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	1. An Exact Sequence of Groups of Self-homotpy equivalences
	Yu Haibo,ZHAO Hao
	Mathematics 27 April 2017
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	Abstract:Groups of self-equivalences of the objects in two categories are studied. We show that these two kinds of groups are connected via an exactsequence which is split in some cases.
	TO cite this article:Yu Haibo,ZHAO Hao. An Exact Sequence of Groups of Self-homotpy equivalences[OL].[27 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4727121


	2. On Convergence of the Product $widetilde{delta}_{s+4}widetilde l_{1}g_{0}$ in the Adams Spectral Squences
	Yu Haibo,ZHAO Hao
	Mathematics 27 April 2017
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	Abstract:Abstract. In this paper we verifythe convergence of the product $widetilde{delta}_{s+4}widetilde l_{1}g_{0}in { mExt}_{mathcal{A}}^{s+9,t+s}(mathbb{Z}/p,mathbb{Z}/p)$ in theAdams spectral sequences, where $pgeq 11$,$0leq sleq p-5$, and $t=(s+3+(s+5)p+(s+4)p^{2}+(s+4)p^{3})q$, $q=2(p-1)$.
	TO cite this article:Yu Haibo,ZHAO Hao. On Convergence of the Product $widetilde{delta}_{s+4}widetilde l_{1}g_{0}$ in the Adams Spectral Squences [OL].[27 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4727073

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	3. The homotopy groups of $L_2T(m)/(p^{[rac{m+1}{2}]+2},v_1)$
	Wang Xiangjun, Yuan Zihong
	Mathematics 04 June 2016
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	Abstract:Let $T(m)$ be the Ravenel spectrum characterized by the $BP_$-homology as $BP_[t_1,cdots,t_m]$.It is known that there is a self-map $v_1:Sigma^{2(p-1)}T(m) ightarrow T(m).$ Let $T(m)/(v_1)$ be the cofiber of$v_1$ and $T(m)/(p^{[rac{m+1}{2}]+2}, v_1)$ be the cofiber of$p^{[rac{m+1}{2}+2]}:T(m)/(v_1) ightarrow T(m)/(v_1)$. In thispaper we determined the homotopy groups of\$L_2T(m)/(p^{[rac{m+1}{2}]+2},v_1)$ for $m>1$ by the Adams-Novikovspectral sequence.
	TO cite this article:Wang Xiangjun, Yuan Zihong. The homotopy groups of $L_2T(m)/(p^{[rac{m+1}{2}]+2},v_1)$[OL].[ 4 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4696304


	4. The $Ext$ groups $H^0v_2^{-1}BP_*[t_1]/(4,v_1^infty))$
	Wang Xiangjun, Zhao Dongxu
	Mathematics 04 June 2016
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	Abstract:Let $T(1)$ be the Ravenel spectrum, $T(1)/(4)$ be the cofiber of$4: T(1)longrightarrow T(1)$ and $L_2$ be the localization functor with respect to $v_2^{-1}BP$.To determine the homotopy groups of $L_2T(1)/(4)$, one need to start with determine the $Ext$ groups$Ext_{BP_BP}^{s,t}(BP_, v_2^{-1}BP_[t_1]/(4,v_1^infty)$. In this paper, we determinethe $Ext$ groups $Ext_{BP_BP}^0(BP_, v_2^{-1}BP_[t_1]/(4, v_1^infty))=H^0v_2^{-1}BP_[t_1]/(4,v_1^infty)$by the $2$-Bockstein spectral sequence with$E_1$-term $H^M_1^1[t_1]$.
	TO cite this article:Wang Xiangjun, Zhao Dongxu. The $Ext$ groups $H^0v_2^{-1}BP_*[t_1]/(4,v_1^infty))$[OL].[ 4 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4696081


