共查询到20条相似文献,搜索用时 375 毫秒
1.
Peter Danchev 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):391-402
LetF be a field of characteristicp>0 and letG be an arbitrary abelian group written multiplicatively withp-basis subgroup denoted byB. The first main result of the present paper is thatB is an isomorphism invariant of theF-group algebraFG. In particular, thep-local algebraically compact groupG can be retrieved fromFG. Moreover, for the lower basis subgroupB 1 of thep-componentG p it is shown thatG p/Bl is determined byFG. Besides, ifH is (p-)high inG, thenG p/Hp andH p n[p] for ℕ0 are structure invariants forFG, andH[p] as a valued vector space is a structural invariant forN 0 G, whereN p is the simple field ofp-elements. Next, presume thatG isp-mixed with maximal divisible subgroupD. ThenD andF(G/D) are functional invariants forFG. The final major result is that the relative Ulm-Kaplansky-Mackeyp-invariants ofG with respect to the subgroupC are isomorphic invariants of the pair (FG, FC) ofF-algebras. These facts generalize and extend analogous in this aspect results due to May (1969), Berman-Mollov (1969) and Beers-Richman-Walker (1983). As a finish, some other invariants for commutative group algebras are obtained. 相似文献
2.
In this article we present an inversion algorithm for the determination of the shape of a two-dimensional penetrable obstacle from knowledge of the elastic field generated by an incident plane compressional and shear wave. In particular, Kirsch's improved variant of the linear sampling method, the so called (F * F?)1/4-method is extended to the elastic case. A mathematical analysis that reveals the compactness and normality of the far-field operator is presented. Finally, numerical results are presented showing the robustness of the (F * F?)1/4-method with respect to noise. 相似文献
3.
Emerson de Melo 《代数通讯》2013,41(11):4797-4808
Let M = FH be a finite group that is a product of a normal abelian subgroup F and an abelian subgroup H. Assume that all elements in M?F have prime order p, and F has at most one subgroup of order p. Examples of such groups are dihedral groups for p = 2 and the semidirect product of a cyclic group F by a group H of prime order p such that C F (H) = 1 or |C F (H)| =p and C F/C F (H)(H) = 1. Suppose that M acts on a finite group G in such a manner that C G (F) = 1. We prove that the Fitting height h(G) of G is at most h(C G (H))+ 1. Moreover, the Fitting series of C G (H) coincides with the intersection of C G (H) with the Fitting series of G. 相似文献
4.
Let F be a free pro-p group of finite rank n and Cpr{C_{p^r}} a cyclic group of order p
r
. In this work we classify p-adic representations
Cpr? GLn(\mathbbZp){ C_{p^r}\longrightarrow GL_n(\mathbb{Z}_{p})} that can be obtained as a composite of an embedding Cpr? Aut(F){C_{p^r}\longrightarrow {\rm Aut}(F)} with the natural epimorphism
Aut(F)? GLn(\mathbbZp){{\rm Aut}(F)\longrightarrow GL_n(\mathbb{Z}_{p})} . 相似文献
5.
The first part of this paper is devoted to the study of FN{\Phi_N} the orthogonal polynomials on the circle, with respect to a weight of type f = (1 − cos θ)
α
c where c is a sufficiently smooth function and ${\alpha > -\frac{1}{2}}${\alpha > -\frac{1}{2}}. We obtain an asymptotic expansion of the coefficients F*(p)N(1){\Phi^{*(p)}_{N}(1)} for all integer p where F*N{\Phi^*_N} is defined by
F*N (z) = zN [`(F)]N(\frac1z) (z 1 0){\Phi^*_N (z) = z^N \bar \Phi_N(\frac{1}{z})\ (z \not=0)}. These results allow us to obtain an asymptotic expansion of the associated Christofel–Darboux kernel, and to compute the
distribution of the eigenvalues of a family of random unitary matrices. The proof of the results related to the orthogonal
polynomials are essentially based on the inversion of the Toeplitz matrix associated to the symbol f. 相似文献
6.
Assuming m − 1 < kp < m, we prove that the space C
∞(M, N) of smooth mappings between compact Riemannian manifolds M, N (m = dim M) is dense in the Sobolev space W
k,p
(M, N) if and only if π
m−1(N) = {0}. If π
m−1(N) ≠ {0}, then every mapping in W
k,p
(M, N) can still be approximated by mappings M → N which are smooth except in finitely many points. 相似文献
7.
