1、The explicit formula is more practical and convenient than others.

2、For each failure mode, an explicit formula is derived for the prediction of shear strength.

3、The normwise structured backward error of an approximate eigen-pair is defined and its explicit formula is given.

4、For critical state model, the author derives an explicit formula of matrix h, which is used in implicit computation scheme.

5、For Bingham type plastic fluid modal, the explicit formula for calculating the pumping pressure is obtained, which can be used to choose the pump type.

6、A two-strain SIR epidemic model is discussed and an explicit formula for the basic reproductive number is derived by analyzing the local stability of the trivial equilibrium.

7、This thesis also presents an explicit formula that converts a triangular SBGB patch of degree n to a degenerate rectangular SBGB patch of degree nxn by reparametrization and the SBGB dual bases.

8、At each iteration, a master direction is obtained by solving one direction finding subproblem which always possesses a solution, and an auxiliary direction is yielded by an explicit formula.

9、Now, so these are mathematical examples given by explicit formulas.

10、Modified explicit formulas for optimal LC prototype filter design

11、The explicit formulas of matrixes composing the stiffness are given.

12、The parameters of canonical polynomials can be obtained by using explicit formulae.