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	1. A note on the Lipschitz classification of Bedford-McMullen carpets
	ZHANG Lu,LUO Jun
	Mathematics 24 February 2022
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	Abstract:The topological structure of fractal sets is a hot topic in the study of fractal geometry and recently there have been a lot of results on the Lipschitz classification of fractal squares. This note mainly considers a class of Bedford-McMullen carpets. By studying the connectedness, the structure of cut-points and so on, this note provides a Lipschitz classification of $20$ different kinds of Bedford-McMullen carpets.
	TO cite this article:ZHANG Lu,LUO Jun. A note on the Lipschitz classification of Bedford-McMullen carpets[OL].[24 February 2022] http://en.paper.edu.cn/en_releasepaper/content/4756449


	2. On the Asymptotic upper curvature of hyperbolic products
	XIE Gui-Ling,XIAO Ying-Qing
	Mathematics 15 May 2017
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	Abstract:M. Bonk and T. Foertsch introduced the notion of asymptotic upper curvature for Gromov hyperbolic spaces and suggested to study the asymptotic upper curvature of hyperbolic products. In this paper, we study these problems and prove that$$K_u(Y_{Delta,o})leqmax{K_u(X_1),K_u(X_2)},$$where $(X_1,o_1),(X_2,o_2)$ are two point Gromov hyperbolic spaces, $Y_{Delta,o}$ is their hyperbolic product and $K_u(X)$ is the asymptotic upper curvature of a hyperbolic space $X$. Moreover, we obtain some extra conditions to sure that $K_u(Y_{Delta,o})$ is no smaller than $K_u(X_2)$.
	TO cite this article:XIE Gui-Ling,XIAO Ying-Qing. On the Asymptotic upper curvature of hyperbolic products[OL].[15 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733628

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	3. An intrinsic rigidity theorem for closed minimal hypersurfaces in $mathbb{S}^5$with constant nonnegative scalar curvature
	TANG Bing,YANG Ling
	Mathematics 15 January 2016
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	Abstract:Let $M^4$ be a closed minimal hypersurface in $mathbb{S}^5$ with constant nonnegative scalar curvature. Denote by$f_3$ the sum of the cubes of all principal curvatures, by $g$ the number of distinct principal curvatures. We prove that, if both $f_3$ and $g$ are constant, then $M^4$ is isoparametric. Moreover, We give all possible values for squared length of the second fundamental form of $M^4$. This result provides another piece of supporting evidence to the Chern conjecture.
	TO cite this article:TANG Bing,YANG Ling. An intrinsic rigidity theorem for closed minimal hypersurfaces in $mathbb{S}^5$with constant nonnegative scalar curvature[OL].[15 January 2016] http://en.paper.edu.cn/en_releasepaper/content/4676205


	4. Bernstein type theorems forspacelike stationary graphs in Minkowski spaces
	MA Xiang, WANG Peng, YANG Ling
	Mathematics 15 January 2016
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	Abstract:For entire spacelike stationary 2-dimensional graphs in Minkowski spaces, we establish Bernstein type theorems under specific boundedness assumptions either on the $W$-function or on the total (Gaussian) curvature. These conclusions imply the classical Bernstein theorem for minimal surfaces in $R^3$ and Calabi's theorem for spacelike maximal surfaces in $R_1^3$.
	TO cite this article:MA Xiang, WANG Peng, YANG Ling. Bernstein type theorems forspacelike stationary graphs in Minkowski spaces[OL].[15 January 2016] http://en.paper.edu.cn/en_releasepaper/content/4676202


	5. R function of entanglement of formation
	LI Bin ,YU Zu-Huan
	Mathematics 02 December 2015
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	Abstract:By an explicit investigation of the property of the function R, which appeared when computing the entanglement of formation for isotropic states and in a tight lower bound of entanglement of formation for arbitrary bipartite mixed states, we give an analytic proof that the the results in these papers are valid for any dimensions.
	TO cite this article:LI Bin ,YU Zu-Huan. R function of entanglement of formation[OL].[ 2 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4668188


