Sentence examples for the relation involving from inspiring English sources

Using the initial conditions, we obtain an algebraic equation whose solution is given by F ( s ) = G ( s ) ( s + b ) 2 + a 2. By means of the convolution product and the relation involving the inverse Laplace transform L − 1 [ 1 ( s + b ) 2 + a 2 ] = exp ( − b x ) a sin a x, we get y ( x ) = 1 a ∫ 0 x e − b ( x − ξ ) sin [ a ( x − ξ ) ] f d ξ. which is exactly Eq. (5).

The relation involves an effective elastic material law (N varepsilon)), (varepsiloninmathbb{R}) for the truss model in (3.5a).

The most natural and convenient way to express the relation involves the algebraic concept of exact sequences: sequences of objects (in this case groups) and morphisms (in this case group homomorphisms) between them such that the image of one morphism equals the kernel of the next.

Any other instance of a class is assumed to have the relations involving the prototype instance of the class as well as the relations in the prototype instances of the super-classes.

However, the modulus ratio obtained from the relations involving the joint factor, Jf, indicate a definite decrease in the modulus ratio with a decrease in the quality of the rock mass.

The most interesting possibility is that gesture might nonetheless reveal spatial analogies that is, spatial models of relational structure even though the relations involved in positive and negative feedback are not inherently spatial.

And so on for the relations involved in other paradigmatic relational situations.

Here we investigate the possibility that people reason about such causal patterns in part by using spatial analogies that is, spatial models of the relations involved.

A convenient equation to define the stress strain relation involving two fluids can be obtained from Biot's theory of poroelasticity (Santos et al. 1990a, b; Ravazzoli et al. 2003).

The non-linear relation involving displacement and mechanical parameters is adequately recognized by the neural network techniques.

The new hybrid method developed combines an empirical relation involving the energy of the lowest triplet state of Tb3+ complexes with extremely fast semiempirical quantum mechanical calculations.