Sentence examples for proven for each from inspiring English sources

The absence of contaminating DNA was proven for each sample by quantitative real-time PCR using gyrB-specific primers.

Selectivity was proven for each test substance in the chromatogram, and linearity was given between 600 and 10,000 ng/ml for OCT and between 400 and 10,000 ng/ml for PH.

Thus, in both cases, (15) is proved for each i ((1leq ileq k-1)).

This proves, for each i ∈ Λ, that F ( T i ) ⊂ C n.

A unique Nash equilibrium is achieved and proved for each game.

The global asymptotic stability of the observer-error dynamics is proved for each class of the processes.

Then, we prove for each layer L i, we have t i ≤t i−1+9⌈2(ρ+2)/3⌉2 T. We prove this by induction.

For example, [616, Problem 7.1.9] proves: For each (alpha in {mathbb {Z}}^nu ), let (Delta _alpha ) be the cube of side 3 centered at (alpha ) and (chi _alpha ) its characteristic function.

Theorem 3.3 A function φ ∈ BC ( R N X X ) is in PAP 0 ( R N X X ) if and only if for each ϵ > 0, the set C ϵ = { x ∈ R N : ∥ φ ( x ) ∥ ≥ ϵ } is an ergodic zero set in R N. Proof If φ ∈ PAP 0 ( R N X X ), we prove for each ϵ > 0 the set C ϵ is an ergodic zero set in R N, i.e., lim r → ∞ m ( C ϵ ∩ K r ) m ( K r ) = 0. (3.3).

It is estimated that about 90% could be sterilized in the solid phase; however, it should be proved for each drug that ionizing radiation does not change any of its physicochemical properties (6).

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