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Title of Document: BAYESIAN BELIEF NETWORK AND FUZZY LOGIC ADAPTIVE MODELING OF DYNAMIC SYSTEM: EXTENSION AND COMPARISON Ping Danny Cheng, M.S., 2010 Directed by: Professor Mohammad Modarres, Mechanical Engineering Department The purpose of this thesis is to develop, expand, compare and contrast two methodologies, namely BBN and FLM, which are used in the modeling of the dynamics of physical sy...

The Birman–Murakami–Wenzl algebra (BMW algebra) of type Dn is shown to be semisimple and free over Z[δ±1, l±1]/(m(1− δ)− (l− l−1)) of rank (2n + 1)n!! − (2n−1 + 1)n!, where n!! = 1 · 3 · · · (2n − 1). We also show it is a cellular algebra over suitable rings. The Brauer algebra of type Dn is a homomorphic ring image and is also semisimple and free of the same rank, but over the ring Z[δ±1]. A r...