R. Thangadurai 《Archiv der Mathematik》2002,78(5):386-396
A polynomial P(X) with coefficients {ǃ} of odd degree N - 1 is cyclotomic if and only if¶¶P(X) = ±Fp1 (±X)Fp2(±Xp1) ?Fpr(±Xp1 p2 ?pr-1) P(X) = \pm \Phi_{p1} (\pm X)\Phi_{p2}(\pm X^{p1}) \cdots \Phi_{p_r}(\pm X^{p1 p2 \cdots p_r-1}) ¶where N = p1 p2 · · · pr and the pi are primes, not necessarily distinct, and where Fp(X) : = (Xp - 1) / (X - 1) \Phi_{p}(X) := (X^{p} - 1) / (X - 1) is the p-th cyclotomic polynomial. This is a conjecture of Borwein and Choi [1]. We prove this conjecture for a class of polynomials of degree N - 1 = 2r pl - 1 N - 1 = 2^{r} p^{\ell} - 1 for any odd prime p and for integers r, l\geqq 1 r, \ell \geqq 1 . 相似文献
8.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
9.
San Ling 《Israel Journal of Mathematics》1997,99(1):29-54
Forp≥3 a prime, we compute theQ-rational cuspidal subgroupC(p
r
) of the JacobianJ
0(p
r
) of the modular curveX
0(p
r
). This result is then applied to determine the component group Φ
p
r
of the Néron model ofJ
0(p
r
) overZ
p
. This extends results of Lorenzini [7]. We also study the action of the Atkin-Lehner involution on thep-primary part ofC(p
r
), as well as the effect of degeneracy maps on the component groups. 相似文献
10.
Let
d−1{(x1,…,xd)
d:x21+···+x2d=1} be the unit sphere of the d-dimensional Euclidean space
d. For r>0, we denote by Brp (1p∞) the class of functions f on
d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on
d−1,
and Pλk(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of Brp in Lq(
d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces XN of Lq(
d−1).The main result in this paper is that for r2(d−1)2,where ANBN means that there exists a positive constant C, independent of N, such that C−1ANBNCAN.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions. 相似文献
11.
Ana Pea 《Mathematische Nachrichten》1998,189(1):195-207
In this paper we extend a result by Bourgain-Lindenstrauss-Milman (see [1]). We prove: Let 0 < ? < 1/2, 0< r < 1, r< p < 2. There exists a constant C = C(r,p,?) such that if X is any n-dimensional subspace of Lp(0, l), then there exists Y ? ?Nr with d(X, Y) ≦ 1 + ?, whenever N > Cn. As an application, we obtain the following partial result: Let 0 < r < 1. There exist constants C = C(r) and C' = C' (r) such that if X is any n-dimensional subspace of Lr(0,1), then there exists Y ? Nr with d(X, Y) ≦ C (logn)l/r, whenever N ≧ C'n. 相似文献
12.
Jianwei Zhou 《Acta Mathematica Hungarica》2006,111(1-2):29-41
Summary We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of
the Grassmann manifold GF(n,N) in the Lie group GF(N) defined naturally makes GF(n,N) a totally geodesic submanifold; (2) The imbedding S7→SO(8) defined by octonians makes S7a totally geodesic submanifold inSO(8); (3) The natural inclusion of the Lie group GF(N) in the sphere ScN^2-1(√N) of gl(N,F)is minimal. Therefore the natural imbedding GF(N)<span style='font-size:10.0pt;font-family:"Lucida Sans Unicode"'>→gl(N,F)is formed by the eigenfunctions of the Laplacian on GF(N). 相似文献
13.
Yakov G. Berkovich 《Israel Journal of Mathematics》1991,73(1):107-112
A. Kulakoff [9] proved that forp>2 the numberN
k
=N
k
(G) of solutions of the equationx
p
k
=e in a non-cyclicp-groupG is divisible byp
k+1. This result is a generalization of the well-known theorem of G. A. Miller asserting that the numberC
k
=C
k
(G) of cyclic subgroups of orderp
k
>p>2 is divisible byp. In this note we show that, as a rule: (1) ifk>1, thenN
k
≡0(modp
k+p
); (2) ifk>2, thenC
k
≡0(modp
p
). These facts are generalizations of many results from [1–5,8,9]. 相似文献
14.
本文研究了环Fpm+uFpm+u2Fpm上长度为ps的循环码分类.通过建立环Fpm+uFpm+u2Fpm到环Fpm+uFpm的同态,给出了环Fpm+uFpm+u2Fpm上长度为ps的循环码的新分类方法.应用这种方法,得到了环Fpm+uFpm+u2Fpm长度为ps的循环码的码词数. 相似文献
15.
