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1.
In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres πt-6S which is represented by hngor3 ∈ ExtA6,t(Zp,Zp) in the Adams spectral sequence, where t=2pn(p-1) 6(p2 p 1)(p-1) and p≥7 is a prime number.This article generalizes the result and proves the existence of a new nontrivial family of filtration s 6 in the stable homotopy groups of spheres πt1-s-6S which is represented by hngors 3 6 ExtAs 6,t1(Zp, Zp) in the Adams spectral sequence, where n≥4, 0≤s相似文献   

2.
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p.  相似文献   

3.
Let P_k(p, A, B) be the class of functions f(z) = z~p-sum from n=k to ∞(|α_(n+′p|Z~((n+)~-)p) k≥2 analytic in the unit disc E={z:|z|<1} and satisfying the condition |(zf′(z)/f(z)-p)/(Ap-Bzf (z)/f(z))|<1. for z∈E and -1≤B相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
Let Pk(p, A, B) be the class of functions (?) k ≥2 analytic in the unit disc E={z:|z|<1} and satisfying the condition |(zf′(z)/f(z)-p)/(Ap-Bzf(z)/f(z))|<1. for z∈E and -1≤Bk(p, A, B) under the assumption - 1 ≤B< 0 .  相似文献   

7.
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1).  相似文献   

8.
马统一 《数学季刊》2012,(2):259-269
Haberl and Ludwig introduced the L_p-intersection body I_pK for an originsymmetric star body K in R~n,where p < 1 and p ≠ 0.In this paper,we consider the Busemann-Petty’s problem for L_p-intersection bodies I_pK and I_pL.That is,whether I_pK ■ IpL implies Vol_n(K) ≤ Vol_n(L).We obtain that for two origin-symmetric star bodies K and L in R~n,such that(R~n,||·||K) embeds in L_p and I_pK ■ IpL,then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0.  相似文献   

9.
It is well known[l]that a closed linear operator A with dense domain in(an ordered)Banach space E senerates a C_O—semigroup if and only if the resolvent set p(A)contains(ω,+∞),andsup{‖(λ-ω)~nR(λ,A)~n‖:λ>ω,n∈N}<+∞(1)for someω.Sometimes,the condition(l)is not easy to verify.However,for the socalled resolvent positive operators(that is for someω,p(A)(?)(ω,+∞)and for allλ>ω,R(λ,A)=(λ-A)~1≥0),in[2],there are some easy-verified conditions.Here in thisnote,we establish another easy-verified condition.Let E_+be the positive cone of E,and  相似文献   

10.
This study proves a general result on convergence of α2x ∈ ExtA^s+2.tq+2q+1 (Zp, Zp) in the Adams spectral sequence and as a consequence, the study detects some new families in the stable homotopy groups of spheres πtq+2q-4S which is represented in the Adams spectral sequence by α2fn,α2fn,α2huhmhn ∈ ExtA^5,tq+2q+1(Zp,Zp) with tq=p^n+1q+2p^nq,2p^n+1q_P^nq,p^uq+p^mq+p^nq,respectively, where α2∈Extα^2,2q+1(Zp,Zp),fn∈ExtA^3,p^n+1q+2p^nq(Zp,Zp),fn∈ExtA^3,2p^n+2q+p^nq(Zp,Zp),hn∈ExtA^1,p^nq(Zp,Zp)and p≥5 is a prime,q=2(p=-1),n≥2.  相似文献   

11.
Let Z/(pe) be the integer residue ring modulo pe with p an odd prime and integer e ≥ 3. For a sequence (a) over Z/(pe), there is a unique p-adic decomposition (a) = (a)0 (a)1·p … (a)e-1 ·pe-1, where each (a)i can be regarded as a sequence over Z/(p), 0 ≤ i ≤ e - 1. Let f(x) be a primitive polynomial over Z/(pe) and G' (f(x), pe) the set of all primitive sequences generated by f(x) over Z/(pe). For μ(x) ∈ Z/(p)[x] with deg(μ(x)) ≥ 2 and gcd(1 deg(μ(x)),p- 1) = 1,set ψe-1 (x0, x1,…, xe-1) = xe-1·[ μ(xe-2) ηe-3 (x0, x1,…, xe-3)] ηe-2 (x0, x1,…, xe-2),which is a function of e variables over Z/(p). Then the compressing map ψe-1: G'(f(x),pe) → (Z/(p))∞,(a) (→)ψe-1((a)0, (a)1,… ,(a)e-1) is injective. That is, for (a), (b) ∈ G' (f(x), pe), (a) = (b) if and only if ψe - 1 ((a)0, (a)1,… , (a)e - 1) =ψe - 1 ((b)0,(b)1,… ,(b)e-1). As for the case of e = 2, similar result is also given. Furthermore, if functions ψe-1 and ψe-1 over Z/(p) are both of the above form and satisfy ψe-1((a)0,(a)1,… ,(a)e-1) = ψe-1((b)0,(b)1,… ,(b)e-1) for (a),(b) ∈ G'(f(x),pe), the relations between (a) and (b), ψe-1 and ψe-1 are discussed.  相似文献   

12.
NOTES ON GLAISHER'S CONGRUENCES   总被引:1,自引:0,他引:1  
Let p be an odd prime and let n≥1,k≥0 and r be integers,denote by Bk the kth Bernoulli number,It is proved that(i) If r≥1 is odd and suppose 1≥r+4,then ∑j=1^p-1 1/(np+j)^r=-(2n+1)r(r+1)/2(r+2)Bp-r-2p^2(mod p^3).(ii)If r≥2 is even and suppose p≥r+3, then p-1∑j=1 1/(np+j)^r=r/r+1Bv-r-1p(mod P^2).(iii) p-1∑j=1 1/(np+j)p-2=-(2n+1)p(mod P^2).This result generalizes the Glaisher‘s congruence. As a corollary, a generalization of the Wolsten-holme‘s theorem is obtained.  相似文献   

13.
Letp be any odd prime number. Letk be any positive integer such that . LetS = (a 1,a 2,...,a 2p−k ) be any sequence in ℤp such that there is no subsequence of lengthp of S whose sum is zero in ℤp. Then we prove that we can arrange the sequence S as follows:
(1)
whereuv,u +v ≥ 2p - 2k + 2 anda -b generates ℤp. This extends a result in [13] to all primesp andk satisfying (p + 1)/4 + 3 ≤k ≤ (p + 1)/3 + 1. Also, we prove that ifg denotes the number of distinct residue classes modulop appearing in the sequenceS in ℤp of length 2p -k (2≤k ≤ [(p + 1)/4]+1), and , then there exists a subsequence of S of lengthp whose sum is zero in ℤp.  相似文献   

14.
We determine exact values for the k-error linear complexity L k over the finite field of the Legendre sequence of period p and the Sidelnikov sequence of period p m  − 1. The results are
for 1 ≤ k ≤ (p m  − 3)/2 and for k≥ (p m  − 1)/2. In particular, we prove
  相似文献   

15.
We prove that every [n, k, d] q code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .   相似文献   

16.
LetA be the linear operator inL p (0, 1), 1<p<∞,p≠2, defined by ,xL p (0, 1),s∈[0,1]. We show that the real values of numbers in the numerical range ofA have maximum , whereq=p/(p−1). This amounts to an inequality between integrals, for which we determine the case of equality.  相似文献   

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