Complementary pairs of symmetric $2$-designs are equivalent to coherent Configurations of type $(2, 2; 2)$.D. G. Higman studied these coherent Configurations and adjacency algebras of coherent Configurations over a field of characteristic zero. These are always semisimple.  We investigate these algebras over fields of any characteristic prime and the structures.

Recently, it has been obtained a lot of results on hyperconvex space (see [1, 2, 3, 5]). In this paper we develop some of those results for Modular hyperconvex spaces.

In recent years, many authors have focused on hyperconvex space and obtained a lot of valuable results (see [1, 2, 3, 5]). In this paper we develop some of those results for Modular hyperconvex spaces. As a consequence we show that Ar (Xr) Í er (Xr) Í Hr (Xr) where, Ar (Xr), er (Xr), and Hr (Xr) are Modular admissible subsets, Modular externally hyperconvex subsets and Modular hyperconvex subsets in Xr, respectively.

Smart systems in general, and specifically neural networks, are expected to be of great assistance in large scale matrix computation. However it was necessary to work with smaller problems at first step. To this end, a method based on using perceptrons and Kohonen networks for determining the first three modal frequencies of frames of up to 20 stories high and two bays wide from their stiffness and mass matrices, was developed. This paper introduces this Modular network as a preferable alternative for designing smart systems for learning large scale mapping problems in structural engineering, and in addition, reports the successful application of this Modular network to the eigenvalue and modal frequency determination of shear frame structures.