Sentence examples for defined provided that from inspiring English sources

Then lim n → ∞ A 0 n ⊂ dom T so that the possibility of Ty being undefined is excluded and then Ty is defined provided that there is no finite or infinite jump discontinuities at y.

Indeed, in a way similar to the argument of Remark 3.2, iterative scheme (25) is well defined provided that for each n ≥ 0, the point z n belongs to U ( r ′ ) for some r ′ ∈ ( 0, r ).

One also sees that products of two matrices of the given type is well defined (provided as usual that the column-index and row-index sets match), is again of the same type, and corresponds to the composition of linear maps.

We define the function space as follows: provided that is defined for and is rd-continuous function and nonnegative.

Unnecessary care was defined as services and drugs provided that were judged by a panel of doctors to lead to no improvement in patient outcomes.

Types of outcome measures—We extracted data into 2×2 tables for comparisons of the diagnosis of hypertension provided that clearly defined thresholds for the diagnosis of hypertension were used.

provided that equation defines a fuzzy.

In sum, performance is ideally defined broadly, provided that the set of performance measures remains comprehensible for providers.

In this case the relation between F and f is If a random variable X has a probability density function f(x), its "expectation" can be defined by provided that this integral is convergent.

A function ψ ∈ C ( R n ) is called a multiplier from L p ( R n ; E 1 ) to L p ( R n ; E 2 ) if the mapping f → T ψ f = F − 1 ψ F f for f ∈ S ( R n ; E 1 ) is well defined and provided that there is a constant C so that ∥ T ψ f ∥ L p ( R n ; E 2 ) ≤ C ∥ f ∥ L p ( R n ; E 1 ).

Let's let the legal system, defined by our Constitution, provide that answer".