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1.
Nigel Byott 《manuscripta mathematica》1991,73(1):289-311
LetL/K be a totally ramified, finite abelian extension of local fields, let
and
be the valuation rings, and letG be the Galois group. We consider the powers
of the maximal ideal of
as modules over the group ring
. We show that, ifG has orderp
m
(withp the residue field characteristic), ifG is not cyclic (or ifG has orderp), and if a certain mild hypothesis on the ramification ofL/K holds, then
and
are isomorphic iffr≡r′ modp
m
. We also give a generalisation of this result to certain extensions not ofp-power degree, and show that, in the casep=2, the hypotheses thatG is abelian and not cyclic can be removed. 相似文献
2.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1986,38(1):195-204
Summary LetX be a positive random variable with the survival function
and the densityf. LetX have the moments μ=E(X) and μ2=E(X
2) and put ε=|1-μ2/2μ2|. Put
and
. It is proved that the following inequalities hold:
, for allx>0, ifq(x) is monotone and that
, ifq
1
(x) is monotone. It is also shown that Brown's inequality
which holds wheneverq
1
(x) is increasing is not valid in general whenq
1 is decreasing.
The Institute of Statistical Mathematics 相似文献
3.
Let K be a field and
a non-trivial valuation ring of K withm as its maximal ideal. Denote by
and
the rings of polynomials f∈K[X] and rational functions f∈K(X) resp. such that
. We prove that for one variable X we have
if and only if the completion of (K,
) is locally compact or algebraically closed. In the second case—i.e. if K is dense in the algebraic closure of (K,
)—we even get
for any number of variables X=(X1,...,Xn).
This work contains parts of the second author's thesis [Ri] written under the supervision of the first author. 相似文献
4.
We obtain a set of necessary and sufficient conditions for
to imply
for 1 <k ≤ s < ∞. Using this result we establish several inclusion theorems as well as conditions for the equivalence of
and
. 相似文献
5.
Let
and
be a perturbed eigenpair of a diagonalisable matrixA. The problem is to bound the error in
and
. We present one absolute perturbation bound and two relative perturbation bounds.
The absolute perturbation bound is an extension of Davis and Kahan's sin θ Theorem from Hermitian to diagonalisable matrices.
The two relative perturbation bounds assume that
and
are an exact eigenpair of a perturbed matrixD
1
AD
2
, whereD
1 andD
2 are non-singular, butD
1
AD
2 is not necessarily diagonalisable. We derive a bound on the relative error in
and a sin θ theorem based on a relative eigenvalue separation. The perturbation bounds contain both the deviation ofD
1 andD
2 from similarity and the deviation ofD
2 from identity.
This work was partially supported by NSF grant CCR-9400921. 相似文献
6.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
7.
Sandra Di Rocco 《manuscripta mathematica》1996,91(1):35-59
Let
be the set of surfaces,S, polarized by a k-very ample line bundle,L, with genus≤3k+1. All the elements (S, L) of
are listed. The classification of surfaces polarized by ak-very ample line bundle of degree ≤4k+4 is completed by proving that this class of surfaces is a subset of
. 相似文献
8.
Akira Endô 《manuscripta mathematica》1990,69(1):107-132
Let p be an odd prime number and n a natural number. Let K be a (2,...,2)-extension of the pn−th cyclotomic number field obtained by adjoining
,...,
, where m1,...,mt are rational integers. We get a system of generators of the minus part of the Stickelberger ideal of K, and calculate its
index. This index is described as a product of some determinants of rational integer components. From this result, it is shown
that the relative class number of K is expressed as this index. 相似文献
9.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献
10.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
11.
Shripad M. Garge 《Proceedings Mathematical Sciences》2005,115(4):411-427
The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning
of such order coincidences through the transitive actions of compact Lie groups.
It is a theorem of Artin and Tits that a finite simple group is determined by its order, with the exception of the groups
(A3(2), A2(4)) and(B
n
(q), C
n
(q)) forn ≥ 3,q odd. We investigate the situation for finite semisimple groups of Lie type. It turns out that the order of the finite
group H(
) for a split semisimple algebraic groupH defined over
, does not determine the groupH up to isomorphism, but it determines the field
under some mild conditions. We then put a group structure on the pairs(H
1,H
2) of split semisimple groups defined over a fixed field
such that the orders of the finite groups H1(
) and H2(
) are the same and the groupsH
i
have no common simple direct factors. We obtain an explicit set of generators for this abelian, torsion-free group. We finally
show that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of
compact Lie groups. 相似文献
12.