Weiyi Su 《Journal of Approximation Theory》1986,47(4)
At present there are only a few approximate identity kernels for the Walsh system, for example, the pN-truncated Dirichlet kernel DpN − 1(t) = ∑j = 0pN − 1 wj(t) [6]; the Abel-Poisson kernel λγ(t) = ∑k = 0∞ γkwk(t) [3], and so on. In [6], Zheng has introduced a new kind of approximate identity kernels for the Walsh system—the kernels of product type. In the present paper we discuss the approximation properties of such product type kernels. Estimates of their moments as well as a direct approximation theorem are obtained. Then, to establish an inverse approximation theorem, we need the p-adic derivative of product type kernels and we estimate this derivative in L1-norm. 相似文献
16.
Greg W. Anderson 《Israel Journal of Mathematics》2003,138(1):139-156
Forx ∈ ℝ
n
andp≥1 put ‖x‖
p
:=(n
−1Σ|x
i|
p
)1/p
. An orthogonal direct sum decomposition ℝ2k
=E⊕E
⊥ where dimE=k and
‖x‖2/‖x‖1≤C is called here a (k, C)-splitting. By a theorem of Kašin there existsC>0 such that (k, C)-splittings exist for allk, and by the volume ratio method of Szarek one can takeC=32eπ. All proofs of existence of (k, C)-splittings heretofore given are nonconstructive.
Here we investigate the representation of (k, C)-splittings by matrices with integral entries. For everyC>8e
1/2
π
−1/2 and positive integerk we specify a positive integerN(k, C) such that in the set ofk by 2k matrices with integral entries of absolute value not exceedingN(k, C) there exists a matrix with row span a summand in a (k, C)-splitting. We haveN(k, C)≤218k
fork large enough depending onC. We explain in detail how to test a matrix for the property of representing a (k, C)-splitting. Taken together our results yield an explicit (if impractical) construction of (k, C)-splittings. 相似文献
17.
Armin Rainer 《Annals of Global Analysis and Geometry》2009,35(3):249-266
Let V be a real finite dimensional representation of a compact Lie group G. It is well known that the algebra of G-invariant polynomials on V is finitely generated, say by σ
1, . . . , σ
p
. Schwarz (Topology 14:63–68, 1975) proved that each G-invariant C
∞-function f on V has the form f = F(σ
1, . . . , σ
p
) for a C
∞-function F on . We investigate this representation within the framework of Denjoy–Carleman classes. One can in general not expect that f and F lie in the same Denjoy–Carleman class C
M
(with M = (M
k
)). For finite groups G and (more generally) for polar representations V, we show that for each G-invariant f of class C
M
there is an F of class C
N
such that f = F(σ
1, . . . , σ
p
), if N is strongly regular and satisfies
where m is an (explicitly known) integer depending only on the representation. In particular, each G-invariant (1 + δ)-Gevrey function f (with δ > 0) has the form f = F(σ
1, . . . , σ
p
) for a (1 + δm)-Gevrey function F. Applications to equivariant functions and basic differential forms are given.
相似文献
18.
Gabriele Nebe 《Journal of Algebra》1998,210(2):189
This paper describes the ring-theoretic structure of the group rings ofSL2(p2) over thep-adic integers. 相似文献
19.
Esther Beneish 《Algebras and Representation Theory》2012,15(3):581-592
Let G be the symmetric group on n letters. Procesi and Formanek have shown that C
n
, the center of the generic division algebra of degree n defined over a field F, is stably isomorphic to F(Bn)GF(B_{n})^{G} where B
n
is a specific ZG-lattice. We refer to B
n
as the Procesi–Formanek lattice. The question of the stable rationality of C
n
is a long standing problem for which few results are known. Let F be an algebraically closed field of characteristic zero, let p be an odd prime, and let Bp*=HomZ(Bp,Z)B_{p}^{*}=Hom_{Z}(B_{p},Z) be the dual of the Procesi–Formanek lattice. We show that F(Bp*)GF(B_{p}^{*})^{G} is stably rational over F. An interesting question is whether there exists a connection between C
p
and F(Bp*)GF(B_{p}^{*})^{G}. 相似文献
20.
Salah Mecheri 《Mathematische Nachrichten》2007,280(7):794-801
In this paper we use recent results [14] to establish various characterizations of the global minimum of the map Fψ : U → ?+ defined by Fψ (X) = ‖ψ (X)‖p (1 < p < ∞) where ψ: U → Cp is a map defined by ψ (X) = S +? (X), with ?: B (H) → B (H) a linear map and S ∈ Cp , and U = {X ∈ B (H): ? (X) ∈ Cp }. Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献