	5. A note on balls in cone metric spaces
	Ge Xun
	Mathematics 09 February 2015
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	Abstract:In this brief note, we give some relations among balls and their closures in cone metric space. In particular, we give an example to show that $overline{{yin X:d(x,y)lldelta}} e{yin X:d(x,y)ledelta}$ for a cone metric space $(X,d)$, which corrects an error in a paper (Acta Mathematica Sinica, 26(2010), 489--496).
	TO cite this article:Ge Xun. A note on balls in cone metric spaces[OL].[ 9 February 2015] http://en.paper.edu.cn/en_releasepaper/content/4631429


	6. Non-implications of Granularity-Wise Separations in Covering Approximation Spaces
	Ge Xun
	Mathematics 12 September 2014
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	Abstract:This paper investigates some granularity-wise separations in covering approximation spaces with covering approximation operators $underline{C_2}$ and $overline{C_2}$ (in the sense of K. Qin, Y. Gao and Z. Pei) to give some non-implications for these separations, which will be help to richen and deepen researches of covering approximation spaces.
	TO cite this article:Ge Xun. Non-implications of Granularity-Wise Separations in Covering Approximation Spaces[OL].[12 September 2014] http://en.paper.edu.cn/en_releasepaper/content/4609584


	7. Betti numbers of locally standard 2-torus manifolds
	CHEN Jun-Da,LU Zhi
	Mathematics 11 February 2014
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	Abstract:Let $M^n$ be a smooth closed $n$-manifold with a locally standard $({Bbb Z}_2)^n$-action. This paper studies the relationship among the mod 2 Betti numbers of $M^n$, the mod 2 Betti numbers and the $h$-vector of the orbit space of the action.
	TO cite this article:CHEN Jun-Da,LU Zhi. Betti numbers of locally standard 2-torus manifolds[OL].[11 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4584995


	8. Examples of quasitoric manifolds as special unitary manifolds
	LU Zhi,WANG Wei
	Mathematics 11 February 2014
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	Abstract:This paper shows that for each $ngeq 5$ with only $n ot= 6$, there exists a $2n$-dimensional specially omnioriented quasitoric manifold $M^{2n}$ which represents a nonzero element in $Omega_*^U$. This provides the counterexamples of Buchstaber--Panov--Ray conjecture.
	TO cite this article:LU Zhi,WANG Wei. Examples of quasitoric manifolds as special unitary manifolds[OL].[11 February 2014] http://en.paper.edu.cn/en_releasepaper/content/4584998


	9. Continuity in complete $Omega$-lattices based on Cauchy ideals
	LAI Hong-Liang
	Mathematics 25 January 2014
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	Abstract:Let $Omega$ be a complete residuated lattice. Complete $Omega$-ordered sets are generalizations of classical complete lattices in the $Omega$-valued logic and are called complete $Omega$-lattices. It is shown that each Cauchy idea in a complete $Omega$-lattice can be generated by a directed subset and a complete $Omega$-lattice is continuous if and only if the tensor is Scott continuous. Furthermore, it is shown that each completely distributive complete $Om$-lattice is continuous.
	TO cite this article:LAI Hong-Liang. Continuity in complete $Omega$-lattices based on Cauchy ideals[OL].[25 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4584022


	10. Continuous $Omega$-domains based on Cauchy ideals
	LAI Hong-Liang
	Mathematics 24 January 2014
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	Abstract:Categories enriched on a commutative, unital quantale $(Om,)$ make a good framework of quantitative domain theory. In this paper, for a complete residuated lattice $(Omega,)$ with $Om$ being a continuous lattice, a notion of continuity in liminf complete $Om$-categories is introduced based on the directness being described by Cauchy ideals. Moreover, the way below relations, algebraic objects and retractions are characterized and the relationships with continuity is studied. It is shown that continuous liminf complete $Om$-categories can be viewed as continuous $Omega$-domains.
	TO cite this article:LAI Hong-Liang. Continuous $Omega$-domains based on Cauchy ideals[OL].[24 January 2014] http://en.paper.edu.cn/en_releasepaper/content/4583933

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