On a new one-parameter generalization of dual-complex Jacobsthal numbers

In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.

An Interactive Morphological Matrix Computational Design Tool: A Hybrid of Two Methods

This paper builds on previous concept generation techniques explored at the University of Missouri - Rolla and presents an interactive concept generation tool aimed specifically at the early concept generation phase of the design process. Research into automated concept generation design theories led to the creation of two distinct design tools: an automated morphological search that presents a designer with a static matrix of solutions that solve the desired input functionality and a computational concept generation algorithm that presents a designer with a static list of compatible component chains that solve the desired input functionality. The merger of both the automated morphological matrix and concept generation algorithm yields an interactive concept generator that allows the user to select specific solution components while receiving instantaneous feedback on component compatibility. The research presented evaluates the conceptual results from the hybrid morphological matrix approach and compares interactively constructed solutions to those returned by the non-interactive automated morphological matrix generator using a dog food sample packet counter as a case study.