Sentence examples for functions hence from inspiring English sources

The absolute magnitude of this phase is irrelevant for the observable quantities calculated from these wave functions; hence, the theory describing, for example, the motion of an electron should be the same when the phase of its wave function is changed everywhere in space.

In other words, there is no unique solution that serves all functions, hence the "non-uniqueness" theory.

The ODS are calculated from Frequency Response Functions hence responses recorded on the structure can be directly used without the need of modal identification.

In addition, we obtain the eigen-solutions to SFSLP-I & -II analytically, also as non-polynomial functions, hence completing the whole family of the Jacobi poly-fractonomials.

The MATF evaluates the evaluated node on the basis of different network functions, hence more informed and prompt decisions about the trustworthiness of nodes can be taken.

In reality, demand profiles are not smooth functions, hence a random daily variation on the profile is generated between 80% and 120%.

The extremal principle usually yields information about an integral involving the sought-for function, hence the name integral equation.

g is a monotone nondecreasing function, hence, (bar{w} tau geq0).

➢ has an decreasing failure rate function, hence increasing mean residual life function.

The F1,nis the usual empirical distribution function, hence the name given above.

Since is an increasing function, hence for and some constants, one has (2.18).