GPaSSiW（n, re, p）, which are generated by a random bipartite graph G＊ （n, ~rt, p） on n ＋ rn vertices.展开更多
Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore,...Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.展开更多
文摘Emergent Geometry of KP Hierarchy Jian ZHOU Abstract We explain how to construct a quantum deformation of a spectral curve associated to a tau-function of the KP hierarchy.This construction is applied to Witten-Kontsevich taufunction to give a natural explanation of some earlier work.We also apply it to higher WeilPetersson volumes and Witten’s r-spin intersection numbers.
基金the Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)the Natural ScienceFoundation of Shaanxi Province(2005A08,2006A14)
文摘Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional Brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are discussed.The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is obtained.The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are presented.Furthermore,it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.
文摘Correlations of active and passive random intersection graphs are studied in this paper. We present the joint probability generating function for degrees of GactVe（n, re, p） and GPaSSiW（n, re, p）, which are generated by a random bipartite graph G＊ （n, ~rt, p） on n ＋ rn vertices.
基金Supported by the Natural Science Foundation of Hunan Province（2017JJ3085＋16C0635） Supported by the China Postdoctoral Science Foundation（2016M601644）
文摘Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown.
