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A possible connection between the existence of three quark-lepton generations and the triality property of SO(8) group (the equality between 8-dimensional vectors and spinors) is investigated.

For any root system and any commutative ring, we give a relatively simple presentation of a group related to its Steinberg group St. This includes the case of infinite root systems used in Kac–Moody theory, for which the Steinberg group was defined by Tits and Morita–Rehmann. In most cases, our group equals St, giving a presentation with many advantages over the usual presentation of St. This e...

This paper presents a canonical dual approach for solving a nonconvex global optimisation problem with a sum of double-well and log-sum-exp functions. Such a problem arises extensively in mechanics, robot designing, information theory and network communication systems. It includes fourth-order polynomial minimisation problems and minimax problems. Based on the canonical duality theory, this non...