共查询到20条相似文献,搜索用时 78 毫秒
1.
Let (
t
)
t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent
0 is the Haar measure on some compact subgroupK. Then all the measures
1
are supported by theK-contraction groupC
K() of the topological automorphism ofG. We prove here the structure theoremC
K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation. 相似文献
2.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
3.
We express the real connective K-theory groups
o4k–1(B
Q
) ofthe quaternion group Q
of order = 2
j
8 in terms of therepresentation theory of Q
by showing
o4k–1(B
Q
) =
Sp(S
4k+3/Q
)where is any fixed point free representation of Q
in U(2k + 2). 相似文献
4.
D. Y. Ye 《Journal of Optimization Theory and Applications》1993,76(2):287-304
LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR
m
, and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper. 相似文献
5.
On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results 总被引:1,自引:0,他引:1
Gerold Alsmeyer 《Journal of Theoretical Probability》2003,16(1):217-247
A result by Elton(6) states that an iterated function system
of i.i.d. random Lipschitz maps F
1,F
2,... on a locally compact, complete separable metric space
converges weakly to its unique stationary distribution if the pertinent Liapunov exponent is a.s. negative and
for some
. Diaconis and Freedman(5) showed the convergence rate be geometric in the Prokhorov metric if
for some p>0, where L
1 denotes the Lipschitz constant of F
1. The same and also polynomial rates have been recently obtained in Alsmeyer and Fuh(1) by different methods. In this article, necessary and sufficient conditions are given for the positive Harris recurrence of (M
n
)
n0 on some absorbing subset
. If
and the support of has nonempty interior, we further show that the same respective moment conditions ensuring the weak convergence rate results mentioned above now lead to polynomial, respectively geometric rate results for the convergence to in total variation or f-norm
f
, f(x)=1+d(x,x
0)
for some (0,p]. The results are applied to various examples that have been discussed in the literature, including the Beta walk, multivariate ARMA models and matrix recursions. 相似文献
6.
Richard Sowers 《Probability Theory and Related Fields》1992,92(3):393-421
Summary In this paper we establish a large deviations principle for the invariant measure of the non-Gaussian stochastic partial differential equation (SPDE)
t
v
=v
+f(x,v
)+(x,v
)
. Here is a strongly-elliptic second-order operator with constant coefficients, h:=DH
xx-h, and the space variablex takes values on the unit circleS
1. The functionsf and are of sufficient regularity to ensure existence and uniqueness of a solution of the stochastic PDE, and in particular we require that 0<mM wherem andM are some finite positive constants. The perturbationW is a Brownian sheet. It is well-known that under some simple assumptions, the solutionv
2 is aC
k
(S
1)-valued Markov process for each 0<1/2, whereC
(S
1) is the Banach space of real-valued continuous functions onS
1 which are Hölder-continuous of exponent . We prove, under some further natural assumptions onf and which imply that the zero element ofC
(S
1) is a globally exponentially stable critical point of the unperturbed equation
t
0 = 0 +f(x,0), that has a unique stationary distributionv
K,
on (C
(S
1), (C
K
(S
1))) when the perturbation parameter is small enough. Some further calculations show that as tends to zero,v
K,
tends tov
K,0, the point mass centered on the zero element ofC
(S
1). The main goal of this paper is to show that in factv
K,
is governed by a large deviations principle (LDP). Our starting point in establishing the LDP forv
K,
is the LDP for the process , which has been shown in an earlier paper. Our methods of deriving the LDP forv
K,
based on the LDP for are slightly non-standard compared to the corresponding proofs for finite-dimensional stochastic differential equations, since the state spaceC
(S
1) is inherently infinite-dimensional.This work was performed while the author was with the Department of Mathematics, University of Maryland, College Park, MD 20742, USA 相似文献
7.
Mike Jacroux Dexter C. Whittinghill III 《Annals of the Institute of Statistical Mathematics》1988,40(2):407-418
In this paper we consider the problem of determining and constructing E- and MV-optimal block designs to use in experimental settings where treatments are applied to experimental units occurring in b blocks of size k, k. It is shown that some of the well-known methods for constructing E- and MV-optimal unequally replicated designs having k fail to yield optimal designs in the case where . Some sufficient conditions are derived for the E- and MV-optimality of block designs having and methods for constructing designs satisfying these sufficient conditions are given. 相似文献
8.
If X is a smooth curve defined over the real numbers , we show that K
n
(X) is the sum of a divisible group and a finite elementary Abelian 2-group when n 2. We determine the torsion subgroup of K
n
(X), which is a finite sum of copies of and 2, only depending on the topological invariants of X() and X(), and show that (for n 2) these torsion subgroups are periodic of order 8. 相似文献
9.
