To the Graduate Council: I am submitting herewith a thesis written by ...

Chapter 4: Algorithm Overview 57Table 4.2: List of entropy type measures of the form= == ⋅ϕ ⋅ ϕ Measure h ( x )φ 1 ( x )φ 2 ( x ) v i1 x − x log( x )x v2 ( 1 r ) log x−1r−3 x log( x )−1r−4 ( s r ) log( x )x x v− x rr5 ( 1 )arctan( x )sx r sin( s log x ) x r cos( s log x ) v6−1( m − r ) log( x )r−m+ 1x x v−1− r m7 ( m( m r )) log( x )8 ( 1 t ) log x9 ( 1−s ) ( x −1)−1t+s−1−−1t− − t10 ( t 1)1 ( x −1)11 ( 1 − s ) ( e −1)12( − s ) ( xr− 1 x)s−11−1−1−1)xxxsxx x vsxsx x vx 1 x v( s − 1)x log( xx vrx x v13 x − x r log( x )x v14 ( s r ) x−1r s−x − xx v15 (sin s)-1 x− x r sin( slog x )x v161x( 1 + )log( 1 + λ ) −λλ( 1 + λ x )log( 1 + λx)x v17 x − sin( sx )xlog( )2sin(s / 2 )x vsin( xs ) sin( sx )18 x log( )2 sin( s / 2 ) 2sin(s / 2 )19 x − x log( x )x w i20 x − log( x )1 v i21−1r−1( 1 − r ) log xx 1 v i22 ( 1 − s ) ( e −1)23( − s ) ( xr− 1 x( s 1)log(x )s−11−1−1−1)− 1 v ir−1x 1 v ixvvvv