A pull back theorem in the Adams spectral sequence

This paper proves that, for any generator x∈ExtA^s,tq（Zp,Zp）, if （1L ∧i）＊Ф＊（x）∈ExtA^s＋1,tq＋2q（H＊L∧M, Zp） is a permanent cycle in the Adams spectral sequence （ASS）, then b0x ∈ExtA^s＋1,tq＋q（Zp, Zp） also is a permenent cycle in the ASS. As an application, the paper obtains that h0hnhm∈ExtA^3,pnq＋p^mq＋q（Zp, Zp） is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy groups of spheres πp^nq＋p^mq＋q-3S, where p ≥5 is a prime, s ≤ 4, n ≥m＋2≥4 and M is the Moore spectrum.     

Detection of Some Elements in the Stable Homotopy Groups of Spheres

Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.     

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   

Two New Families in the Stable Homotopy Groups of Sphere and Moore Spectrum

This paper proves the existence of an order p element in the stable homotopy group of sphere spectrum of degree pnq pmq q - 4 and a nontrivial element in the stable homotopy group of Moore spectum of degree pnq pmq q - 3 which are represented by h0(hmbn-1-hnbm-1) and i*(h0hnhm) in the E2-terms of the Adams spectral sequence respectively, where p≥7 is a prime, n≥m 2≥4, q = 2(p - 1).     

σ-相关同伦元素的非平凡性

本文中,通过几何方法证明了σ相关同伦元素在球面稳定同伦群π_mS中是非平凡的,其中m=p~(n+1)q+2p~nq+(s+3)p~2q+(s+3)pq+(s+3)q-8,p≥7是奇素数,n3,0≤sp-3,且q=2(p-1).该σ相关同伦元素在Adams谱序列的E_2-项中由■_s+3■_ng0表示.     

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).     

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.     

Toda-Smith谱同伦群的具有第六滤子的新非平凡元素族

当p≥7,n≥3时,本文找到一个永久循环 ,它在Adams谱序列中收敛到 的一个非零元素,由Adams分解得到 ,使得 ,进而得到 并且它具有第六滤子．     

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).     

一类特殊分布纪录值之和的中心极限定理

摘要：设{X，Xn,n≥1)为独立同分布的服从某连续分布F的随机变量序列，X^(1)=X1，X^(2),X^(3),…为其纪录值序列．令ψ(u)=F^-1(1-e^-u)．其中F^-1是F的反函数．本文研究当ψ(u)=log^pu时Tn=∑k=1^nX^(k)=^dn∑k=1^nψ(Sn)的极限性质．解决了户为所有正整数时Tn的中心极限定理．     

一类pnm阶群的构造

本文研究了一类特殊的pnm阶有限群的构造.利用求解数论同余方程的方法和群的扩张理论,得到了具有m阶循环正规子群,其补子群为循环群的Pnm阶有限群的构造及相关的计数定理.     

COMPARISON OF PRODUCTS OF THE VARIETIES OF LIE ALGEBRAS

Abstract

In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle.     

ADDITIVE FAMILIES OF INVARIANTS OF FORMS OF DEGREE d

Abstract

Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I _n, is a GL _n,(F)- invariant of forms of degree d in x₁, …, x _n, over F. We call {I _n} an additive family of invariants if I _p+q (f ⊥ g) = I _p(f).I _q(g) whenever f; g are forms of degree d over F in x _l, …, x _p; …, x _q respectively, and where (f ⊥ g)(x _l, …, x _p+q) = f(x ₁, …, x _p,) + g (x _p+1, …, x _p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review.     

小康判别函数的建立与分析

近几年，国内在研究小康水平的定量指标分析中，应用较多的有综合评分法、层次分析法和模糊识别法。这几种方法比单项指标更全面、灵活，但在权数的确定上都难以克服人为因素的影响。当指标之间存在两个或两个以上的高度相关时，对问题的研究总存在一定的局限性。为了科学地研究小康问题，本文基于判别分析，建立城市小康的判别系数，来综合评价出我国城市小康水平的定量标准。     

一类线性微分方程解的零点分布

一、引言关于 k 阶线性常微分方程解的零点分布,S.Bank,G.Frank 和 I.Laine 最近证明了如下的结果.     

有限Abel群上子集等价类的计数

设G为一有限Abel群，|G|=v,D1,D2是G的两个子集，如果存在t∈Zv,(t,v)=1,s∈G使D1＝tD2 s，则称D1与D2是等价的。文中给出了G的k-子集等价类的计数公式，同时也给出了G的的所有子集等价类的计数公式。