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1.
Hélène Barcelo 《Journal of Algebraic Combinatorics》1993,2(1):5-23
We describe a straightening algorithm for the action of S
n on a certain graded ring
. The ring
appears in the work of C. de Concini and C. Procesi [2] and T. Tanisaki [8], and more recently in the work of A. Garsia and C. Procesi [4]. This ring is a graded version of the permutation representation resulting from the action of S
n on the left cosets of a Young subgroup. As a corollary of our straightening algorithm we obtain a combinatorial proof of the fact that the top degree component of
affords the irreducible representation of S
n indexed by . 相似文献
2.
Gerold Alsmeyer 《Journal of Theoretical Probability》2002,15(2):259-283
It is proved that for each random walk (S
n
)
n0 on
d
there exists a smallest measurable subgroup
of
d
, called minimal subgroup of (S
n
)
n0, such that P(S
n
)=1 for all n1.
can be defined as the set of all x
d
for which the difference of the time averages n
–1
n
k=1
P(S
k
) and n
–1
n
k=1
P(S
k
+x) converges to 0 in total variation norm as n. The related subgroup
* consisting of all x
d
for which lim
n P(S
n
)–P(S
n
+x)=0 is also considered and shown to be the minimal subgroup of the symmetrization of (S
n
)
n0. In the final section we consider quasi-invariance and admissible shifts of probability measures on
d
. The main result shows that, up to regular linear transformations, the only subgroups of
d
admitting a quasi-invariant measure are those of the form
1×...×
k
×
l–k
×{0}
d–l
, 0kld, with
1,...,
k
being countable subgroups of
. The proof is based on a result recently proved by Kharazishvili(3) which states no uncountable proper subgroup of
admits a quasi-invariant measure. 相似文献
3.
Palle E. T. Jorgensen 《Integral Equations and Operator Theory》1999,35(2):125-171
This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let
be a Hilbert space, and let be a representation ofL
(
) on
. LetR be a positive operator inL
(
) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on
(bounded, but noncontractive) such that
where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of
which reduces such thatM acts as a shift on one part, and the residual part is
() =
n
[M
n
], where [M
n
] is the closure of the range ofM
n
. The shift part is present, we show, if and only if ker (M
*){0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation , we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL
2(E
n
) L
2(), whereE
n , n=1,2,3,..., , are measurable subsets which form a tiling of ; i.e., the union is up to zero measure, and pairwise intersections of differentE
n
's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.Terminology used in the paper
the one-torus
-
Haar measure on the torus
-
Z
the Zak transform
-
X=ZXZ
–1
transformation of operators
-
a given Hilbert space
-
a representation ofL
(
) on
-
R
the Ruelle operator onL
(
)
-
M
an operator on
-
R
*,M
*
adjoint operators
Work supported in part by the U.S. National Science Foundation. 相似文献
4.
Let
, the parameter space, be an open subset ofR
k
,k1. For each
, let the r.v.'sX
n
,n=1, 2,... be defined on the probability space (X, P
) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the -field of Borel subsets ofS. ForhR
k
and a sequence of p.d. normalizing matrices
n
=
n
k × k
(0 set
n
*
= * = 0 +
n
h, where 0 is the true value of , such that *,
. Let
n
(*, *)( be the log-likelihood ratio of the probability measure
with respect to the probability measure
, whereP
n
is the restriction ofP
over
n
= (X
1,X
2,...,X
n
. In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account. 相似文献
5.
Bruno Kahn 《K-Theory》2002,25(2):99-139
Let A be a commutative semi-local ring containing 1/2. We construct natural isomor-phisms
if A is nonexceptional. We deduce that, for a nonexceptional scheme X quasi-projective or regular over Z[1/2], the groups K
n(X,Z/2) and
are finite for n dim(X)-1. When X is a variety over F
p or Q
p with p odd, we also obtain finiteness results for K
*(X) and
. Finally, using higher Chern classes with values in truncated étale cohomology, we show that, for X over Z[1/2], of Krull dimension d, quasi-projective over an affine base (resp. smooth over a field or a discrete valua-tion ring), K
n(X,Z/2) is isomorphic for n 3 (resp. for n 2) to
, up to controlled torsion depending only on n and d (not on ). Here, is the projection from the étale site of X to its Zariski site and denotes truncation in the derived category. 相似文献
6.
