共查询到20条相似文献,搜索用时 15 毫秒
1.
Shirong Li 《中国科学A辑(英文版)》1998,41(11):1121-1127
The class ℱpc of all finite groupsG is defined such thatX≤G implies that there exists an ℱ-subnormal subgroupS ofG containingX such thatX is ℱ-subabnormal inS, where ℱ is a saturated formation, closed under taken subgroups. Groups in ℱpc are characterized by ℱ-projectors and ℱ-covering subgroups.
Project supported by the National Natural Science Foundation of China (Grant No. 19760001) and the Natural Science Foundation
of Guangxi Autonomous Region. 相似文献
2.
Micheal N. Dyer 《Commentarii Mathematici Helvetici》1993,68(1):333-339
The purpose of this paper is to generalize a theorem of J. F. Adams. He showed in [A] that ifX is a subcomplex of an aspherical 2-complex and the fundamental groupG ofX has no non-trivial perfect subgroups, thenX is aspherical. We weaken the hypothesis onG to “no infinite perfect subgroups”. 相似文献
3.
Michael Hochman 《Journal d'Analyse Mathématique》2006,100(1):1-51
It is a theorem of Wyner and Ziv and Ornstein and Weiss that if one observes the initialk symbolsX
0,…,X
k−1 of a typical realization of a finite valued ergodic process with entropyh, the waiting time until this sequence appears again in the same realization grows asymptotically like 2
hk
[7, 12]. A similar result for random fields was obtained in [8]: in this case, one observes cubes in ℤ
d
instead of initial segments.
In the present paper, we describe generalizations of this. We examine what happens when the set of possible return times is
restricted. Fix an increasing sequence of sets of possible times {W
n
} and defineR
k
to be the firstn such thatX
0,…,X
k−1 recurs at some time inW
n
. It turns out that |W
R
k
| cannot drop below 2
hk
asymptotically. We obtain conditions on the sequence {W
n
} which ensure that |W
R
k
| is asymptotically equal to 2
hk
.
We consider also recurrence densities of initial blocks and derive a uniform Shannon-McMillan-Breiman theorem. Informally,
ifU
k,n
is the density of recurrences of the blockX
0,…,X
k−1 inX
−n
,…,X
n
, thenU
k,n
grows at a rate of 2
hk
, uniformly inn. We examine the conditions under which this is true when the recurrence times are again restricted to some sequence of sets
{W
n
}.
The above questions are examined in the general context of finite-valued processes parametrized by discrete amenable groups.
We show that many classes of groups have time-sequences {W
n
} along which return times and recurrence densities behave as expected. An interesting feature here is that this can happen
also when the time sequence lies in a small subgroup of the parameter group. 相似文献
4.
Michael Razar 《Israel Journal of Mathematics》1979,32(2-3):97-106
It has been long conjectured that ifn polynomialsf
1, …,f
n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf
1, …,f
n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically. 相似文献
5.
A subgroupX of the locally finite groupG is said to beconfined, if there exists a finite subgroupF≤G such thatX
g∩F≠1 for allg∈G. Since there seems to be a certain correspondence between proper confined subgroups inG and non-trivial ideals in the complex group algebra ℂG, we determine the confined subgroups of periodic simple finitary linear groups in this paper.
Dedicated to the memory of our friend and collaborator Richard E. Phillips 相似文献
6.
Jean Bourgain Jeff Kahn Gil Kalai Yitzhak Katznelson Nathan Linial 《Israel Journal of Mathematics》1992,77(1-2):55-64
LetX be a probability space and letf: X
n
→ {0, 1} be a measurable map. Define the influence of thek-th variable onf, denoted byI
f
(k), as follows: Foru=(u
1,u
2,…,u
n−1) ∈X
n−1 consider the setl
k
(u)={(u
1,u
2,...,u
k−1,t,u
k
,…,u
n−1):t ∈X}.
More generally, forS a subset of [n]={1,...,n} let the influence ofS onf, denoted byI
f
(S), be the probability that assigning values to the variables not inS at random, the value off is undetermined.
Theorem 1:There is an absolute constant c
1
so that for every function f: X
n
→ {0, 1},with Pr(f
−1(1))=p≤1/2,there is a variable k so that
Theorem 2:For every f: X
n
→ {0, 1},with Prob(f=1)=1/2, and every ε>0,there is S ⊂ [n], |S|=c
2(ε)n/logn so that I
f
(S)≥1−ε.
These extend previous results by Kahn, Kalai and Linial for Boolean functions, i.e., the caseX={0, 1}.
Work supported in part by grants from the Binational Israel-US Science Foundation and the Israeli Academy of Science. 相似文献
7.
