球面稳定同伦群的两个新元素h0(b1)3(γ)s和(b1)3g0(γ)s

本文证明了当p(＞-)11,3(<-)s＜p-3时,h0(b1)3∈Ext7,3p2q+qA(H*V(2),Zp),(b1)3g0∈Ext8,3p2q+pq+2q(H*V(2),Zp)在Adams谱序列中分别收敛到π*V(2)的非零元,h0(b1)3(γ)s∈Ext7+s,(s+3)p2q+(s-1)pq+(s-3)A(Zp,Zp)在Adams谱序列中分别收敛到π*S的非零p阶元.     

球面稳定同伦群的两个新元素h_0(b_1)~3_s)和(b_1)~3g_0_s)

本文证明了当p≥11,3≤s相似文献   

球面稳定同伦群的(~γ)t(~l)1g0新元素族

首先给出了May谱序列Es1,t,u项的几个结果,然后利用这些结果和关于ExtsP,t(Zp,Zp)的一个估计(P为由mod p Steenrod代数A的所有循环缩减幂Pi(i≥0)生成的子代数)得出了乘积~γt~l1g0∈Ext*A,*(Zp,Zp)(3≤t＜p-2)在Adams谱序列的收敛性,其中g0∈Ext2A,pq+2q(Zp,Zp),~l1∈Ext3A,p2q+2pq(Zp,Zp).     

乘积元b0g0(γ)s在Adams谱序列中的收敛性

决定球面稳定同伦群是同伦中的一个中心问题,同时也是非常困难的问题之一.Adams谱序觌是其计算的最有效的工具.在本文,令p>5为素数,A表示模p的Steenrod代数.我们利用Adams谱序列和May谱序列证明了,在球面稳定同伦群π*S中,存在一族在Adams谱序列中由b0g0γs∈Exts+4,sp2q+(s+1)pq+sq+s-3A(ZpZp)所表示的新的非平凡元素,其中q=2(p-1),3≤s相似文献   

球面稳定同伦群中的一族新元素及h0b12在π*V(1)中的收敛性

对连通有限型谱X,Y,存在着Adams谱序列(ASS){Ers,t,dr}满足(1)drErs,t→Ers+r,t+r-1是谱序列的微分,(2)E2s,t≌ExtAs,t(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S,Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,V(1)的稳定同伦群.本文通过Adams谱序列,发现了球谱S的稳定同伦群中的一族非零元素~γth0b02及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b12.在利用Adams谱序列求解同伦群的过程中,需要计算有关ExtAs,t(H*X,H*Y)的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出ExtAs,t(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).     

(i1i)*(b12k0)及(i1i)*(b31k0)在π*V(1)中的收敛性

对连通有限型谱X,y,存在Adams谱序列{Es,tr,dr},满足(1)dr:Es,t,r→Es+r,t+r-1,r是谱序列的微分, (2)Es,t,2≌Exts,t,A(H*X,H*y),(3)收敛到[∑t-sY,X].当X分别是球谱S,Moore谱M,Toda-smith谱V(1)时,(πt-X)p分别是S,M,V(1)的稳定同伦群.利用Adams 谱序列,证明了(i1i)*(62,1k0)及(i1i)*(b3,1k0)是永久循环但不是边缘,因此收敛到π*V(1)中的非零元,其中P为奇索数,q=2p-2.     

球面稳定同伦群中非平凡元素γ_sξ_n

当p≥5, n≥0时,(i_1i_0)_*(h_n)∈Ext_■~(1,p~nq)(H~*K,Z_p)在Adams谱序列中是永久循环,并且收敛到π_(p~nq-1)K中的非零元.本文在此基础上,考虑了涉及第三希腊字母类乘积元素的收敛性,并且扩大了球面稳定同伦群中非平凡元素滤子s+1的取值范围,即当p+1 s+1 2p时,■_sh_n∈Ext_■~(s+1,t)(Z_p,Z_p)在Adams谱序列中是永久循环,并且收敛到π_(t-s-1)S中的非零元γ_sξ_n,其中p≥7, n≥3, t=p~nq+sp~2q+(s-1)pq+(s-2)q+s-3,q=2(p-1).     

