An analysis of the box and trapezoidal schemes for linear singularly perturbed boundary value problems
Stability and convergence results are derived for the box and trapezoidal schemes applied to boundary value problems for linear singularly perturbed first order systems of o.d.e.'s without turning points.

title: Product Integration for the Generalized Abel Equation
abstract: 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.

title: Bifurcation in difference approximations to two-point boundary value problems
abstract: Numerical methods for bifurcation problems of the form (*) LyAXf(y), By =0, where f(0) = 0 and f'(0) * 0, are considered. Here y is a scalar function, X is a real scalar, L is a linear differential operator and By = 0 represents some linear homogeneous two-point boundary conditions. Under certain assumptions, it is shown that if (*) is replaced by an appropriate difference scheme, then there exists a unique branch of nontrivial solutions of the discrete problem in a neighborhood of a branch of nontrivial solutions of (*) bifurcating from the trivial solution and that the discrete branch converges to the continuous one. Error estimates are derived and an illustrative numerical example is included.

title: Symmetric graphs with projective subconstituents
abstract: 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 , it was shown that s 3. We prove the following partial result:

title: Algorithm 546: SOLVEBLOK [F4]
abstract: Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for dtrect commercial advantage, the ACM copymght notice and the title of the pubhcation and its date appear, and notme is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to repubhsh, requires a fee and/or specific permission.

title: On the Approximation of Fixed Points of Nonlinear Compact Operators
abstract: Certain methods for the approximate solution of $x - Kx = 0$, where K is a compact operator, lead to a family of operator equations $x - K_n x = 0$, $n \geqq 1$, where $K_n $,$n \geqq 1$, are collectively compact and converge pointwise to K. In this paper a new and simplified proof of the existence and uniqueness of a solution of $x - K_n x = 0$ in a neighborhood of an isolated solution of $x - Kx = 0$ is given.

title: Presentations for (G,s)-transitive graphs of small valency
abstract: 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.

title: Groups with a $(B,\,N)$-pair and locally transitive graphs
abstract: Let Γ be an undirected graph and G a subgroup of aut (Γ). We denote by d(x, y) the distance between two vertices x and y, by E(Γ) the edge set of Γ, by V(Γ) the vertex set of Γ, by Γ(x) the set of neighbors of the vertex x and by G(x) the permutation group induced by the stabilizer G(x) on Γ(x). For each i e N, let G^x) = {a \ a e G(y) for every y with d(x, y) < ϊ). An s-path is an ordered sequence (x0, ••-,#«) of s + 1 vertices xt with xt e jP(Xi_i) for 1 < i < s and ^ ^ xt_2 for 2 < i < s. For each vertex x, let WS(JC) be the set of s-paths (x0, , xs) with x = x0. We say that the graph Γ is locally (G, s)-transitive if for every vertex x, G(x) acts transitively on Ws(x) but not on Ws+1(x) (compare , ). If, in addition, G acts transitively on V(Γ), then Γ is called (G, s)-transitive; otherwise Γ is bipartite with vertex blocks Vo and Vλ and G acts transitively on both Vo and VΊ, assuming that Γ is connected and s > 1. Now let G be a finite group with a (B, iV)-pair whose Weyl group is a dihedral group Z)2w of order 2n (n > 2) and .Γ be the incidence graph of the associated coset geometry as defined in [3, p. 129] (or [2, (15. 5. 1)]). The graph Γ has the following properties: (A) V(Γ) = Vo U V1 with Vo Π V1 0 and Γ(x) c F ^ for every vertex x e ^ (ί = 0 and 1). For j = 0 and 1 there exists a dt e N such that \Γ(x)\ = dt + 1 for every vertex xe Vi% The diameter of Γ is πand the girth 2n. (B) Γ is locally (G, τι + l)-transitive. A generalized n-gon of order (d0, dλ) is, by definition, an incidence structure whose incidence graph has the properties listed in (A). W. Feit and G. Higman have shown in  that finite generalized ra-gons of order (d0, dλ) with dod1 > 1 exist only for n = 2, 3, 4, 6, 8 and 12, that

title: On finite Moufang polygons
abstract: We show that a finite generalized polygon Γ is Moufang with respect to a groupG if and only if for every flag {x, y} of Γ, the subgroupG1(x, y) ofG fixing every element incident with one ofx, y acts transitively on the set of apartments containing the elementsu, x, y, w, whereu≠y (resp.w≠x) is an arbitrary element incident withx (resp.y).

title: On Distance-Transitive Graphs
abstract: 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 )

title: Über symmetrische Graphen und die projektiven Gruppen