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The research contents on this topic consists of the following three aspects.(1) The redundant term is discovered in Santilli s second method.As a result, a more simple construction formula for self-adjoint systems is obtained by cancelling the redundant term.(2) Hojman s method is studied by the following two aspects.Firstly, the improved Hojman s method is specified by selecting a set of gauge functions to satisfy the regularity condition.