共查询到18条相似文献,搜索用时 741 毫秒
1.
王玉玉 《数学物理学报(B辑英文版)》2008,28(2):321-332
In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s + 5 in the stable homotopy groups of spheres πrS,which is represented by 0 ≠γ^-s+3hnhm∈Ext^s+5,A ^t(Zp,Zp)in the Adams spectral sequence,where r=q(p^m+p^n+(s+3)p^2+(s+2)p+(s+1))-5,t=p^mq+p^nq+(s+3)p^2q+(s+2)pq+(s+1)q+s,p≥7,m≥n+2〉5,0≤s〈p-3,q=2(p-1). 相似文献
2.
Sums of Five Almost Equal Prime Squares 总被引:5,自引:0,他引:5
Claus BAUER 《数学学报(英文版)》2005,21(4):833-840
Let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 (mod 24) can be written as N=p1^2+p2^2+P3^2+p4^2 +p5^2, where │√N5-Pi│≤N^1/2-19/850+∈. 相似文献
3.
On sums of a prime and four prime squares in short intervals 总被引:1,自引:1,他引:0
In this paper, we prove that each sufficiently large integer N ≠1(mod 3) can be written as N=p+p1^2+p2^2+p3^2+p4^2, with
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
|p-N/5|≤U,|pj-√N/5|≤U,j=1,2,3,4,
where U=N^2/20+c and p,pj are primes. 相似文献
4.
Let Ω IR^N, (N ≥ 2) be a bounded smooth domain, p is Holder continuous on Ω^-,
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
1 〈 p^- := inf pΩ(x) ≤ p+ = supp(x) Ω〈∞,
and f:Ω^-× IR be a C^1 function with f(x,s) ≥ 0, V (x,s) ∈Ω × R^+ and sup ∈Ωf(x,s) ≤ C(1+s)^q(x), Vs∈IR^+,Vx∈Ω for some 0〈q(x) ∈C(Ω^-) satisfying 1 〈p(x) 〈q(x) ≤p^* (x) -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^+ ≤ q- ≤ q+. As usual, p* (x) = Np(x)/N-p(x) if p(x) 〈 N and p^* (x) = ∞- if p(x) if p(x) 〉 N. Consider the functional I: W0^1,p(x) (Ω) →IR defined as
I(u) def= ∫Ω1/p(x)|△|^p(x)dx-∫ΩF(x,u^+)dx,Vu∈W0^1,p(x)(Ω),
where F (x, u) = ∫0^s f (x,s) ds. Theorem 1.1 proves that if u0 ∈ C^1 (Ω^-) is a local minimum of I in the C1 (Ω^-) ∩C0 (Ω^-)) topology, then it is also a local minimum in W0^1,p(x) (Ω)) topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation (P) defined below. 相似文献
5.
Guang Shi Lü 《数学学报(英文版)》2006,22(3):907-916
In this paper we sharpen Hua's result by proving that each sufficiently large integer N congruent to 5 modulo 24 can be written as N=p1^2+p2^2+p3^2+p4^2+p5^2,with │pj-√N/5│≤U=N^1/2-1/28+ε,where pj are primes. 相似文献
6.
Local and Global Existence of Solutions to Initial Value Problems of Nonlinear Kaup-Kupershmidt Equations 总被引:6,自引:0,他引:6
Shuang Ping TAO Shang Bin CUI 《数学学报(英文版)》2005,21(4):881-892
This paper is devoted to studying the initial value problems of the nonlinear Kaup Kupershmidt equations δu/δt + α1 uδ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x,t)∈ E R^2, and δu/δt + α2 δu/δx δ^2u/δx^2 + βδ^3u/δx^3 + γδ^5u/δx^5 = 0, (x, t) ∈R^2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup- Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ H^s(R), and s ≥ 5/4 for the first equation and s≥301/108 for the second equation. 相似文献
7.
