Sentence examples for transform the boundary from inspiring English sources

The essence of the second and third equations in (2.4), (3.3), (4.3), and (5.3) is that they transform the boundary conditions on the line (6.4).

In order to prove the main results, we need to transform the boundary value problem (1.5) into a fixed point problem.

We transform the boundary value problem (1.4) into a fixed point problem (x=mathcal{B}x), where (mathcal{B}:mathcal{C}rightarrowmathcal{C}) is defined by (4.1).

In order to obtain the main results, we first transform the boundary value problem (1.5)–(1.6) into a fixed point problem.

One approach is to transform the boundary value problems for k-regular functions and poly-harmonic functions into equivalent boundary value problems for regular functions in Clifford analysis by the Almansi type decomposition theorem [15].

We transform the boundary value problem (1.5)–(1.6) into a fixed point problem (u={mathcal{A}}u), where ({mathcal{A}}:mathcal{C}rightarrow mathcal{C}) is defined by (3.1).

The amount of expression data generated in our study had the potential to transform the boundaries and extent of previous feature annotations in the carnation genome [ 27].

corresponding to the eigenvalue, transforms obeying (2.5) to obeying (2.2) and transforms the boundary conditions as follows: (1) boundary conditions (a) transform to and ;   (2) boundary conditions (b) transform to and (3.13);   (3) boundary conditions (c) transform to (3.2) and ;   (4) boundary conditions (d) transform to (3.2) and (3.13).  .

By application of Fourier transforms the boundary value problem for the velocity potential is solved, leading to an integral expression for the generated sound field.

By transforming the boundary value problem into an equivalent integral equation, and employing the Banach fixed point theorem and the Schauder fixed point theorem, existence results for the solutions are obtained.

It is shown that transforming the boundary value problem given by (2.2) with any one of the four combinations of Dirichlet and non-Dirichlet boundary conditions at the end points using (3.1) results in a boundary value problem with one extra eigenvalue in each case.