A. Yu. Volovikov 《Journal of Mathematical Sciences》2009,159(6):790-793
Let G be a finite group and X be a G-space. For a map f: X → ℝ
m
, the partial coincidence set A(f, k), k ≤ |G|, is the set of points x ∈ X such that there exist k elements g
1,…, g
k
of the group G, for which f(g
1
x) = ⋅⋅⋅ = f(g
k
x) holds. We prove that the partial coincidence set is nonempty for G = ℤ
p
n
under some additional assumptions.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 8, pp. 61–67, 2007. 相似文献
8.
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
9.
Robert Deville 《Israel Journal of Mathematics》1989,67(1):1-22
We show that ifX is a Banach space and if there is a non-zero real-valuedC
∞-smooth function onX with bounded support, then eitherX contains an isomorphic copy ofc
0(N), or there is an integerk greater than or equal to 1 such thatX is of exact cotype 2k and, in this case,X contains an isomorphic copy ofl
2k(N). We also show that ifX is a Banach space such that there is onX a non-zero real-valuedC
4-smooth function with bounded support and ifX is of cotypeq forq<4, thenX is isomorphic to a Hilbert space. 相似文献
10.
A. Schrijver 《Discrete and Computational Geometry》1991,6(1):527-574
In this paper we describe a polynomial-time algorithm for the following problem:given: a planar graphG embedded in ℝ2, a subset {I
1, …,I
p} of the faces ofG, and pathsC
1, …,C
k inG, with endpoints on the boundary ofI
1 ∪ … ∪I
p; find: pairwise disjoint simple pathsP
1, …,P
k inG so that, for eachi=1, …,k, P
i is homotopic toC
i in the space ℝ2\(I
1 ∪ … ∪I
p).
Moreover, we prove a theorem characterizing the existence of a solution to this problem. Finally, we extend the algorithm
to disjoint homotopic trees. As a corollary we derive that, for each fixedp, there exists a polynormial-time algorithm for the problem:given: a planar graphG embedded in ℝ2 and pairwise disjoint setsW
1, …,W
k of vertices, which can be covered by the boundaries of at mostp faces ofG;find: pairwise vertex-disjoint subtreesT
1, …,T
k ofG whereT
i
(i=1, …, k). 相似文献
11.
G. Schlüchtermann 《manuscripta mathematica》1991,73(1):397-409
A sufficient condition is given when a subspaceL⊂L
1(μ,X) of the space of Bochner integrable function, defined on a finite and positive measure space (S, Φ, μ) with values in a Banach spaceX, is locally uniformly convex renormable in terms of the integrable evaluations {∫
A
fdμ;f∈L}. This shows the lifting property thatL
1(μ,X) is renormable if and only ifX is, and indicates a large class of renormable subspaces even ifX does not admit and equivalent locally uniformly convex norm. 相似文献
12.
E. G. Straus 《Israel Journal of Mathematics》1963,1(4):221-223
For any two positive integersk, l and anyɛ>0 there exists anN(k, l, ɛ) so that given anyl convex bodiesC
1, …,C
l symmetric about the origin inE
n withn≧N there exists a subspaceE
k so that eachC
i intersectsE
k, or has a projection intoE
k, in a set which is nearly spherical (asphericity <ɛ). The measure of the totality ofE
k which intersect a given body inE
n in a nearly ellipsoidal set is considered and an affine invariant measure is introduced for that purpose. 相似文献
13.
LetH be any complex inner product space with inner product <·,·>. We say thatf: ℂ→ℂ is Hermitian positive definite onH if the matrix
is Hermitian positive definite for all choice ofz
1,…,z
n inH for alln. It is strictly Hermitian positive definite if the matrix (*) is also non-singular for any choice of distinctz
1,…,z
n inH. In this article, we prove that if dimH≥3, thenf is Hermitian positive definite onH if and only if
whereb
k,l
≥0 for allk, l in ℤ, and the series converges for allz in ℂ. We also prove thatf of the form (**) is strictly Hermitian positive definite on anyH if and only if the setJ={(k,l):b
k,l
>0} is such that (0,0)∈J, and every arithmetic sequence in ℤ intersects the values {k−l: (k, l)∈J} an infinite number of times. 相似文献
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14.