	6. Local invariants of unitary operations in four-qubit quantum system
	LI Bin ,YU Zu-Huan
	Mathematics 18 November 2015
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	Abstract:we investigate the local invariants for four-qubit states and seek for some equivalent condition on the local equivalent operators with regard to the action of $SO(4)otimesSO(4)$. In order to find fewer enough invariants, by thinking of the kind of local equivalence as a special case of that with regard to the action of $SO(2^4),$ then we strengthen our result until we find the complete set of the invariants. In addition, we can obtain a result about the case of three extbf{-}qubit quantum system.
	TO cite this article:LI Bin ,YU Zu-Huan. Local invariants of unitary operations in four-qubit quantum system[OL].[18 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4663169


	7. On Ricci tensor of focal submanifolds of isoparametric hypersurfaces
	Li Qichao,Yan Wenjiao
	Mathematics 08 June 2014
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	Abstract: $mathcal{A}$-manifolds and $mathcal{B}$-manifolds, introduced by A.Gray, are two significant classes of Einstein-like Riemannian manifolds. A Riemannian manifold is Ricci parallel if and only if it is simultaneously an $mathcal{A}$-manifold and a $mathcal{B}$-manifold. The present paper proves that both focal submanifolds of each isoparametric hypersurface in unit spheres with $g=4$ distinct principal curvatures are $mathcal{A}$-manifolds. As for the focal submanifolds with $g=6$, $m=1$ or $2$, only one is an $mathcal{A}$-manifold, and neither is a $mathcal{B}$-manifold.
	TO cite this article:Li Qichao,Yan Wenjiao. On Ricci tensor of focal submanifolds of isoparametric hypersurfaces[OL].[ 8 June 2014] http://en.paper.edu.cn/en_releasepaper/content/4599805


	8. Existence of homogeneous geodesics on homogeneous Randers spaces
	Yan Zaili, Deng Shaoqiang
	Mathematics 23 December 2013
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	Abstract:A geodesic of a Finsler space $(M, F)$ is called homogeneous if it is the orbit of a one-parameter transformation group of isometries of $(M, F)$. In this paper we show that every homogeneous Randers space admits at least a homogeneous geodesic through any point.
	TO cite this article:Yan Zaili, Deng Shaoqiang. Existence of homogeneous geodesics on homogeneous Randers spaces[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577145


	9. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II
	Xie Qihong
	Mathematics 13 December 2012
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	Abstract:A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, first the author proves that smooth toric varieties are strongly liftable, hence the Kawamata-Viehweg vanishing theorem holds for smooth projective toric varieties. Second, the author proves the Kawamata-Viehweg vanishing theorem for normal projective surfaces which are birational to a strongly liftable smooth projective surface. Finally, the author deduces the cyclic cover trick over W2(k), which can be used to construct a large class ofliftable smooth projective varieties.
	TO cite this article:Xie Qihong. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II[OL].[13 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503779


	10. Gradient Estimates and Liouville Theorems for Dirac-harmonic maps
	CHEN Qun, Jürgen Jost,SUN Linlin
	Mathematics 07 August 2012
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	Abstract:Dirac-harmonic map is the mathematical version of the super-symmetric nonlinear sigma model in quantum field theory, it includes the two important special cases: harmonic map and harmonic spinor. Many progresses have been made in the existence, regularity, blowup analysis, etc.. Most of the previous results deal with Dirac-harmonic maps from compact manifolds, it is the main aim of the present paper to derive properties of Dirac-harmonic maps from non-compact complete manifolds. Precisely, the authors established gradient estimates for Dirac-harmonic maps from non-compact complete Riemannian spin manifolds into regular balls of the target manifolds, and then apply these estimates to obtain Liouville theorems for Dirac-harmonic maps under certain conditions of the curvatures or energies, especially, they proved Liouville theorems of Dirac-harmonic maps under small energy density conditions.
	TO cite this article:CHEN Qun, Jürgen Jost,SUN Linlin. Gradient Estimates and Liouville Theorems for Dirac-harmonic maps[OL].[ 7 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4486492

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