共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Norio Konno 《Journal of Theoretical Probability》1995,8(4):833-876
In this paper we consider the basic contact process with infection rate λ and stirring rateD. We study the asymptotic behavior of the critical value
and survival probability
asD→∞. 相似文献
3.
Andrew J. Sommese 《Milan Journal of Mathematics》1997,67(1):49-75
Let
be an algebraic submanifold of complex projective space ℙ
N
. Assume thatn:=dim
and let
denote the restriction of the hyperplane section bundle
to
. The meromorphic map
associated to
fork≥1 ties together the pluricanonical maps of the surface sections of
. Known results show that the behavior of
is far better than one would expect from experience with the pluricanonical mappings of algebraic surfaces. In this article
we discuss the known results on the structure of the mappings
and describe the open problems.
Conferenza tenuta il 5 giugno 1997 相似文献
4.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
5.
Consider the parameter space Θ which is an open subset of ℝ
k
,k≧1, and for each θ∈Θ, let the r.v.′sY
n
,n=0, 1, ... be defined on the probability space (X,A,P
θ) and take values in a Borel setS of a Euclidean space. It is assumed that the process {Y
n
},n≧0, is Markovian satisfying certain suitable regularity conditions. For eachn≧1, let υ
n
be a stopping time defined on this process and have some desirable properties. For 0 < τ
n
→ ∞ asn→∞, set
h
n
→h ∈R
k
, and consider the log-likelihood function
of the probability measure
with respect to the probability measure
. Here
is the restriction ofP
θ to the σ-field induced by the r.v.′sY
0,Y
1, ...,
. The main purpose of this paper is to obtain an asymptotic expansion of
in the probability sense. The asymptotic distribution of
, as well as that of another r.v. closely related to it, is obtained under both
and
.
This research was supported by the National Science Foundation, Grant MCS77-09574.
Research supported by the National Science Foundation, Grant MCS76-11620. 相似文献
6.
We consider the Poisson equation −Δu=f with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain Ω with cracks. Multigrid methods for
the computation of singular solutions and stress intensity factors using piecewise linear functions are analyzed. The convergence
rate for the stress intensity factors is
whenfεL
2(Ω) and
whenfεH
1(Ω). The convergence rate in the energy norm is
in the first case and
in the second case. The costs of these multigrid methods are proportional to the number of elements in the triangulation.
The general case wherefεH
m
(Ω) is also discussed.
The work of the first author was partially supported by NSF under grant DMS-96-00133 相似文献
7.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
8.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献
9.
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
10.
Wang Yuan 《数学学报(英文版)》1993,9(4):382-389
Let
be a quadratic form with integer coefficients and letp denote a prime. Cochrane[1] proved that ifn≥4 then
has a solution
satisfying
, where
. The aim of the present paper is to generalize the above result to finite fields. 相似文献
11.
A. O. Gokhman 《Journal of Mathematical Sciences》2000,101(3):3073-3087
This article is devoted to the study of representations of Ck {
} functions f invariant with respect to finite Coxeter groups W in the form f=F op, where p is a base in the algebra of W-invariant
polynomials. We examine the lowering of smoothness of F as compared with f and conclude that this lowering has an anisotropic
nature and that, more precisely, at each point Po it is described by a vector {
}. We examine the cases W=An, Bn, Dn, {
}; in each case the greatest component {
} of {
} is equal to the Coxeter number of the stabilizer Wyo of the point yo, where po=p(yo). Bibliography: 22 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 46–70.
Translated by S. Yu. Pilyugin. 相似文献
12.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献
13.
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
14.
V. Yu. Popov 《Mathematical Notes》2000,67(4):495-504
An example of a series of varieties of rings
with the finite basis property is constructed for which the word problem in the relatively free ring
of rankn in the variety
is decidable if and only ifn <p.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000. 相似文献
15.
16.
Summary Continuing the program initiated in the first paper of this series, representations of the Lie algebra
of the Poincaré group
are constructed by forming suitable direct integrals of representations of SL(2, C) and extending them to
by means of four additional momentum operators whose matrix elements are derived in a basis adapted to the direct integral
structure. The representations obtained here include Wigner’s representations with positive mass and spin
and Wigner’s representations with zero mass, spin
and helicity ±
.
Lavoro eseguito con contributo del C.N.R. nell’ambito dell’attività di ricerca del Gruppo Nazionale per la Fisica Matematica
e per le applicazioni della Matematica alla Fisica ed all’Ingegneria.
Entrata in Redazione il 12 marzo 1972. 相似文献
17.
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
18.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
19.
R. Carroll 《Journal of Nonlinear Science》1994,4(1):519-544
Summary We use the SDiff(2) framework of Takasaki and Takebe and the (L, M) program (L is the Lax operator andMω=ωλ) to show that
=semiclassical limit ofM is
, where (
) are action angle variables in the Gibbons-Kodama theory of Hamilton-Jacobi type for dispersionless KP. We also show
is the semiclassical limit ofWxW
−1 (W is the gauge operator), whereG=WxW
−1 is a quantity studied by the author in an earlier paper in connection with symmetries. We give then a semiclassical version
of the Jevicki-Yoneya action principle for 2D gravity, where again
arises in calculations, and this yields directly the Landau-Ginsburg equation that corresponds to the semiclassical limit
of an integrated string equation. For KdV we also show how inverse scattering data are connected to Hamiltonians for dispersionless
KdV. We also discuss Hirota bilinear formulas relative to the dispersionless hierarchies and establish various limiting formulas. 相似文献
20.
Given H≥0 and bounded convex curves α1, ...,⇌n, α in the plane z=0 bounding domains D1, …, Dn, D, respectively, with
if i ∈ j and with Di ⊂ D, we obtain several results proving the existence of a constanth depending only on H and on the geometry of the curves
αi, α such that the Dirichlet problem for the constant mean curvature H equation:
where
may accept or not a solution. 相似文献