We identify a weak critical set in each cyclic latin square of order greater than 5. This provides the first example of an infinite family of weak critical sets. The proof uses several constructions for latin interchanges which are generalisations of those introduced by Donovan and Cooper.

For symmetric inde®nite tridiagonal matrices, block LDL factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots. Ó 1999 Elsevier Science Inc. All rights reserved. AMS classi®cation: 65F05; 65G05

We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges its two parts. To prove this, we study the relationship between symmetric bipartite graphs and graphs with loops.

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.

We propose a clustering heuristic based on circuit con-nectivity which produces a large number of small clusters of nearly equal size. We investigate a two phase partitioning heuristic. Cell interchanges are applied to a clustered circuit and subsequently to the original circuit. Numerical results demonstrate our two phase heuristic produces better partitions with less computational eeort than ...

A series of field evaluations was performed at three freeway interchange ramps in Michigan that possessed significant horizontal curvature to assess the impacts a dynamic speed feedback sign (DSFS) on driver selection and brake response while approaching entering ramp curve. DSFS with 15 in. full-matrix display temporarily installed each exit locations. The programmed same message location, whi...