Sentence examples for begin by defining some from inspiring English sources

We begin by defining some Banach spaces.

We begin by defining some notation explicitly.

We begin by defining some terms used throughout the manuscript.

We begin by defining some smooth compactly supported functions which will be used several times in the sequel.

We begin by defining some terminology that we shall be using in the sequel.

We begin by defining some key concepts, a scoring function for pathways and a computational problem of finding branching, high scoring pathways.

These models begin by defining an input space, with some coordinates being linear (representing position or spatial frequency) and others circular (representing orientation), need to be mapped to the two-dimensional plane in some optimal fashion [61], [62], [64], [116], [122] [126].

For example, you have to begin by defining the Places in question, like Mall, Downtown, School and so on.

The critic must begin by defining the problem presented by his particular material and the consequent limitations of his inquiry.

He received applause when he told the audience that in the fight against terrorism, "I suggest that we begin by defining Islamism as our adversary".

The Montgomery County lessons begin by defining terms like "prejudice," "homosexual" and "transgender," and warn students not to assume that because they are not yet attracted to the opposite sex, they must be gay.