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1.
Dominique Arlettaz 《Central European Journal of Mathematics》2004,2(1):50-56
This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism
b
n
: π
n
(X)→H
n
(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
n
(X)→E
n
(X), F
n
(X)→(E∧F)
n
(X), F
n
(X)→H
n
(X;π
0
F) and F
n
(X)→H
n+t
(X;π
t
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in
terms of the order of the Postnikov invariants of the spectrum F. 相似文献
2.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
3.
StrongwayShi 《高校应用数学学报(英文版)》2000,15(1):45-54
Abstract. Let {Xn,n≥1} be a stationary strongly mixing random sequence satisfying EX1=u, 相似文献
4.
Marco Antei 《Israel Journal of Mathematics》2011,186(1):427-446
Let S be a connected Dedekind scheme and X an S-scheme provided with a section x. We prove that the morphism between fundamental group schemes π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) induced by the canonical morphism from X to its Albanese scheme Alb
X/S
(when the latter exists) fits in an exact sequence of group schemes 0 → (NS
X/S
τ
)⋎ → π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) → 0, where the kernel is a finite and flat S-group scheme. Furthermore, we prove that any finite and commutative quotient pointed torsor over the generic fiber X
η
of X can be extended to a finite and commutative pointed torsor over X. 相似文献
5.
《Acta Mathematica Hungarica》2003,100(1-2):1
A symmetric operator X^ is attached to each operator X that leaves the domain of a given positive operator A invariant and makes the product AX symmetric. Some spectral properties of X^ are derived from those of X and, as a consequence, various conditions ensuring positivity of products of the form AX
1 ... X
n are proved. The question of ^-complete positivity of the mapping p → Ap(X
1,...,X
n) defined on complex polynomials in n variables is investigated. It is shown that the set ω is related to the McIntosh-Pryde
joint spectrum of (X
1,...,X
n) in case all the operators A, X
1,...,X
n are bounded. Examples illustrating the theme of the paper are included.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
Nir Ben David 《Israel Journal of Mathematics》2009,170(1):317-335
A finite group G is of central type (in the non-classical sense) if it admits a non-degenerate cohomology class [c] ∈ H
2(G, ℂ*) (G acts trivially on ℂ*). Groups of central type play a fundamental role in the classification of semisimple triangular complex
Hopf algebras and can be determined by their representation-theoretical properties.
Suppose that a finite group Q acts on an abelian group A so that there exists a bijective 1-cocycle π ∈ Z
1(Q,Ǎ), where Ǎ = Hom(A, ℂ*) is endowed with the diagonal Q-action. Under this assumption, Etingof and Gelaki gave an explicit formula for a non-degenerate 2-cocycle in Z
2(G, ℂ*), where G:= A × Q. Hence, the semidirect product G is of central type.
In this paper, we present a more general correspondence between bijective and non-degenerate cohomology classes. In particular,
given a bijective class [π] ∈ H
1(Q,Ǎ) as above, we construct non-degenerate classes [cπ] ∈ H
2(G,ℂ*) for certain extensions 1 → A → G → Q → 1 which are not necessarily split. We thus strictly extend the above family of
central type groups. 相似文献
7.
负相依随机变量的自正则化中心极限定理与部分和的方差估计 总被引:1,自引:0,他引:1
§ 1 IntroductionWe firstintroduce some concepts.Random variables X and Y are called negative dependent ( ND) if for any pair ofmonotonically non-decresing functions f and g,Cov{ f( X) ,g( Y) }≤ 0 .Clearly itis equivalenttoP( X≤ x,Y≤ y)≤ P( X≤ x) P( Y≤ y)for all x,y∈R.A random sequence{ Xi,i≥ 1 } is said to be negative quadrant dependent( NQD) if any pairof variables Xi,Xj( i≠j) are ND.A sequence of random variables{ Xi,i≥ 1 } is said to be linear negative quadrand depend… 相似文献
8.
R. Vosylius 《Lithuanian Mathematical Journal》2008,48(4):463-476
We continue the investigation of regular representations of the extended Galilean group {ie463-01} acting on the smooth canonical
fiber bundle π: R
n+1 → I R
n
. First-and second-order nonholonomic affine connections Γ
1, Γ
2, Γ
1,2 are constructed using the results presented in papers [3, 4, 5, 6]. 相似文献
9.
We find the exact asymptotics (asn→∞) of the bestL
1-approximations of classesW
1
r
of periodic functions by spliness∈S
2n, r∼-1
(S
2n, r∼-1
is a set of 2π-periodic polynomial splines of orderr−1, defect one, and with nodes at the pointskπ/n,k∈ℤ) such that V
0
2π
s(
r-1)≤1+ɛ
n
, where {ɛ
n
}
n=1
∞
is a decreasing sequence of positive numbers such that ɛ
n
n
2→∞ and ɛ
n
→0 asn→∞.
Dnepropetrovsk University, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 435–444,
April, 1999. 相似文献
10.
Let X
1
, X
2
, ..., Xn be n independent identically distributed real random variables and Sn = Σ
n=1
n
Xi. We obtain precise asymptotics forP (Sn ∈ nA) for rather arbitrary Borel sets A1 in terms of the density of the dominating points in A. Our result extends classical theorems in the field of large deviations
for independent samples. We also obtain asymptotics forP (Sn ∈ γnA), with γn/n → ∞.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I. 相似文献
11.
