Sentence examples for used separation of from inspiring English sources

Mr. Buchanan, the public choice pioneer, has noted that the framers of the Constitution wisely used separation of powers and an independent judiciary to curb the effects of self-seeking special interests on government.

A change in the element type used, separation of the linear response region, and the termination of the analysis after ultimate failure of the structure were applied to the analysis.

Some researchers used the method for combining Fourier transform with Laplace transform method (Kumar et al. 2010; Feng 2012), and others have used separation of variables to solve the equations (Min et al. 2004; Wu et al. 2008).

We use separation-of-cones techniques and ideas from multivariable operator theory to show that polynomial hyponormality does not imply subnormality for Hilbert space operators.

First we transform the MCNLS to the stationary state ones by using separation of variables.

The governing equations, subject to boundary and continuity conditions, are solved by using separation of variables and double finite integral transforms.

By using separation of the variables it is shown that different types of solution are possible depending on the degree of damping present.

The exact solutions for free vibrations of orthotropic rectangular thin plates are presented in an elegant way using separation of variables method.

Now using separation of variables and Lemma 2.3, we get the solution of problem (1.1) as follows: u x,t)=sum_{n=1}^{infty}bigl(f(x), varphi_{n}(x bigr t^{alpha}E_{alpha,1+alpha}bigl(- lambda_{n}t^{alpha}bigr)varphi_{n}(x).

Integrating this using separation of variables and the initial condition μ ( 0 ) = μ 0, we find μ ( t ) = w − α A e ( α − w ) t + w where  A = μ 0 w − w μ 0 − α. (18).

This analytical solution is derived by solving the scalar Helmholtz equation using separation of variables in spherical coordinate system [ 14].