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Application of the combinational sequencing theory for innovative design based on diagrammatics

Riznyk V.

Machine Graphics and Vision

2003

Vol. 12, No. 1

83-98

The paper psoposes application of the combinational sequencing theory, namely the concept of Ideal Ring Bundles (IRBs), for design of high performance engineering devices or systems with non-uniform structure based on diagrammatics approach. An ordinary IRB is a ring-like sequence of positive integers which form perfect partitions of a finite interval [1,S] of integers. The sums of connected sub- sequences of an IRB enumerate the set of integers [1, S] exactly once. This property makes IRBs useful in applications which need to partition sets with the smallest possible number if intersections. Appication of the idea of "perfect" combinational configurations for innovative design provides a better understanding of the role of a geometric structure in behavior of natural and man- made objects. It also helps configure systems with fewer elements and bonds than at present, while maintaining or improving on reliability, precision, resolving ability, and functionality, using combinatoral techniques based on the remarkable properties and structural perfection of one- and multidimensional IRBs. The objectives of the IRB concept are: development of a scientific basis for technologically optimum distributed systems theory using diagrammatic, generalization of these methods and results to the improvement and optimization of a larger class of thechnological systems, and development of new directions in fundamental and applied researcg in systems engineering based on diagrammatics for designing a wholr range of high-performance devices, systems or technologies, including applications to coded design of signals for communications and radar, positioning of elemnets in an antenna array, and other areas to which the IRB concept can be applied.