Some algebraic invariants

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  • Thi s int roduc tion to Gro up The ory, wit h its emp hasis on Lie Gro ups and the ir app licat ion to the stu dy of sym metri es of the fun damen tal con stitu ents of mat ter, has its ori gin in a one -seme ster cou rse tha t I tau ght at Yal e Uni versi ty for mor e tha n ten yea rs. The cou rse was dev elope d for Sen iors, and adv anced Jun iors, maj oring in the Phy sical Sci ences .

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  • The stability analysis of linear time invariant delay differential- algebraic equations (DDAEs) is analyzed. Examples are delivered to demonstrate that the eigenvalue-based approach to analyze the exponential stability of dynamical systems is not valid for an arbitrarily high index system, and hence, a new concept of weak exponential stability (w.e.s) is proposed. Then, we characterize the w.e.s in term of a spectral condition for some special classes of DDAEs.

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