Summary LetG be the coadjoint group of a finite-dimensional complex Lie algebrag. Forg solvable, the Dixmier-map is known to be a homeomorphism
of the orbit space
/G onto the space χ of primitive ideals in the enveloping algebra U(G) [6,15]. For
, the Dixmier-map is known to be a bijection (and in general not a homeomorphism)
with the space χl of all completely prime primitive ideals [7, 16]. Here we derive from a result ofW. SOERGEL [18], that this map issheet- wise a homeomorphism onto the image. Here a sheet is a maximal irreducible subset consisting of orbits of a fixed dimension; obviouslyg decomposes into finitely many sheets [3]. The results of this paper hold more generally forg semisimple, if one restricts to a sheet of polarizable orbits, where a Dixmier-map can be defined.
Relative to a fixed polarization (a parabolic subalgebra)p ⊂g let I be the annihilator of the generic module induced from p. The „relative enveloping algebra“
) has been studied e.g. bySOERGEL [19, 18]. Its center Z is described here by a relative Harish-Chandra isomorphism of the normalization
with a suitable ring of group invariants (3.2). We study here the extension
ofU by
. We suggest that this very mild central extension ofU generates good properties and is very suitable for the study of the Dixmier-map (cf.4.3,5.6).
In particular, we conjecture in case
: Every minimal primitive ideal of
is generated by a maximal ideal of the center. This would generalize for
a well known theorem ofM. Duflo (casep Borel, where
).
AsJ. Dixmier communicated in a letter, the main result here is exactly what he had hoped for when he first introduced a notion of sheets
many years ago.
Added in proof: This conjecture will be proved in a subsequent paper. 相似文献
Added in proof: This conjecture will be proved in a subsequent paper. 相似文献
13.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
14.
V. Totik 《Periodica Mathematica Hungarica》1985,16(2):115-126
It is proved that an integrable functionf can be approximated by the Kantorovich type modification of the Szász—Mirakjan and Baskakov operators inL
1 metric in the optimal order {n
–1} if and only if
2
f is of bounded variation where
and
, respectively. 相似文献
15.
Kôichi Inada 《Annals of the Institute of Statistical Mathematics》1984,36(1):207-215
Summary This paper considers the problem of estimating a normal mean from the point of view of the estimation after preliminary test
of significance. But our point of view is different from the usual one. The difference is interpretation about a null hypothesis.
Let
denote the sample mean based on a sample of sizen from a normal population with unknown mean μ and known varianceσ
2. We consider the estimator that assumes the value
when
and the value
when
where ω is a real number such that 0≤ω≤1 andC is some positive constant. We prove the existence of ω, satisfying the minimax regret criterion and make a numerical comparison
among estimators by using the mean square error as a criterion of goodness of estimators. 相似文献
16.
M. B. Zvyagina 《Journal of Mathematical Sciences》1998,89(2):1122-1126
Let Λ be an associative ring with identity and let
be the category of left unitary Λ-modules. A subcateqory
of the category
is said to be small if the pairwise nonisomorphic objects of
form a set. The main result of this paper consists of the fact that for every small full subcategory
, there exists a ring Γ such that
is dual to a small full subcategory of the category
. Some applications of this result are indicated. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 66–73. 相似文献
17.
A graphG is embeddable in its complement
ifG is isomorphic with a subgraph of
. A complete characterization is given of those (p,p−1) graphs which are embeddable in their complements. In particular, letG be a (p,p−1) graph wherep≧6 ifp is even andp≧9 ifp is odd; thenG is embeddable in
if and only ifG is neither the starK
1,p−1 norK
1,n
∪C
3 withn≧4. 相似文献
18.
LetW be an open Riemann surface and
ap-sheeted (1<p<∞) unlimited covering surface ofW. Denote by Δ1 (resp.,
) the minimal Martin boundary ofW (resp.,
). For ζ ∈ Δ, let
ζ be the (cardinal) number of the set of pionts
which lie over ζ and
the class of open connected subsetsM ofW such thatM∪{ζ} is a minimal fine neighborhood of ζ. Our main result is the following:
, where
is the number of components of π-1
M and π is the projection of
ontoW. Moreover, some applications of the above results are discussed whenW is the unit disc. 相似文献
19.
Alexander Prestel 《Israel Journal of Mathematics》1991,73(2):199-205
LetK be an (infinite) number field. IfK is elementarily determined by its absolute Galois groupG(K) (see (1.1) below), thenK is isomorphic to
, R ∩
or some henselian subfield of
. 相似文献
20.
Zeng Guangxing 《中国科学A辑(英文版)》1999,42(3):272-280
For an ordered field (K,T) and an idealI of the polynomial ring
, the construction of the generalized real radical
ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing
is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project. 相似文献