We define a rank variety for a module of a noncocommutative Hopf algebra
A = L \rtimes GA = \Lambda \rtimes G where
L = k[X1, ..., Xm]/(X1l, ..., Xml), G = (\mathbbZ/l\mathbbZ)m\Lambda = k[X_1, \dots, X_m]/(X_1^{\ell}, \dots, X_m^{\ell}), G = (\mathbb{Z}/\ell\mathbb{Z})^m and char k does not divide ℓ, in terms of certain subalgebras of A playing the role of “cyclic shifted subgroups”. We show that the rank variety of a finitely generated module M is homeomorphic to the support variety of M defined in terms of the action of the cohomology algebra of A. As an application we derive a theory of rank varieties for the algebra Λ. When ℓ=2, rank varieties for Λ-modules were constructed
by Erdmann and Holloway using the representation theory of the Clifford algebra. We show that the rank varieties we obtain
for Λ-modules coincide with those of Erdmann and Holloway. 相似文献
15.
Heike Siebert 《Journal d'Analyse Mathématique》2006,98(1):145-168
LetF be a family of mappingsK-quasiregular in some domainG. We show that if for eachf∈F, there existsk>1 such that thek-th iteratef
k
off has no fixed point, thenF is normal. Moreover, we examine to what extent this result holds if we consider only repelling fixed points, rather than
fixed points in general. We also prove thatF is quasinormal, ifF contains only quasiregular mappings that do not have periodic points of some period greater than one inG. This implies that a quasiregular mappingf:ℝ
n
with an essential singularity in ∞ has infinitely many periodic points of any period greater than one. These results generalize
results of M. Essén, S. Wu, D. Bargmann and W. Bergweiler for holomorphic functions. 相似文献
16.
Jürgen Eckhoff 《Israel Journal of Mathematics》1988,62(3):283-301
LetP be a family ofn boxes inR
d
(with edges parallel to the coordinate axes). Fork=0, 1, 2, …, denote byf
k
(P) the number of subfamilies ofP of sizek+1 with non-empty intersection. We show that iff
r
(P)=0 for somer≦n, then
where thef
k
(n, d, r) are ceg196rtain definite numbers defined by (3.4) below. The result is best possible for eachk. Fork=1 it was conjectured by G. Kalai (Israel J. Math.48 (1984), 161–174). As an application, we prove a ‘fractional’ Helly theorem for families of boxes inR
d
. 相似文献
17.
Haskell P. Rosenthal 《Israel Journal of Mathematics》1970,8(3):273-303
Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inL
p
, each of mean zero, is shown to be isomorphic tol
2,l
p
,l
2⊕l
p
, or a new spaceX
p
, and the linear topological properties ofX
p
are investigated. It is proved thatX
p
is isomorphic to a complemented subspace ofL
p
and another uncomplemented subspace ofL
p
, whence there exists an uncomplemented subspace ofl
p
isomorphic tol
p
. It is also proved thatX
p
is not isomorphic to the previously knownℒ
p
spaces.
The work for this research was partially supported by the National Science Foundation GP-12997. 相似文献
18.
Let G
m,n be the class of strategic games with n players, where each player has m≥2 pure strategies. We are interested in the structure of the set of correlated equilibria of games in G
m,n when n→∞. As the number of equilibrium constraints grows slower than the number of pure strategy profiles, it might be conjectured
that the set of correlated equilibria becomes large. In this paper, we show that (1) the average relative measure of the set
of correlated equilibria is smaller than 2−n; and (2) for each 1<c<m, the solution set contains c
n correlated equilibria having disjoint supports with a probability going to 1 as n grows large. The proof of the second result hinges on the following inequality: Let c
1, …, c
l be independent and symmetric random vectors in R
k, l≥k. Then the probability that the convex hull of c
1, …, c
l intersects R
k
+ is greater than or equal to .
Received: December 1998/Final version: March 2000 相似文献
19.
LetG be ap-vertex planar graph having a representation in the plane with nontriangular facesF
1,F
2, …,F
r. Letf
1,f
2, …,f
r denote the lengths of the cycles bounding the facesF
1,F
2, …,F
r respectively. LetC
3(G) be the number of cycles of length three inG. We give bounds onC
3(G) in terms ofp,f
1,f
2, …,f
r. WhenG is 3-connected these bounds are bounds for the number of triangles in a polyhedron. We also show that all possible values
ofC
3(G) between the maximum and minimum value are actually achieved.
This research was supported in part by the U.S.A.F. Office of Scientific Research, Systems Command, under Grant AFOSR-76-3017
and the National Science Foundation under Grant ENG79-09724. 相似文献
20.
Let Gn,k denote the oriented grassmann manifold of orientedk-planes in ℝn. It is shown that for any continuous mapf: Gn,k → Gn,k, dim Gn,k = dim Gm,l = l(m −l), the Brouwer’s degree is zero, providedl > 1,n ≠ m. Similar results for continuous mapsg: ℂGm,l → ℂGn,k,h: ℍGm,l → ℍGn,k, 1 ≤ l < k ≤ n/2, k(n — k) = l(m — l) are also obtained. 相似文献