平行六边形区域上的快速离散傅立叶变换 总被引:6,自引:0,他引:6
In this paper, we propose a fast algorithm for computing the DGFT (Discrete Generalized Fourier Transforms) on hexagon domains [6], based on the geometric properties of the domain. Our fast algorithm (FDGFT) reduces the computation complexity of DGFT from O(N4) to O(N2 log N). In particulary, for N =2^P23^P34^P45^P56^P6, the floating point computation working amount equals to(17/2P2 16p3 135/8p4 2424/25p5 201/2P6)3N^2. Numerical examples are given to access our analysis. 相似文献
8.
we study an initial-boundary-value problem for the "good" Boussinesq equation on the half line
{δt^2u-δx^2u+δx^4u+δx^2u^2=0,t〉0,x〉0.
u(0,t)=h1(t),δx^2u(0,t) =δth2(t),
u(x,0)=f(x),δtu(x,0)=δxh(x).
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data (f, h, h1, h2) belong to the product space
H^5(R^+)×H^s-1(R^+)×H^s/2+1/4(R^+)×H^s/2+1/4(R^+)
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered. 相似文献
{δt^2u-δx^2u+δx^4u+δx^2u^2=0,t〉0,x〉0.
u(0,t)=h1(t),δx^2u(0,t) =δth2(t),
u(x,0)=f(x),δtu(x,0)=δxh(x).
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data (f, h, h1, h2) belong to the product space
H^5(R^+)×H^s-1(R^+)×H^s/2+1/4(R^+)×H^s/2+1/4(R^+)
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered. 相似文献
9.
In this paper, we show that the nonorientable genus of Cm + Cn, the join of two cycles Cm and Cn, is equal to [((m-2)(n-2))/2] if m = 3, n ≡ 1 (mod 2), or m ≥ 4, n ≥ 4, (m, n) (4, 4). We determine that the nonorientable genus of C4 +C4 is 3, and that the nonorientable genus of C3 +Cn is n/2 if n ≡ 0 (mod 2). Our results show that a minimum nonorientable genus embedding of the complete bipartite graph Km,n cannot be extended to an embedding of the join of two cycles without increasing the genus of the surface. 相似文献
10.
Precise Rates in the Law of Iterated Logarithm for the Moment of I.I.D. Random Variables 总被引:1,自引:0,他引:1
Ye JIANG Li Xin ZHANG 《数学学报(英文版)》2006,22(3):781-792
Let{X,Xn;n≥1} be a sequence of i,i.d, random variables, E X = 0, E X^2 = σ^2 〈 ∞.Set Sn=X1+X2+…+Xn,Mn=max k≤n│Sk│,n≥1.Let an=O(1/loglogn).In this paper,we prove that,for b〉-1,lim ε→0 →^2(b+1)∑n=1^∞ (loglogn)^b/nlogn n^1/2 E{Mn-σ(ε+an)√2nloglogn}+σ2^-b/(b+1)(2b+3)E│N│^2b+3∑k=0^∞ (-1)k/(2k+1)^2b+3 holds if and only if EX=0 and EX^2=σ^2〈∞. 相似文献
11.
Xi Mei WU Qin YUE 《数学学报(英文版)》2007,23(11):2061-2068
Let F = Q(√-p1p2) be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol (p1/p2) = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold: (1) The quartic residue symbols (p1/p2)4 = (p2/p1)4 = 1; (2) Either both
p1 and p2 are represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=ε(2x^2-p1y^2),x,y∈Z,ε∈{±1},where h+(2p1) is the narrow class number of Q(√2p1),Moreover, we also generalize these results. 相似文献
12.
Xiu Gui LIU 《数学学报(英文版)》2007,23(3):385-392
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
13.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
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
14.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
15.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
16.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
17.
Guo Xin WEI 《数学学报(英文版)》2007,23(6):1075-1082
In this paper, we give a characterization of tori S^1 ( √ nr+2-n/nr)×S^n-1(√ n-2/nr) and S^m ( √n/m ) ×S^n-m (√n-m/n). Our result extends the result due to Li (1996)on the condition that M is an n-dimensional complete hypersurface in Sn+1 with two distinct principal curvatures. Keywords principal curvature, Clifford torus, Gauss equations 相似文献
18.