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1.
Daan Krammer 《Inventiones Mathematicae》2000,142(3):451-486
We study a linear representation ρ:B
n
? GL
m
(Z[q
±1,t
±1]) with m=n(n-1)/2. We will show that for n=4, this representation is faithful. We prove a relation with the new Charney length function. We formulate a conjecture implying
that ρ is faithful for all n.
Oblatum 15-VI-1999 & 24-II-2000?Published online: 18 September 2000 相似文献
2.
F. E. A. Johnson 《K-Theory》2005,34(2):141-150
In [F.E.A. Johnson, Stable Modules and the D(2)-Problem, LMS Lecture Notes In Mathematics, vol. 301, CUP (2003)], for finite groups G, we gave a parametrization of the stable class of the augmentation ideal of Z[G] in terms of stably free modules. Whilst the details of this parametrization break down immediately for infinite groups,
nevertheless one may hope to find parallel arguments for restricted classes of infinite groups. Subject to the restriction
that Ext1(Z, Z[G]) = 0, we parametrize the minimal level in Ω1(Z) by means of stably free modules and give a lower estimate for the size of Ω1(Z). 相似文献
3.
4.
Jeremy Rickard 《Publications Mathématiques de L'IHéS》1994,80(1):81-94
If a finite group G acts on a quasi-projective variety X, then H*c(X,Z/n), the étale cohomology with compact support of X with coefficients inZ/n, has aZ/n[G]-module structure. It is well known that there is a finer invariant, an object RΓc(X,Z/n) of the derived category ofZ/n[G]-modules, whose cohomology is H*c(X,Z/n). We show that there is a finer invariant still, a bounded complex Λc(X,Z/n) of direct summands of permutationZ/n[G]-modules, well-defined up to chain homotopy equivalence, which is isomorphic to RΓc(X,Z/n) in the derived category. This complex has many properties analogous to those of the simplicial chain complex of a simplicial
complex with a group action. There are similar results forl-adic cohomology. 相似文献
5.
A. M. Sedletskii 《Journal of Mathematical Sciences》2008,155(1):170-182
Some conditions on sequences (λ
n
) and (μ
n
) to be nearby are given in order that the corresponding systems of complex exponentials (exp(iλ
n
t)) and (exp(iμ
n
t)) be simultaneously uniformly minimal in L
p
(−π, π), 1 ≤ p < ∞, and in C[−π, π].
__________
Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions),
Vol. 25, Theory of Functions, 2007. 相似文献
6.
Summary Let Fn, n≧ 1, denote the sequence of generic filiform (connected, simply connected) Lie groups. Here we study, for each Fn, the infinite dimensional simple quotients of the group C*-algebra of (the most obvious) one of its discrete cocompact subgroups Dn. For Dn, the most attractive concrete faithful representations are given in terms of Anzai flows, in analogy with the representations
of the discrete Heisenberg group H3 ⊆G3 on L2(T) that result from the irrational rotation flows on T; the representations of Dn generate infinite-dimensional simple quotients An,θ of the group C*-algebra C*(Dn). For n>1, there are other infinite-dimensional simple quotients of C*(Dn) arising from non-faithful representations of Dn. Flows for these are determined, and they are also characterized and represented as matrix algebras over simple affine Furstenberg
transformation group C*-algebras of the lower dimensional tori. 相似文献
7.
Extremal probabilities for Gaussian quadratic forms 总被引:1,自引:0,他引:1
Denote by Q an arbitrary positive semidefinite quadratic form in centered Gaussian random variables such that E(Q)=1. We prove that for an arbitrary x>0, inf
Q
P(Q≤x)=P(χ2
n
/n≤x), where χ
n
2
is a chi-square distributed rv with n=n(x) degrees of freedom, n(x) is a non-increasing function of x, n=1 iff x>x(1)=1.5364…, n=2 iff x[x(2),x(1)], where x(2)=1.2989…, etc., n(x)≤rank(Q). A similar statement is not true for the supremum: if 1<x<2 and Z
1
,Z
2
are independent standard Gaussian rv's, then sup0≤λ≤1/2
P{λZ
1
2
+(1−λ)Z
2
2
≤x} is taken not at λ=0 or at λ=1/2 but at 0<λ=λ(x)<1/2, where λ(x) is a continuous, increasing function from λ(1)=0 to λ(2)=1/2, e.g. λ(1.5)=.15…. Applications of our theorems include asymptotic
quantiles of U and V-statistics, signal detection, and stochastic orderings of integrals of squared Gaussian processes.
Received: 24 June 2002 / Revised version: 26 January 2003
Published online: 15 April 2003
Research supported by NSA Grant MDA904-02-1-0091
Mathematics Subject Classification (2000): Primary 60E15, 60G15; Secondary 62G10 相似文献
8.
