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1.
切于已知球的单形宽度   总被引:3,自引:1,他引:2  
Let w(△n) denote the width of a non-degenerate simplex △n in En and r(△n) denote the inradius of the simplex.Then, in this paper, we prove the ine-qunlity as below: Theorem:w(△n)≤βnr(△n) where βn =(n1/2(n+1))/([(n+1)/2]1/2(n+1-[(n+1)/2])1/2) The equality holds if and only if the simplex is regular.  相似文献   

2.
设G为有限群,如对每个质数r都有|NG(R1)|=|N(Un(q))(R2)|,那么G≌Un(q),此处R1∈Sylr(G),R2∈Sylr(Un(q)),n=4或5.  相似文献   

3.
设un为n阶酉群。u∈L1(Un)的Fourier级数的第二型Cesáro平均为σNα(u,U)=KN*αu(U),其中 KNα(U)=sum from (N≥li>…>ln≥-N)(Al1α…A1uN(f)Xf(U)),U∈Un为相应的核函数。本文给出“Lebesgue常数”‖KNα(L1(Un))的精确估计,并由此建立了酉群上函数的Fourier级数按第二型Cesáro求和收敛于自身的条件。  相似文献   

4.
设Pn(x)为[0,∞)上次数不超过n的代数多项式,则有‖p′n(x)e-x[0,∞)≤(6.3n+1)‖pn(x)e-x[0,∞).若pn(x)同时又是奇函数或偶函数,则有‖p′n(x)e-x[0,∞)≤(1.8+7n1/2)‖p相似文献   

5.
王军  王毅 《中国科学A辑》2000,30(3):232-240
设n和k是任意正整数 ,p是素数 ,L(kn) (p)是交换p 群 (Z/pkZ)n 的子群格 ,则存在正整数N(n ,k) ,使得当p >N(n ,k)时 ,L(kn) (p)具有强Sperner性质 .  相似文献   

6.
设Fq 是奇数阶有限域. 本文主要借助X2mpn+1 在Fq 上的不可约因式分解来确定有限域Fq上所有长为2mpn 的负循环码和自对偶的负循环码的生成多项式, 这里p 是q-1 的奇素因子, m 和n是正整数.  相似文献   

7.
设{Xn, n ≥1}是独立同分布随机变量序列, Un 是以对称函数(x, y) 为核函数的U -统计量. 记Un =2/n(n-1)∑1≤i h(Xi, Xj), h1(x) =Eh(x, X2). 在一定条件下, 建立了∑n=2(logn)δ-1EUn2I {I U n |≥n 1/2√lognε}及∑n=3(loglognε)δ-1/logn EUn2 I {|U n|≥n1/2√log lognε} 的精确收敛速度.  相似文献   

8.
右半平面内解析函数的准确零(R)级   总被引:6,自引:2,他引:4  
Let f(s)=(?)anem3(s=σ+it),0<λn↑+∞), where (?)(n/logU(λn))=E<+∞,(?)(log|αn|/λn)=0.  相似文献   

9.
三角域上Bernstein多项式的Lipschitz常数   总被引:1,自引:0,他引:1  
设T是平面上以T1,T2,T3为顶点的三角形,f(p)为定义在T上的函数,称Bn(f,P):=(?)f(i/n,j/n,k/n)Bi,j,kn(P),为f的n次Bernstein多项式,这儿Bi,j,kn(P):(n!)/(i!j!k!)uivjωk是Bernstein基函数,(u,v,w)是P关于T的重心坐标。 B.M.Brown等人对单变量的Bernstein多项式证明了如果f∈LipAλ,0<λ≤1,则对所有的n,都有Bα(f,x)∈LipAλ。本文的目的是对定义在三角域T:{(x,y):x≥0,y≥0,x+y≤1}上的Bernstein多项式证明了类似的结果: 设f(P)∈LipAλ,0<λ≤1,则对所有的n,Bn(f,P)∈Lip(21/2λA)λ,并且,在一定意义上,常数21/2λA是最好的。 上述结果对于任意的锐角或直角三角形T,也是成立的。 最后还指出,当T可为钝角三角形时,则不存在同一常数C,使对所有的n和任意三角形T,有Bn(f,P)∈Lipcλ。  相似文献   