Let {X
n
; n ≥ 1} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set
S
n
= Σ
k=1
n
X
k
, M
n
= max
k≤n
|S
k
|, n ≥ 1. Suppose σ
2 = EX
12 + 2Σ
k=2∞ EX
1
X
k
(0 < σ < ∞). In this paper, the exact convergence rates of a kind of weighted infinite series of E{M
n
−σɛ√n log n}+ and E{|S
n
| − σɛ√n log n}+ as ɛ ↘ 0 and E{σɛ√π
2
π/8logn − M
n
}+ as ɛ ↗ ∞ are obtained. 相似文献
12.
K. V. Storozhuk 《Siberian Mathematical Journal》2011,52(6):1104-1107
Let X be a Banach space and let T: X → X be a power bounded linear operator. Put X
0 = {x ∈ X ∣ T
n
x → 0}. Assume given a compact set K ⊂ X such that lim inf
n→∞
ρ{T
n
x, K} ≤ η < 1 for every x ∈ X, ∥x∥ ≤ 1. If $\eta < \tfrac{1}
{2}
$\eta < \tfrac{1}
{2}
, then codim X
0 < ∞. This is true in X reflexive for $\eta \in [\tfrac{1}
{2},1)
$\eta \in [\tfrac{1}
{2},1)
, but fails in the general case. 相似文献
13.
L.R. Mutafchiev 《Acta Mathematica Hungarica》2000,87(1-2):47-69
Let Y
s,n
denote the number of part sizes ≧ s in a random and uniform partition of the positive integer n that are counted without multiplicity. For s = λ(6n)1/2/π + o(n
1/4), 0 ≦ λ < ∞, as n → ∞, we establish the weak convergence of Y
s,n
to a Gaussian distribution in the form of a central limit theorem. The mean and the standard deviation are also asymptotically
determined.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
14.
Andrea Sambusetti 《manuscripta mathematica》1999,99(4):541-560
We prove that MinEnt (Y) ∥Y∥ = MinEnt(X) ∥X∥, for manifolds Y whose fundamental group is a subexponential extension of the fundamental group of some negatively curved, locally symmetric
manifold X. This is a particular case of a more general result holding for an arbitrary representation ρ : π1 (Y) →π1 (X), which relates the minimal entropy and the simplicial volume of X to some invariants of the couple (Y, ker (ρ)). Then, we discuss some applications to the minimal volume problem and to Einstein metrics.
Received: 23 December 1998 相似文献
15.
Let X
i
, i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z
n
= E (exp (n
Φ (∑
i
=1
n
X
i
/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without
the central limit theorem assumption.
Received: 19 September 1997 / Revised version:22 April 1999 相似文献
16.
We will consider global problems in the ringK[X
1, …,X
n] on the polynomials with coefficients in a subfieldK ofC.
LetP=(P
1, …,P
n):K
n
→K
n be a polynomial map such that (P
1,…,P
n) is a quasi-regular sequence generating a proper ideal, the main thing we do is to use the algebraic residues theory (as
described in [5]) as a computational tool to give some result to test when a map (P
1, …,P
n) is a proper map by computing a finite number of residue symbols. 相似文献
17.
We introduce an extension, indexed by a partially ordered set P and cardinal numbers κ,λ, denoted by (κ,<λ)⇝P, of the classical relation (κ,n,λ)→ρ in infinite combinatorics. By definition, (κ,n,λ)→ρ holds if every map F: [κ]
n
→[κ]<λ
has a ρ-element free set. For example, Kuratowski’s Free Set Theorem states that (κ,n,λ)→n+1 holds iff κ ≥ λ
+n
, where λ
+n
denotes the n-th cardinal successor of an infinite cardinal λ. By using the (κ,<λ)⇝P framework, we present a self-contained proof of the first author’s result that (λ
+n
,n,λ)→n+2, for each infinite cardinal λ and each positive integer n, which solves a problem stated in the 1985 monograph of Erdős, Hajnal, Máté, and Rado. Furthermore, by using an order-dimension
estimate established in 1971 by Hajnal and Spencer, we prove the relation $(\lambda ^{ + (n - 1)} ,r,\lambda ) \to 2^{\left\lfloor {\tfrac{1}
{2}(1 - 2^{ - r} )^{ - n/r} } \right\rfloor }
$(\lambda ^{ + (n - 1)} ,r,\lambda ) \to 2^{\left\lfloor {\tfrac{1}
{2}(1 - 2^{ - r} )^{ - n/r} } \right\rfloor }
, for every infinite cardinal λ and all positive integers n and r with 2≤r<n. For example, (ℵ210,4,ℵ0)→32,768. Other order-dimension estimates yield relations such as (ℵ109,4,ℵ0) → 257 (using an estimate by Füredi and Kahn) and (ℵ7,4,ℵ0)→10 (using an exact estimate by Dushnik). 相似文献
18.
David Mejzler 《Israel Journal of Mathematics》1987,57(1):1-27
LetX
1, ...,X
n be independent random variables, letF
i be the distribution function ofX
i (1≦i≦n) and letX
1n
≦... ≦X
nn be the corresponding order statistics. We consider the statisticsX
kn, wherek=k(n),k/n → 1 andn−k → ∞. Under some additional restrictions concerning the behaviour of the sequences {a
n>0,b
n,k(n),F
n} we characterize the class of all distribution functionsH such that Prob{(X
kn
−b
n
)/a
n
<x)}→H.
Dedicated to the Memory of N. V. Smirnov (1900–1966) 相似文献
19.
20.
A. Szankowski 《Israel Journal of Mathematics》1972,11(3):292-296
We construct a separable reflexive Banach spaceX which is complementably universal for all finite dimensional Banach spaces. By this we mean: for every finite dimensional
Banach spaceE there is isometric embeddingi:E→X such that there exists a projectionP: →
→
onto
with ‖P‖=1. 相似文献