Matthew R. Brown 《Journal of Algebraic Combinatorics》2002,15(2):107-125
If a GQ S of order (s, s) is contained in a GQ S of order (s, s
2) as a subquadrangle, then for each point X of S\S the set of points
of S collinear with X form an ovoid of S. Thas and Payne proved that if S=
(4,q),q even, and
is an elliptic quadric for each XS\S,thenS
(5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex. 相似文献
7.
Let
be the prime factorization of a positive integer k and let b
k
(n) denote the number of partitions of a non-negative integer n into parts none of which are multiples of k. If M is a positive integer, let S
k
(N; M) be the number of positive integers N for which b
k(n
) 0(mod
M). If
we prove that, for every positive integer j
In other words for every positive integer j,
b
k(n) is a multiple of
for almost every non-negative integer n. In the special case when k=p is prime, then in representation-theoretic terms this means that the number ofp -modular irreducible representations of almost every symmetric groupS
n is a multiple of p
j. We also examine the behavior of b
k(n) (mod
) where the non-negative integers n belong to an arithmetic progression. Although almost every non-negative integer n (mod t) satisfies b
k(n) 0 (mod
), we show that there are infinitely many non-negative integers n r (mod t) for which b
k(n) 0 (mod
) provided that there is at least one such n. Moreover the smallest such n (if there are any) is less than 2
. 相似文献
8.
Gerold Alsmeyer 《Mathematical Methods of Operations Research》1986,30(3):A111-A134
Let
1, 2, ... be a sequence of i.i.d. random variables with positive mean
and finite variance
and letr(b), b0, be real numbers tending to 0 asb . Definings
n=1+...+n andS
n=Sn(b)=sn+r(b)n, the stopping time =(b)=inf {n>/1:Sn >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR
b=s+r(b)–b. It turns out that the limiting distribution ofR
b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.
Zusammenfassung Seien 1, 2, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners 1, s2, ... der zugehörige Summenprozeß,S n= Sn(b)=sn+r(b)n fürn1 und =(b)=inf {n1: Sn>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR b=s +r(b) –b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.相似文献
9.
Mark C. Ho 《Integral Equations and Operator Theory》2001,41(2):179-188
Let
be the unit circle {z|z|=1} and
n
c
n
e
in
be a bounded measurable function on
. Theslant Toeplitz operator A
onL
2 (
) is defined by A
e
n
,e
m
=c
2m–n
for allm, n wheree
n
(z)=z
n
,
. In this paper, we continue the study initiated in [6] onA
*
, the adjoint ofA
. Specifically, we will show that for a certain dense set of continuous functions on
,A
*
is similar to some constant multiple of either a shift, or a shift plus a rank one operator. 相似文献
10.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
11.
Anthony Bak 《K-Theory》1991,4(4):363-397
A functorial filtration GL
n
=S–1L
n
S0L
n
S
i
L
n
E
n of the general linear group GL
n, n 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S–1 L
n
(A)/S0L
n
(A) is abelian, that S0L
n
(A)
S1L
n
(A)
is a descending central series, and that S
i
L
n
(A) = E
n(A) whenever i the Bass-Serre dimension of A. In particular, the K-functors k
1 S
i
L
n
=S
i
L
n
/E
n are nilpotent for all i 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S
i
L
n
(A)/S
i+1 L
n
(A)S
i
L
n+ 1(A)/S
i+1
L
n + 1 (A) is injective whenever n i + 3, so that one has stability results without stability conditions, and if A is commutative then S0L
n
(A) agrees with the special linear group SL
n
(A), so that the functor S0L
n
generalizes the functor SL
n
to noncommutative rings. Applying the above to subgroups H of GL
n
(A), which are normalized by E
n(A), one obtains that each is contained in a sandwich GL
n
(A, )
H
E
n(A, ) for a unique two-sided ideal of A and there is a descending S0L
n
(A)-central series GL
n
(A, )
S0L
n
(A, )
S1L
n
(A, )
S
i
L
n
(A, )
E
n(A, ) such that S
i
L
n
(A, )=E
n(A, ) whenever i Bass-Serre dimension of A.Dedicated to Alexander Grothendieck on his sixtieth birthday 相似文献
12.
H. Queffelec 《Monatshefte für Mathematik》1992,114(2):135-138
Let (c
n)
nZ
be a double-sided sequence of complex numbers; if, for quasi-all (i.e. in the Baire sense) choices of signs (
n)
nZ
, (
n
c
n)
nZ
is a Fourier-Stieltjes sequence, then we prove that (c
n)
nZ
l
2 (Z); this extends a result of Littlewood and at the same time provides a very simple proof of this result. 相似文献
13.
