Applications of the combinatorial configurations for optimization of technological systems

Abstract

This paper involves techniques for improving the quality indices of engineering devices or systems with nonuniform structure (e.g. arrays of sonar antenna arrays) with respect to performance reliability, transmission speed, resolving ability, and error protection, using novel designs based on combinatorial configurations such as classic cyclic difference sets and novel vector combinatorial configurations. These design techniques makes it possible to configure systems with fewer elements than at present, while maintaining or improving on the other operating characteristics of the system. Several factors are responsible for distinguish of the objects depending an implicit function of symmetry and non-symmetry interaction subject to the real space dimensionality. Considering the significance of circular symmetric field, while an asymmetric subfields of the field, further a better understanding of the role of geometric structure in the behaviour of system objects is developed. This study, therefore, aims to use the appropriate algebraic results and techniques for improving such quality indices as combinatorial varieties, precision, and resolving ability, using remarkable properties of circular symmetry and non-symmetry mutual penetration as an interconnection cyclic relationships, and interconvertible dimensionality models of optimal distributed systems. Paper contains some examples for the optimization relating to the optimal placement of structural elements in spatially or temporally distributed technological systems, to which these techniques can be applied, including applications to coded design of signals for communications and radar, positioning of elements in an antenna array, and development vector data coding design.