10.
本文通过Cauchy留数定理和算子方法导出了一些形如∑i=0n (-1)n-i(n i)Um+k+i, k+i =f(n) 和∑i=02n(-1 )i(2n i) Um+k+i, k+i = g(n)的差分恒等式,这里Un, κ表示Dyck路在不同条件下的计数公式,f(n),g(n)与m(n)只和n有关的函数.  相似文献   

11.
赵红梅  唐国平 《数学进展》2008,37(2):163-170
记ZG为有限群G的整群环,△n(G)为增广理想△(G)的n次幂,Qn(G)=△"(G)/△n 1(G)为G的增广商群.本文考虑了二面体群D2tk(k 奇)和m次对称群Sm,证明了Qn(D2tk)为秩不超过2t 1的基本2-群以及Qn(Sm)≌Z2.  相似文献   

12.
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p~r,i.e.,a finite homocyclic abelian group.LetΔ~n (G) denote the n-th power of the augmentation idealΔ(G) of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q_n(G)=Δ~n(G)/Δ~(n 1)(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.  相似文献   

13.
Let G be a finite nonabelian group, ℤG its associated integral group ring, and Δ(G) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups Q n (G) = Δ n (G)/Δ n+1(G) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.  相似文献   

14.
On a Problem of Karpilovsky   总被引:5,自引:0,他引:5  
Let G be a finite elementary group. Let n (G) denote the nth power of the augmentation ideal (G) of the integral group ring G. In this paper, we give an explicit basis of the quotient group Qn(G) = n(G)/n+1 (G) and compute the order of Qn (G).2000 Mathematics Subject Classification: 16S34, 20C05  相似文献   

15.
Let G be a group, ZG the integral group ring of G, and I(G) its augmentation ideal. Let H be a subgroup of G. It is proved that the subgroup of G determined by the product I(H)I(G)I(H) equals 3(H), i.e., the third term in the lower central series of H. Also, the subgroup determined by I(H)I(G)In(H) (resp., In(H)I(G)I(H)) for n > 1 equals Dn+2(H), the (n + 2)th dimension subgroup of H.Supported by the National Board for Higher Mathematics, India.1991 Mathematics Subject Classification: 20C05, 20C07  相似文献   

16.
温亚男  常山 《大学数学》2017,33(3):9-13
群环理论将群论和环论有机地结合了起来,是代数学中的重要分支之一,其中增广理想和增广商群是群环理论中的一个经典课题.设G有限群,分别记的Burnside环及其增广理想为Ω(G)和Δ(G).本文对任意正整数n,具体构造了Δ~n(I_p)作为自由交换群的一组基,并确定了商群Δ~n(I_p)/Δ~(n+1)(I_p)的结构,其中I_p=〈a,b|a~(p~2)=b~p=1,b~(-1)ab=a~(p+1)〉,p为奇素数.  相似文献   

17.
Denote by D m the dihedral group of order 2m. Let ℛ(D m ) be its complex representation ring, and let Δ(D m ) be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient Δ n (D m )/Δ n+1(D m ) for each positive integer n.  相似文献   

18.
The article proposes a solution to the fundamental question of finding all additive relations among n-fold Pfister classes in the Witt ring and provides evidence for the solution by presenting the nth power of the augmentation ideal of an integral group ring of a group of exponent 2. The proposed solution generalizes Milnor's conjecture for quadratic forms, whose proof has been announced by V. Voevodsky.  相似文献   

19.
Guoping Tang 《K-Theory》2001,23(1):31-39
This note presents powers of the augmentation ideal of an integral group ring of an elementary p-group, generalizing results of Bak and Vavilov for elementary 2-groups and of Parmenter for elementary 3-groups.  相似文献   

20.
Let H be a finite abelian group of odd order, D be its generalized dihedral group, i.e., the semidirect product of C2 acting on H by inverting elements, where C2 is the cyclic group of order two. Let Ω (D) be the Burnside ring of D, Δ(D) be the augmentation ideal of Ω (D). Denote by Δn(D) and Qn(D) the nth power of Δ(D) and the nth consecutive quotient group Δn(D)/Δn+1(D), respectively. This paper provides an explicit Z-basis for Δn(D) and determines the isomorphism class of Qn(D) for each positive integer n.  相似文献   

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