球面稳定同伦群中的一族新元素及h_0b_1~2在π_*V(1)中的收敛性

对连通有限型谱x,y,存在着Adams谱序列(ASS){Es,tr,dr}满足(1)dr:Es,tr→Es r,t r-1r 是谱序列的微分,(2)Es,t2≌Exts,tA(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S, Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,v(1)的稳定同伦群.本文通过Adams 谱序列,发现了球谱S的稳定同伦群中的一族非零元素γth0b21及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b21.在利用Adams谱序列求解同伦群的过程中,需要计算有关Exts,tA(H*X,H*Y) 的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出Exts,tA(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).     

Adams谱序列上的非平凡乘积b_0k_0δ_(s+4)

主要用May谱序列证明了非平凡的乘积b_0k_0δ_(s+4)∈Ext_A~(s+8,t)(Z_p,Z_p),其中p是大于等于7的素数,0≤sp-4,q=2(p-1),t=(s+4)p~3q+(s+3)p~2q+(s+5)pq+(s+2)q+s.     

球面稳定同伦群的一族新元素(γ)th0b41

证明了在Adams谱序列中存在永久循环元hob41,且可收敛到稳定同伦群π其中V(n)是Toda-Smith谱.进而,利用Yoneda乘积,证明了在Adams谱序列中还存在永久循环元(γ)th0b41收敛到球面稳定同伦群π*(S)的一个非零元.     

The Convergence of (~γ)s(b0hn - h1bn-1)

This paper computes the Thom map on γ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of b2,0, from which it is proved that (~γ)s(b0hn - h1bn-1) for 2 ≤ s ＜ p - 1 are permanent cycles in the ASS.     

球面稳定同伦群中的一个新元素族b1g0(γ)s

设P≥7素数,A为模P的Steenrod代数．我们利用Adams谱序列证明了球面稳定同伦群π*S中,存在由所表示的新的非平凡元素族,其中q=2(p-1),3≤s相似文献   

球面稳定同伦中元素β1γs和α1γs的非平凡性

In this paper, it is proved that for p≥7 an arbitrary odd prime and 3≤s相似文献   

Constructive characterizations of (γp,γ)- and (γp,γpr)-trees

Let G = (V,E) be a graph without isolated vertices.A set S V is a domination set of G if every vertex in V - S is adjacent to a vertex in S,that is N[S] = V.The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S C V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S V is a power domination set of G if all vertices of V can be observed recursively by the following rules: (i) all vertices in N[S] are observed initially,and (ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed (by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively.     

α-Stable characterization of Banach spaces (1 < α < 2)

This work characterizes some subclasses of α-stable (0 < α < 1) Banach spaces in terms of the extendibility to Radon laws of certain α-stable cylinder measures. These result extend the work of S. Chobanian and V. Tarieladze (J. Multivar. Anal.7, 183–203 (1977)). For these spaces it is shown that every Radon stable measure is the continuous image of a stable measure on a suitable L_β space with β = α(1 − α)⁻¹. The latter result extends some work of Garling (Ann. Probab.4, 600–611 (1976)) and Jain (Proceedings, Symposia in Pure Math. XXXI, p. 55–65, Amer. Math. Soc., Providence, R.I.).     

Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family E(α), α ∈ [2, 3)

We develop a precise analysis of J. O’Hara’s knot functionals E^(α), α ∈ [2, 3), that serve as self‐repulsive potentials on (knotted) closed curves. First we derive continuity of E^(α) on injective and regular H² curves and then we establish Fréchet differentiability of E^(α) and state several first variation formulae. Motivated by ideas of Z.‐X. He in his work on the specific functional E⁽²⁾, the so‐called Möbius Energy, we prove C^∞‐smoothness of critical points of the appropriately rescaled functionals $\tilde{E}^{(\alpha )}= {\rm length}^{\alpha -2}E^{(\alpha )}$ by means of fractional Sobolev spaces on a periodic interval and bilinear Fourier multipliers.     

(1/α)-Self similar α-stable processes with stationary increments

In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the α-stable Lévy motion is the only (1/α)-self-similar α-stable process with stationary increments if 0 < α < 1. We also introduce new classes of (1/α)-self-similar α-stable processes with stationary increments for 1 < α < 2.