Sentence examples for representations were given from inspiring English sources

The results were obtained in closed form and conventent graphical representations were given.

In this theorem, sampling representations were given for integral transforms whose kernels are more general than exp ( i x t ).

In this theorem sampling representations were given for integral transforms whose kernels are more general than (exp(ixt)).

The relationships between different line representations are given.

Details of how the windows can be obtained for the Gabor and Malvar representations are given in [11].

First, we present a new characterization in which the equivalence between a WLM signal of order n and their forwards and backwards representations is given.

In this paper, based on fuzzy set and possibility distribution theory, different levels of fuzziness are introduced into the UML class diagram model and the corresponding formal representations are given.

Two examples of InChI representations are given belowin Figures 1 and 2. However, it is important to recognize that InChI strings are intended for use by computers and end-users need not understand any of their details.

Note that for α be a positive integer N, we have ζ N ( s ; x, λ ) = ζ ( s, N ; x, λ ) ( N − 1 ) !, and by Proposition 2.2, their series representations are given as follows.

He calls the proof "an instructive exercise in elementary point-set topology"; it involves viewing sets of positional values as Stone spaces and noticing that their real representations are given by continuous functions.

All of the other crystallographic representations are given by, where is a basis of an icosahedral lattice in.