O. N. Biryukov 《Journal of Mathematical Sciences》2007,146(1):5483-5489
We consider homeomorphisms ƒ of a punctured 2-disk D
2 \ P, where P is a finite set of interior points of D
2, which leave the boundary points fixed. Any such homeomorphism induces an automorphism ƒ
* of the fundamental group of D
2 \ P. Moreover, to each homeomorphism ƒ, a matrix B
ƒ (t) from GL(n, ℤ[t, t
−1]) can be assigned by using the well-known Burau representation. The purpose of this paper is to find a nontrivial lower bound
for the topological entropy of ƒ. First, we consider the lower bound for the entropy found by R. Bowen by using the growth rate of the induced automorphism
ƒ
*. Then we analyze the argument of B. Kolev, who obtained a lower bound for the topological entropy by using the spectral radius
of the matrix B
ƒ (t), where t ∈ ℂ, and slightly improve his result.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 47–55, 2005. 相似文献
9.
Dennis D. Cox 《Annals of the Institute of Statistical Mathematics》1985,37(1):271-288
Summary Given a random sample of sizen from a densityf
0 on the real line satisfying certain regularity conditions, we propose a nonparametric estimator forψ
0=−f
0
′
/f0. The estimate is the minimizer of a quadratic functional of the formλJ(ψ)+∫[ψ
2−2ψ′]dFn where λ>0 is a smoothing parameter,J(·) is a roughness penalty, andF
n
is the empirical c.d.f. of the sample. A characterization of the estimate (useful for computational purposes) is given which
is related to spline functions. A more complete study of the caseJ(ψ)=∫[d
2ψ/dx2]2 is given, since it has the desirable property of giving the maximum likelihood normal estimate in the infinite smoothness
limit (λ→∞). Asymptotics under somewhat restrictive assumptions (periodicity) indicate that the estimator is asymptotically
consistent and achieves the optimal rate of convergence. This type of estimator looks promising because the minimization problem
is simple in comparison with the analogous penalized likelihood estimators.
This research was supported by the Office of Naval Research under Grant Number N00014-82-C-0062. 相似文献
10.
A generalized polynomial is a real-valued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication,
and taking the integer part; a generalized polynomial mapping is a vector-valued mapping whose coordinates are generalized polynomials. We show that any bounded generalized polynomial
mapping u: Z
d
→ R
l
has a representation u(n) = f(ϕ(n)x), n ∈ Z
d
, where f is a piecewise polynomial function on a compact nilmanifold X, x ∈ X, and ϕ is an ergodic Z
d
-action by translations on X. This fact is used to show that the sequence u(n), n ∈ Z
d
, is well distributed on a piecewise polynomial surface (with respect to the Borel measure on that is the image of the Lebesgue measure under the piecewise polynomial function defining ). As corollaries we also obtain a von Neumann-type ergodic theorem along generalized polynomials and a result on Diophantine
approximations extending the work of van der Corput and of Furstenberg–Weiss. 相似文献
11.
Franz Kinzl 《Semigroup Forum》1989,38(1):105-118
Let S be a locally compact semigroup. We study the sequence (λn) of the convolution powers of a probability measure λ on S and their shifts by a probability measure η on S. We shall give
sufficient conditions for lim ‖λn−η*λn‖ = 0 (where ‖.‖ denotes the norm). In particular we consider the case the η is a point measure and we study the subsemigroup
LO(λ) = {x ∈ S : lim ‖λn−δX*λn‖ = 0}. We shall give necessary and sufficient conditions for Lo(λ)=S. In this case we want to treat the problem of the convergence of the sequence (λn). 相似文献
12.
Qi Yu Sun 《数学学报(英文版)》2001,17(1):1-14
Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z
0 be a subset of Z such than n∈Z
0 implies n + 1 ∈Z
0. Denote the space of all compactly supported distributions by D′, and the usual convolution between two compactly supported distributions f and g by f*g. For any bounded sequence G
n
and H
n
, n∈Z
0, in D′, define the corresponding nonstationary nonhomogeneous refinement equation
Φ
n
=H
n
*Φ
n+1
(A·)+G
n
for all n∈Z
0
where Φ
n
, n∈Z
0, is in a bounded set of D′. The nonstationary nonhomogeneous refinement equation (*) arises in the construction of wavelets on bounded domain, multiwavelets,
and of biorthogonal wavelets on nonuniform meshes. In this paper, we study the existence problem of compactly supported distributional
solutions Φ
n
, n∈Z
0, of the equation (*). In fact, we reduce the existence problem to finding a bounded solution of the linear equations
for all n∈Z
0
where the matrices S
n
and the vectors , n∈Z
0, can be constructed explicitly from H
n
and G
n
respectively. The results above are still new even for stationary nonhomogeneous refinement equations.
