共查询到10条相似文献,搜索用时 125 毫秒
1.
S. K. Chua K. C. Toh G. Y. Zhao 《Journal of Optimization Theory and Applications》2004,123(2):291-318
An analytic center cutting-plane method with deep cuts for semidefinite feasibility problems is presented. Our objective in these problems is to find a point in a nonempty bounded convex set in the cone of symmetric positive-semidefinite matrices. The cutting plane method achieves this by the following iterative scheme. At each iteration, a query point that is an approximate analytic center of the current working set is chosen. We assume that there exists an oracle which either confirms that or returns a cut A S
m
{YS
m
: AY AY - } , where 0. If , an approximate analytic center of the new working set, defined by adding the new cut to the preceding working set, is then computed via a primal Newton procedure. Assuming that contains a ball with radius > 0, the algorithm obtains eventually a point in , with a worst-case complexity of O
*(m
3/2) on the total number of cuts generated. 相似文献
2.
KAREL Dekimpe 《Compositio Mathematica》2000,121(2):183-204
In this paper, we study polynomial structures by starting on the Lie algebra level, thenpassing to Lie groups to finally arrive at the polycyclic-by-finite group level. To be more precise,we first show how a general solvable Lie algebra can be decomposed into a sum of two nilpotentsubalgebras. Using this result, we construct, for any simply connected, connected solvable Lie groupG of dim n, a simply transitive action on R
n which is polynomial and of degree n3. Finally, we show the existence of a polynomial structure on any polycyclic-by-finite group , which is of degree h()3 on almost the entire group (h () being the Hirsch length of ). 相似文献
3.
Posterior Sensitivity to the Sampling Distribution and the Prior: More than One Observation 总被引:3,自引:0,他引:3
Sanjib Basu 《Annals of the Institute of Statistical Mathematics》1999,51(3):499-513
Sensitivity of a posterior quantity (f, P) to the choice of the sampling distribution f and prior P is considered. Sensitivity is measured by the range of (f, P) when f and P vary in nonparametric classes
f
and
P
respectively. Direct and iterative methods are described which obtain the range of (f, P) over f
f
when prior P is fixed, and also the overall range over f
f
and P
P
. When multiple i.i.d. observations X
1,...,X
k
are observed from f, the posterior quantity (f, P) is not a ratio-linear function of f. A method of steepest descent is proposed to obtain the range of (f, P). Several examples illustrate applications of these methods. 相似文献
4.
It is well-known that the distribution of a point process defined on a carrier space is uniquely characterised by its finite dimensional joint distributions of counts on disjoint subsets of . In this note, we investigate the common structure of point processes whose distributions are specified by their one dimensional distributions. We also show that, if is such a point process, then a sequence of point processes {
n
} converges in distribution to if and only if {
n
(B)} converges in distribution to (B) for a suitably rich class of sets B.
Supported by ARC Discovery project number DP0209179
Mathmatics Subject Classification (2000):Primary 60G55; Secondary 60E05, 60B10
AcknowledgementI would like to thank a referee for his valuable suggestions on the presentation of this paper. 相似文献
5.
Let G be a finite permutation group on a set with no fixed points in and let m and k be integers with 0 < m < k. For a finite subset of the movement of is defined as move() = maxgG| g \ |. Suppose further that G is not a 2-group and that p is the least odd prime dividing |G| and move() m for all k-element subsets of . Then either || k + m or k (7m – 5) / 2, || (9m – 3)/2. Moreover when || > k + m, then move() m for every subset of . 相似文献
6.
Let be a Fuchsian group of genus at least 2 (at least 3 if is non-oriented). We study the spaces of homomorphisms from to finite simple groups G, and derive a number of applications concerning random generation and representation varieties. Precise asymptotic estimates for |Hom(,G)| are given, implying in particular that as the rank of G tends to infinity, this is of the form |G|()+1+o(1), where () is the measure of . We then prove that a randomly chosen homomorphism from to G is surjective with probability tending to 1 as |G|. Combining our results with Lang-Weil estimates from algebraic geometry, we obtain the dimensions of the representation varieties
, where
is GLn(K) or a simple algebraic group over K, an algebraically closed field of arbitrary characteristic. A key ingredient of our approach is character theory, involving the study of the zeta function G(s)=(1)-s, where the sum is over all irreducible complex characters of G. 相似文献
7.
We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S
| in the spaceL
2(, ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union =12 of two simple piecewise Lyapunov curves we prove that the essential norm |S
| inL
2() is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S
| in the spaceL
2() as well as inL
2(, ) does not depend on the values of the angles and it can be calculated by formula (5). 相似文献
8.
R. V. Belova 《Mathematical Notes》1973,13(6):503-507
If is a bounded open set of a Banach space (B), is a completely continuous mapping of into the same space (B), and E- , where E is the identity transformation, is a uniformly fading mapping of into the Banach space, then the order of on equals ± 1 at every point y of .Translated from Matematicheskii Zametki, Vol. 13, No. 6, pp. 838–848, June, 1973.In conclusion, the author wishes to express her gratitude to her supervisor, K. A. Sitnikov. 相似文献
9.
Let be a locally compact second countable group, F a local field of
characteristic zero and G an F-almost-simple F-algebraic group. In
this paper we study the space X(,G) of Zariski-dense representations
: G = G(F) using the natural morphism of cohomological
functors * : H*(G, ·) H*(, ·) (where H
denotes the continuous cohomology).First let F be a p-adic field. We completely describe the relations
between the geometry and the cohomology of G : using geometric
properties of the Bruhat-Tits building of G we construct natural cocycles
for any irreducible cohomological representation of G. We then
adapt these results to the case where the field F is archimedean.Using these cocycles we obtain a simple cohomological characterization
of representations with bounded image.Our main result is then the construction, using the previous cocycles
and dynamical properties at infinity of , of cohomological
invariants (called volumes) on the space X(,G). These volumes describe
how the image () goes to infinity in G. They have coefficients
in the natural universal infinite-dimensional representation
L(, )$\mathbb{C}$ of .In the case where is a cocompact lattice of SO(n, 1) or SU(n, 1),
we use these volumes to produce new non-trivial numerical invariants
on X(,G), which refine previously known invariants.
Volumes des représentations sur un corps local相似文献
10.
O. V. Shvartsman 《Functional Analysis and Its Applications》2003,37(2):147-154
We find all pairs (,a) consisting of a cocompact Fuchsian group of genus zero and an automorphy factor a of for which the graded algebra of a--automorphic forms is free. 相似文献