Sentence examples for by the initial function from inspiring English sources

∥ u ( x, t ) ∥ m ≤ ∥ u ( x, s ) ∥ m for t ≥ s ≥ 0 ; If N < p, then the solution is uniquely determined by the initial function; If u 0 ( x ) ≥ 0 a.e. in Ω, the solution u ( x, t ) ≥ 0 a.e. in Ω for any fixed t > 0, hence u ( x, t ) is a solution of the problem (1.1 - 1.3 1.1 - 1.3

Furthermore, we have (1) ∥ u ( x, t ) ∥ m ≤ ∥ u ( x, s ) ∥ m for t ≥ s ≥ 0 ;   (2) If N < p, then the solution is uniquely determined by the initial function;   (3) If u 0 ( x ) ≥ 0 a.e. in Ω, the solution u ( x, t ) ≥ 0 a.e. in Ω for any fixed t > 0, hence u ( x, t ) is a solution of the problem (1.1 - 1.3 1.1 - 1.3

By splitting the initial function ϕ into two functions, we deduce the following corollary.

For an atomic picture  A, as in Figure 4, the word we read off by travelling along the top of the atomic picture from left to right gives the initial function, denoted by ι ( A ) = U S ε V, and the word we read off by travelling along the bottom gives the terminal function, denoted by τ ( A ) = U S − ε V. Also, the mirror image of A is denoted by A − 1 = ( U, S, − ε, V ).

A point of contention in the dinosaur-bird debate centers on the initial function of feathers.

"Everything about the feather points to aerodynamic structure, indicating that the initial function of feathers was in an aerodynamic context".

(a3)The initial function is a Borel bounded function.

Maximizing function (12) is equivalent to maximizing the initial function.

with where is the initial function corresponding to the initial function in (1.2).

We have thus generated a class of partial recursive functions, namely those functions that can obtained from the initial functions by means of composition, primitive recursion, and least search.

To show that the class of recursive functions can be represented in the λ-calculus, one follows its definition; the step-by-step construction of an arbitrary recursive function from the initial functions can be mimicked in the λ-calculus.