Received December 30, 1999, Accepted June 15, 2000 相似文献
13.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1999,51(8):1296-1302
We establish the relation between the increase of the quantityM(σ,F) = ∣a
0∣ + ∑
n=1
∞
∣a
n
∣ exp (σλ
n
) and the behavior of sequences (|a
n
|) and (λ
n
), where (λ
n
) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a
0 + ∑
n=1
∞
a
n
e
sλn
,s=σ+it, is the Dirichlet entire series.
Lviv University, Lviv. Translated from Ukrainskii Matematicheskii Zhurmal, Vol. 51, No. 8, pp. 1149–1153, August, 1999. 相似文献
14.
Brice Franke 《Extremes》2011,14(1):127-152
We investigate the recursive sequence Z
n
: = max {Z
n − 1,λ(Z
n − 1)X
n
} where X
n
is a sequence of iid random variables with exponential distributions and λ is a periodic positive bounded measurable function. We prove that the Césaro mean of the sequence λ(Z
n
) converges toward the essential minimum of λ. Subsequently we apply this result and obtain a limit theorem for the distributions of the sequence Z
n
. The resulting limit is a Gumbel distribution. 相似文献
15.
Alvaro Liendo 《Transformation Groups》2011,16(4):1137-1142
Let k
[n] = k[x
1,…, x
n
] be the polynomial algebra in n variables and let
\mathbbAn = \textSpec \boldk[ n ] {\mathbb{A}^n} = {\text{Spec}}\;{{\bold{k}}^{\left[ n \right]}} . In this note we show that the root vectors of
\textAu\textt*( \mathbbAn ) {\text{Au}}{{\text{t}}^*}\left( {{\mathbb{A}^n}} \right) , the subgroup of volume preserving automorphisms in the affine Cremona group
\textAut( \mathbbAn ) {\text{Aut}}\left( {{\mathbb{A}^n}} \right) , with respect to the diagonal torus are exactly the locally nilpotent derivations x
α
(∂/∂x
i
), where x
α
is any monomial not depending on x
i
. This answers a question posed by Popov. 相似文献
16.
To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A
[n]
so that there is canonical isomorphism of rings (H
*(X;ℚ)[2])
[n]
≅H
*(X
[n]
;ℚ)[2n] for the Hilbert scheme X
[n]
of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.
Oblatum 25-I-2001 & 18-IX-2002?Published online: 24 February 2003 相似文献
17.
V. V. Shurygin 《Journal of Mathematical Sciences》2011,177(5):758-771
The Lie jet L
θ
λ of a field of geometric objects λ on a smooth manifold M with respect to a field θ of Weil A-velocities is a generalization of the Lie derivative L
v
λ of a field λ with respect to a vector field v. In this paper, Lie jets L
θ
λ are applied to the study of A-smooth diffeomorphisms on a Weil bundle T
A
M of a smooth manifold M, which are symmetries of prolongations of geometric objects from M to T
A
M. It is shown that vanishing of a Lie jet L
θ
λ is a necessary and sufficient condition for the prolongation λ
A
of a field of geometric objects λ to be invariant with respect to the transformation of the Weil bundle T
A
M induced by the field θ. The case of symmetries of prolongations of fields of geometric objects to the second-order tangent bundle T
2
M are considered in more detail. 相似文献
18.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
19.
V. V. Shchigolev 《Journal of Mathematical Sciences》2007,142(2):2015-2019
In this paper, we calculate the space Ext
GL(n
1
)(L
n
(λ), L
n
(μ)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, L
n
(λ) and L
n
(μ) are rational irreducible GL(n)-modules with highest weights λ and μ, respectively, the restriction of L
n
(λ) to any Levi subgroup of GL(n) is semisimple, λ is a p-restricted weight, and μ does not strictly dominate λ.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 219–226, 2005. 相似文献
20.
Hiroshi Yamashita 《manuscripta mathematica》1993,79(1):1-5
We shall show two sufficient conditions under which the Iwasawa invariants λ
k
and μ
k
of a totally real fieldk vanish for an odd primel, based on the results obtained in [1], [3] and [4]. LetK
n be the composite ofk and thel
n-th cyclotomic extension of the fieldQ of rational numbers. LetC
n be the factor group of thel-class group ofK
n by a subgroup generated by ideals whose prime factors divide the principal ideal (l). Let ϕ1 be an idempotent of the group ringZ
l[Gal(K
1/k)] defined in the below. We shall prove λ
k
= μ
k
=0 if there is a natural numbern such that ε1
C
n
vanishes, under additional conditions concerning ramifications inK
n/k. 相似文献