Sentence examples for the last representations from inspiring English sources

Substituting the last representations into (3.37), we complete the proof of (3.36).

The last representation also implies that (I t,x)) is an even function in x.

More specifically, the last representation is a { 0, 1 } -program, which has n ( n − 1 ) / 2 binary variables and n ( n − 1 ) ( n − 2 ) / 3 inequality constraints.

For the last representation of the revised pattern language, the final graphical overview was combined with corresponding tabulations of the textual design patterns.

From the graphical standpoint the better of the last two representations is without doubt that in Figure 6, corresponding to the representation [D].

This last representation is used to generate the FV locking/unlocking points.

The last of these representations can also be expressed in terms of the parent qf Q G (u)=G −1 u) as begin{array}rcl@ E left[ log g (X) right] = sum_{k=0}^{infty} (k+1) v_{k} {int_{0}^{1}} logleft{gleft[Q_{G} u right]right},u^{k},du, end{array}.

See research article: http://www.biomedcentral.com/1471-2105/11/582/abstract/ Ever since the rise of systems biology at the end of the last century, mathematical representations of biological systems and their activities have flourished.

and the corresponding equation for the Green's function in the energy representation, The last equation reads in (x,y) representation and with the convention (10).

I think that in the last little while, trans representation in the media has been both positive and negative.

For the investigation of the physiology and pathology of the immune responses, computer and mathematical models have been used in the last decades, enabling the representation of biological processes.