The mechanics of the wall are modelled by using a linear differential operator with a single degree of freedom, and the results herein pertain to a spring-backed flexible plate.
High-fitness individuals are chosen as parents to create the next generation of solutions, using a linear ranking selection operator (Chakraborty and Chakraborty, 1997).
Finally, another solution of (1) can be obtained by using a linear combination of the operators X 1, X 2 and X 3, i.e., considering the operator X 1 + a 2 X 2 + a 3 X 3 along with the condition k = 0. Then the similarity variable and similarity solution are z = x − a 2 t − a 3 ( 4 e 1 − e 2 2 ) t 2, u ( x, t ) = 2 e 1 a 3 t + U ( z ), v ( x, t ) = − e 2 a 3 t + V ( z ), (27).
In part three, a fluid finite element is developed; the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability.
The notation A[ x k ] is used to describe a linear operator on a scalar input and A[ x k ] on a vector input.
This source term plays an essential role in quantum mechanics, where this non-linear term is used to perturb a linear operator to obtain a non-linear operator which gives applicable results; see [22].
Since is a linear operator, using (2.15), we have (2.16).
We will use the term operator to mean a linear operator unless stated otherwise.
Carlson and Shaffer [20] used the Hadamard product to define a linear operator L ( a, c ) : A → A by L ( a, c ) f ( z ) = φ ( a, c ; z ) ∗ f ( z ), (2.6).
Suppose a linear operator (2.12).
