Sentence examples for defined by formulae from inspiring English sources

are satisfied, where the functions β 0 and β 1 are defined by formulae (73), (74), and (76), then the operator ℓ, defined by formula (107), belongs to the set V ˜ a b − ( h ).

Many mathematicians, he says, liked the idea that certain structures defined by formulas were simply unimaginable; during the 20th century, he notes, many of them took refuge in wilfully obscure branches of mathematics, on the basis that such work had no military application.

if, where is defined by formula (6.17).

where and are defined by formula (2.19) respectively.

where the functional h − is defined by formula (51).

Let (mathcal{A}_{i}) be the simplices defined by formula (4).

on, where the number j − α ∗ is defined by formula (2.8).

Let a kernel h ( t ) be defined by formulas (1.2) and (3.1).

Then the operator ℓ, defined by formula (102), belongs to the set S a b ( a ).

Let γ0be the number as in Theorem 3.3 which was defined by formula (3.11).

Suppose that A is defined by formula (2.1), (varphi,xi,psi in D(A)).