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Theory and Modern Applications

TableĀ 3 One positive and two negative characteristic roots

From: Continuous solutions of 3rd-order iterative equation of linear dependence

1<āˆ’ r 1 <āˆ’ r 2 < r 3

1<āˆ’ r 1 < r 3 <āˆ’ r 2

1< r 3 <āˆ’ r 1 <āˆ’ r 2

0<āˆ’ r 1 <āˆ’ r 2 < r 3 <1

0<āˆ’ r 1 < r 3 <āˆ’ r 2 <1

0< r 3 <āˆ’ r 1 <āˆ’ r 2 <1

0<āˆ’ r 1 <1<āˆ’ r 2 < r 3

0<āˆ’ r 1 <1< r 3 <āˆ’ r 2

0< r 3 <1<āˆ’ r 1 <āˆ’ r 2

0< r 3 <āˆ’ r 1 <1<āˆ’ r 2

0<āˆ’ r 1 < r 3 <1<āˆ’ r 2

0<āˆ’ r 1 <āˆ’ r 2 <1< r 3