Sentence examples for introducing the functions from inspiring English sources

Introducing the functions and, explicitly given by (2.11). it is directly seen that and are not the fundamental solutions to the respective Hermitean Dirac operators and.

The linearization of these equations is made, in the usual way, by introducing the function (Q= ph)^{2}).

We end this section by introducing the function (varphi (y,t)) by varphi (y,t):= u y,t)+frac{1}{2}(y-1) t^{2}.

We reformulate Problem I as a first-order system with respect to time by introducing the function (v=u_{t}).

An alternative condition can be established by introducing the function f ( t ) = t 1 + ω t 1 / α ̂ − 1 α, (21).

If, then we introduce the functions,, (3.52).

for and introduce the functions and defined by (4.44).

In the previous section, we introduce the functions (phi_{N}), (varphi _{N}), and the real number R with two parameters ({a > 0}) and ({b ge1}).

By the change of variable (t=lnfrac{r}{R}), we introduce the functions (hat{a}_{m}(t):=a_{m}(Re^{t})).

In Section 3, we introduce the function space and energy functional for FBVP (1.1).

Further, introduce the function (1.3).