J. C. Lagarias 《Monatshefte für Mathematik》1993,115(4):299-328
Given a vector of real numbers=(1,...
d
)
d
, the Jacobi-Perron algorithm and related algorithms, such as Brun's algorithm and Selmer's algorithm, produce a sequence of (d+1)×(d+1) convergent matrices {C(n)():n1} whose rows provide Diophantine approximations to . Such algorithms are specified by two mapsT:[0, 1]
d
[0, 1]
d
and A:[0,1]
d
GL(d+1,), which compute convergent matrices C(n)())...A(T())A(). The quality of the Diophantine approximations these algorithms find can be measured in two ways. The best approximation exponent is the upper bound of those values of for which there is some row of the convergent matrices such that for infinitely many values ofn that row of C(n)() has
. The uniform approximation exponent is the upper bound of those values of such that for all sufficiently large values ofn and all rows of C(n)() one has
. The paper applies Oseledec's multiplicative ergodic theorem to show that for a large class of such algorithms and take constant values and on a set of Lebesgue measure one. It establishes the formula where are the two largest Lyapunov exponents attached by Oseledec's multiplicative ergodic theorem to the skew-product (T, A,d), whered is aT-invariant measure, absolutely continuous with respect to Lebesgue measure. We conjecture that holds for a large class of such algorithms. These results apply to thed-dimensional Jacobi-Perron algorithm and Selmer's algorithm. We show that; experimental evidence of Baldwin (1992) indicates (nonrigorously) that. We conjecture that holds for alld2. 相似文献
10.
Let X be a separable Banach space with dual X
*. A countable family of elements {g
i
}X
* is a p-frame (1 p ) if the norm
X
is equivalent to the
p
-norm of the sequence {g
i
()}. Without further assumptions, we prove that a p-frame allows every gX
* to be represented as an unconditionally convergent series g=d
i
g
i
for coefficients {d
i
}
q
, where 1/p+1/q=1. A p-frame {g
i
} is not necessarily linear independent, so {g
i
} is some kind of overcomplete basis for X
*. We prove that a q-Riesz basis for X
* is a p-frame for X and that the associated coefficient functionals {f
i
} constitutes a p-Riesz basis allowing us to expand every fX (respectively gX
*) as f=g
i
(f)f
i
(respectively g=g(f
i
)g
i
). In the general case of a p-frame such expansions are only possible under extra assumptions. 相似文献
11.
We introduce a new property UKK
c
for a Banach space and show for an Orlicz sequence space the following: UKK
c
H
c
2. 相似文献
12.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K
1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K
1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism. 相似文献
13.
The class of realn × n matricesM, known asK-matrices, for which the linear complementarity problemw – Mz = q, w 0, z 0, w
T
z =0 has a solution wheneverw – Mz =q, w 0, z 0 has a solution is characterized for dimensionsn <4. The characterization is finite and practical. Several necessary conditions, sufficient conditions, and counterexamples pertaining toK-matrices are also given. A finite characterization of completelyK-matrices (K-matrices all of whose principal submatrices are alsoK-matrices) is proved for dimensions <4.Partially supported by NSF Grant MCS-8207217.Research partially supported by NSF Grant No. ECS-8401081. 相似文献
14.
R. J. Bagby 《Analysis Mathematica》1982,8(1):3-8
(, ) — R
m
×R
n
. f R
m
×R
n
fp,q, f L
p
(R
m) x y, Lq(Rn). ׃
q,r
cƒ
p,r
, ׃ R
m
×R
n
, , , q r . , ( ¦¦) K
0
(y); p, g r , K
0. 相似文献
15.
Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献
16.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
17.
We develop the notion of t-homogeneous, G-semiregular large sets of t-designs, show that there are infinitely many 3-homogeneous PSL(2, q)-semiregular large sets when q 3 mod 4, two sporadic 3-homogeneous AL(1,32)-semiregular large sets, and no other interesting t-homogeneous G-semiregular large sets for t 3. 相似文献
18.
Pavel Valtr 《Discrete and Computational Geometry》1992,7(1):135-152
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc
(k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying
for fixed
, contains at leastc convex independent points. We determine the exact asymptotic behavior ofc
(k), proving that there are two positive constants=(), such thatk
1/3c
(k)k
1/3. To establish the upper bound ofc
(k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying
. The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties. 相似文献
19.
Erwin Kreyszig 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(5):774-782
We develop Bergman-Vekua integral operator theory on the basis of a new kind of series suggested by polynomial operators (classP
j
operators); in a sense, this is an analog of the Weierstrass approach as opposed to the Cauchy-Riemann approach in classical complex analysis, which also has advantages over the original form in boundary value problems and other applications.Dedicated to the memory of my friend, Peter Henrici 相似文献
20.
Tom Lada 《Applied Categorical Structures》2004,12(1):29-34
It is shown that the direct sum of an L
algebra and a module over it has a natural L
algebra structure. 相似文献