Sentence examples for representations for the first from inspiring English sources

In that way one can find integral representations for the first derivatives of the solution which do not involve the first derivatives of function H.

By decomposing the second order symmetric tensor space into the direct sum of a coaxial tensor subspace and another one orthogonal to it, the closed form representations for the fourth order tangent operator and its inversion are derived in an extremely simple way.

The party was just 0.3% short of the necessary threshold to secure Bundestag representation for the first time.

The party was just 0.3% short of the necessary threshold to secure Bundestag representation for the first time since its formation.

There was British representation for the first time in every final of the biennial event, likely to ensure a full quota of British divers at the Games.

The new electoral law adopts a system of proportional representation for the first time in Lebanese history, replacing the majoritarian principle that has governed the country's elections since independence.

More than half of the MPs are new to politics, only two of six parties elected existed a year ago and there is no Communist party representation for the first time.

Although the left will lose seats in Britain, where voting is by proportional representation for the first time and could rob the Labour Party of some 18 seats, the European Socialists may end up no worse off overall.

We report on an algorithm for fast wavefront sensing that incorporates sparse representation for the first time in practice.

Note that Figure 3(a) is the image of the fourth level of the pyramid representation for the first image.

The Figure8 (a) indicates the bit level representation for the first parents while the Figure8 (b) represents the parent 2 at bit level.