We begin with a direct proof of the fixed point theorem for higher-order contraction mappings; thereafter, we provide a re-metrisation argument that relates higher-order Lipschitz mappings to (first-order) Lipschitz mappings.
To begin with, direct structure tests assess the validity of the model structure by direct comparison with knowledge about the structure of the real system.
Let us begin with direct discrimination and then turn to the indirect form, in order to shed some light on whether the wrongs involved in the two forms are sufficiently analogous to consider them as two types of one and the same kind of wrong, viz., the wrong of discrimination in general.
This could begin with direct action by workers and customers, as the fight for the 40-hour week began in the 1880s with strikes and community support -- consumer boycotts of businesses with exploitive hours.
This can be done by, as before mentioned, making contributions well-written to begin with, conspicuously directing users to an explanation of the markup language, and avoiding overly complex markup.
To begin with it is directed at Mr Yanukovych, with his clumsy duplicity and flagrant corruption.
It might begin with a plaque directing the viewer to the harbor into which Henry Hudson's little wooden ship first sailed in 1609 (oddly enough, the date was Sept. 11), setting everything in motion.
Like "Bloody Bloody," "Peter" began with a direct address to the audience.
THE VISITOR, by Sheri S. Tepper (Eos/HarperCollins, $25.95), begins with a direct hit on Earth by a massive asteroid that shatters civilization as we know it.
Yet the novel begins with a direct challenge to Cuddy: the unearthing of a grotesquely mutilated female corpse, complete with hand-scrawled toe tag instructing Justin to deliver the body to his superior.