Prof. Dr. E. Binz 《Monatshefte für Mathematik》1980,89(4):275-288
OnE(M,
n
), the Fréchet-manifold of all smooth embeddings of a smooth, compact, closed, orientable manifoldM (of dimensionn-1) into
n
two natural metricsG and
are considered. The metric
plays a central rôle in elasticity theory. Using a generalised notion of the Fréchet derivative their respective spraysS and
and the correspoonding Levi-Civita connections are computed. BothS and
are smooth in a well defined sense. In contrast toS the spray
turns out to be trivial. 相似文献
14.
We study the spectrum of the perturbed shift operator
on the space
assuming that the set of values of the function a(n) is finite. It is shown that if the values of a(n) are distributed on the axis Z with a uniform frequency, then the essential part of the spectrum fills a generalized lemniscate. Bibliography: 9 titles. 相似文献
15.
S. Zhang 《Algebra Universalis》1996,35(4):485-505
Let
be a variety of completely regular semigroups. Define
C
* to be the class of all completely regular semigroupsS whose least full and self-conjugate subsemigroupC
*(S) belongs to
. ThenC
* is an operator on the lattice
of varieties of completely regular semigroups. In this note we show that the order ofC
* is infinite. This fact yields that the Mal'cev project is not associative on
. We describe
(C
*)1,
andi 0, in terms of -invariant normal subgroups of the free group over a countably infinite set. The lattice theoretic properties ofC
* are also studied.Presented by W. Taylor. 相似文献
16.
A. Schinzel 《Monatshefte für Mathematik》1986,102(4):309-337
Letk>1 and let
be non-zero algebraic numbers contained in the field
. It is shown that for almost all, in the sense of density integer vectorsn
1,...,n
k
the polynomial
becomes irreducible over
on dividing by the product of all factorsx–, where is a root of unity.Dedicated to Professor E. Hlawka on the occasion of his seventieth birthday 相似文献
17.
LetF be a finite set of cardinality ¦F¦ =q 2,n 1 an integer and :F
n×Fn0 theHamming metric. Acode isomorphism C D between two block codesC,D
Fn is defined as an isometry which can be extended to an isometry of the whole space Fn. Any permutation S
n
of the positions canonically induces a so-calledequivalence map
Aut Fn; any system (1,2,...,n) ofn permutations of the character setF induces a so-calledconfiguration
Aat Fn. The group Aut Fn of all isometries of Fn turns out to be semidirect product of the configuration group with the symmetric group of degreen. The codeword estimating failure probability of a maximum likelihood codeword estimator for aq-nary symmetric channel does not depend on the transmitted codeword, if the automorphism group of the code acts transitively on the set of codewords. When using a systematic (n, k)-encoder, the symbol decoding failure probability does not depend on the transmitted symbol or on the time of transmission if the configuration group and the automorphism group act transitively on the set of codewords resp. on the set of thek information positions.In memoriam Giuseppe Tallini 相似文献
18.
The Jacobian conjecture for polynomial maps :K
n
K
n
is shown to be equivalent to a certain Lie algebra theoretic property of the Lie algebra
of formal vector fields inn variables. To be precise, let
be the unique subalgebra of codimensionn (consisting of the singular vector fields),H a Cartan subalgebra of
,H
the root spaces corresponding to linear forms onH and
. Then every polynomial map :K
n
K
n
with invertible Jacobian matrix is an automorphism if and only if every automorphism of
with (A)
satisfies (A)=A. 相似文献
19.
If is a collection of subsets ofS andw is a nonnegative weight function onS, the problem of selecting a subset belonging to which has maximum weight is solved by a greedy-type algorithm forall w if and only if is the set of independent sets of a matroid. This result is then generalised to show that greedy-type algorithms select an optimum forall linear functionsc·x; x in some compact set
andc > 0 if and only if the convex closure ofU is essentially a polymatroid. A byproduct of this is a new characterization of polymatroids. 相似文献
20.
Martin J. B. Appel Michael J. Klass Ralph P. Russo 《Journal of Theoretical Probability》1999,12(1):27-47
Let U
1, U
2,... be a sequence of i.i.d. random mappings taking values in a space S and let h be a symmetric function on S×S with global maximum
Let {x
n} be any nondecreasing real sequence converging to
Then p=P(H
n>x
n, infinitely often) is either zero or one, where H
n=max{h(U
i, U
j), 1 ijn}. This paper provides a nonrandom series criterion which is necessary and sufficient to determine the value of p. In addition, various sufficient conditions are presented which may be easier to apply. A number of metric space applications are given. 相似文献