119821589
Distance-transitive graphs and generalized polygons
On etablit un theoreme sur un graphe Γ connexe, regulier de valence k≥3, circonference finie g, avec s≥4. Γ est (G,s)-transitif pour G≤aut(Γ) tel que G(x) est fini pour chaque sommet x
122472158
3-transpositions in infinite groups
Let G be a group. A subset D will be called a set of 3-transpositions if | x | = 2 for x e D and | xy | = 3 whenever x, yeD do not commute. We will call the set D closed if xDx −1 = D for each xeD . For each xeD , let For each subset X of D , we denote by [ X ] the graph with vertex set X where two elements x, yeX are joined by an edge whenever they commute. We denote by ( X ) the complement graph; thus two elements x, yeX are joined by an edge of ( X ) whenever they do not commute.
46019521
The nonexistence of 8-transitive graphs
We prove that the inequalitys≦7 holds for finites-transitive graphs assuming that the list of known 2-transitive permutation groups is complete.
120974879
Presentations for (G,s)-transitive graphs of small valency
Given a group G , a subgroup H and an element a ∈ G , we define Γ( G, H, a ) to be the graph on the set of left-cosets of H in G , where two left-cosets g 1 H and g 2 H are adjacent whenever . We will consider this construction only in the case that The first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ( G, H, a ) is an undirected graph) and the second assures that Γ( G, H, a ) is connected.
120339122
Extended generalized hexagons
119635932
On Distance-Transitive Graphs
On suppose que Γ est un graphe non oriente connexe de genre fini g et G est un sous-groupe de aut(Γ) tel que pour chaque sommet x, G(x) est fini et agit transitivement sur l'ensemble des s-chemins (x 0 ,…,x s ) avec x 0 =x. Soit M un entier positif avec M≡3 (mod 8) et soit m=(M+9)/4 et n=max(2m+4,14). Si s≥2(m−1) et s≥(g−M)/2 alors Gm(x 0 ,…,x n )=1 pour chaque n-chemin (x 0 ,…,x n )
119855015
The application of implicit Runge-Kutta and collection methods to boundary-value problems
The solution of a nonlinear system of first order differential equations with nonlinear boundary conditions by implicit Runge-Kutta methods based on interpolatory quadrature formulae is examined. An equivalence between implicit Runge-Kutta and collocation schemes is established. It is shown that the difference equations obtained have a unique solution in a neighbourhood of an isolated solution of the continuous problem, that this solution can be computed by Newton iteration and that it converges to the isolated solution. The order of convergence is equal to the degree of precision of the related quadra- ture formula plus one. The efficient implementation of the methods is discussed and numerical examples are given. 1. Introduction. We investigate the application of certain implicit Runge- Kutta methods (cf. Butcher (2)) to the numerical solution of nonlinear boundary- value problems of the form
6860028
SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems
Abstract : In spline approximation and in the numerical solution of (systems of) ordinary differential equations, one is eventually faced with linear systems of a rather characteristic, almost block diagonal, form which reflects the underlying geometry of the problems. While these systems could be treated as banded systems, it is more efficient, both in the generation of the systems and in their numerical solution, to work explicitly with their block structure. The report describes a package of FORTRAN routines for the solution of an almost block diagonal system by Gauss elimination with scaled row pivoting. Two examples are given. The first involves the solution of an m-th order ordinary differential equation by collocation. The second example offers a package of routines for the solution of a system of first order ODEs by collection at Lobatto points which is then used on a somewhat tricky reentry problem.
53988483
Permutation groups with projective unitary subconstituents
AssTRAcT. Let r be a finite directed graph with vertex set V(I) and edge set EQ7) and let G be a subgroup of aut(I) which we assume to act transitively on both V(r) and E(r). Suppose that for some prime power q, the stabilizer G(x) of a vertex x induces on both {yI(x,y) E E(r)) and {wl(w, x) E E)} a group lying between PSU(3, q2) and Pr1U(3, q2). It is shown that if G acts primitively on V(I), then for each edge (x, y), the subgroup of G(x) fixing every vertex in {wI(x, w) or (y, w) E E(r)) is trivial.
119709952
Product Integration for the Generalized Abel Equation
The solution of the generalized Abel integral equation g(t) f {k(t, s)/(t s)a}f (s) ds, 0 < a < 1, where k(t, s) is continuous, by the product integration analogue of the trapezoidal method is examined. It is shown that this method has order two convergence for a E [al, 1) with al 0.2117. This interval contains the important case a = 2. Convergence of order two for a E (0, al) is discussed and illustrated numerically. The possibility of constructing higher order methods is illustrated with an example.
120998826
Symmetric graphs with projective subconstituents
Let P be an undirected graph and G a subgroup of aut(r) acting transitively on the vertex set of P. Let x be an arbitrary vertex of P. We denote by P(x) the set of vertices adjacent to x and by G(x)F(x) the permutation group induced by the stabilizer G (x) of x in G on P(x); G (x)r(X) is called the subconstituent of the pair (P, G). For each i E N let Gi(x) = {a E G(x)Ia E G(y) if a (x, y) 1 then s 3. In [8], it was shown that s 3. We prove the following partial result: