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161.
Joel Friedman 《Combinatorica》1995,15(1):31-42
For any prime,p, we construct a Cayley graph on the group,G, of affine linear transformations ofℤ/pℤ of degree 2(p−1) and second eigenvalue
652l6/493_2005_Article_BF01294458_TeX2GIFIE1.gif" alt="
$$2\sqrt p $$
" align="middle" border="0">
with the following special property: the adjacency matrix of the graph is supported on the “blocks” associated to the trivial
representation and the irreducible representation of sizep−1. SinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions).
En route we give, for any integerk>1, a simple Cayley graph onp
k nodes of degreep of second eigenvalue
652l6/493_2005_Article_BF01294458_TeX2GIFIE2.gif" alt="
$$ \leqslant (k - 1)\sqrt p $$
" align="middle" border="0">
.
The author wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8858788,
and the Office of Naval Research under Grant N00014-87-K-0467. 相似文献
162.
Youngmee Kwon 《Probability Theory and Related Fields》1995,101(2):211-226
Summary In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is When is this process a semimartingale?. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if < 1, + 0 and not a semimartingale if < < 2.This research is supported by KOSEF grant 941-0100-011-1 相似文献
163.
Summary We study some features concerning the occupation timeA
t of a d-dimensional coneC by Brownian motion. In particular, in the case whereC is convex, we investigate the asymptotic behaviour ofP(A1u0, when the Brownian motion starts at the vertex ofC. We also give the precise integral test, which decides whether a.s., lim inf
t
A
t/(tf(t))=0 or for a decreasing functionf. 相似文献
164.
Chuu-Lian Terng 《Journal of Geometric Analysis》1995,5(1):129-150
An isometricH-action on a Riemannian manifoldX is calledpolar if there exists a closed submanifoldS ofX that meets everyH-orbit and always meets orbits orthogonally (S is called a section). LetG be a compact Lie group equipped with a biinvariant metric,H a closed subgroup ofG ×G, and letH act onG isometrically by (h
1,h
2) ·x = h
1
xh
2
−1
· LetP(G, H) denote the group ofH
1-pathsg: [0, 1] →G such that (g(0),g (1)) ∈H, and letP(G, H) act on the Hilbert spaceV = H
0([0, 1], g) isometrically byg * u = gug
−1 −g′g
−1. We prove that if the action ofH onG is polar with a flat section then the action ofP(G, H) onV is polar. Principal orbits of polar actions onV are isoparametric submanifolds ofV and are infinite-dimensional generalized real or complex flag manifolds. We also note that the adjoint actions of affine
Kac-Moody groups and the isotropy action corresponding to an involution of an affine Kac-Moody group are special examples
ofP(G, H)-actions for suitable choice ofH andG.
Work supported partially by NSF Grant DMS 8903237 and by The Max-Planck-Institut für Mathematik in Bonn. 相似文献
165.
Philippe Choné 《Potential Analysis》1995,4(3):269-296
Let be an open set inR
2 andI be a conformally invariant functional defined onH
1(,R
d
). Letu be a critical point ofI. We show that, ifu is apriori assumed to be bounded, thenu is smooth in , up to (ifu
|
is smooth). This is a partial (positive) answer to a conjecture of S. Hildebrandt [13]. As an application, we establish a regularity result for weak solutions to the equation of surfaces of prescribed mean curvature in a three-dimensional compact riemannian manifold. 相似文献
166.
Relationship between tetrahedron shape measures 总被引:6,自引:0,他引:6
Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle
min
theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form
wherec
0,c
1,e
0, ande
1 are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 相似文献
167.
A sufficient condition for the symplecticness ofq-derivative Runge-Kutta methods has been derived by F. M. Lasagni. In the present note we prove that this condition can only be satisfied for methods withq1, i.e., for standard Runge-Kutta methods. We further show that the conditions of Lasagni are also necessary for symplecticness so that no symplectic multi-derivative Runge-Kutta method can exist.This research has been supported by project PB89-0351 (Dirección General de Investigación Científica y Técnica) and by project No. 20-32354.91 of Swiss National Science Foundation. 相似文献
168.
Asynchronous two-stage iterative methods 总被引:9,自引:0,他引:9
Summary.
Parallel block two-stage iterative methods
for the solution of linear systems of algebraic equations are studied.
Convergence is shown for monotone matrices and for -matrices.
Two different asynchronous versions of these methods
are considered and their convergence investigated.
Received September 7, 1993 / Revised version received April
21, 1994 相似文献
169.
LetX be a real normed linear space,f, f
n, n , be extended real-valued proper closed convex functions onX. A sequence {x
n} inX is called diagonally stationary for {f
n} if for alln there existsx*
n f
n (x
n) such that x*
n * 0. Such sequences arise in approximation methods for the problem of minimizingf. Some general convergence results based upon variational convergence theory and appropriate equi-well-posedness are presented. 相似文献
170.