Sentence examples for be true for arbitrary from inspiring English sources

Based on extensive random sampling on (mathbb{R}_^{n}) for small numbers n it has been conjectured that Conjecture 1.2 might be true for arbitrary (ninmathbb{N}).

Using ultraproducts, it has been shown that the conjecture is true for arbitrary d with the possible exception of a finite set of primes p (depending on d).

We now assume that (67) is true for arbitrary positive integer ℓ and proceed by induction.

Since this is true for arbitrary ϵ > 0, we have α ( W n + 1 ( t ) ) ≤ 4 N ∫ 0 t L ( s ) α ( W n ( s ) ) d s.

Since this is true for arbitrary ϵ > 0, we have α ( ∫ 0 t T ( t − s ) S F, B d s ) ≤ 4 N α ( B ) ∫ 0 1 L ( s ) d s.

While this result is true for arbitrary self-adjoint operators (H), we shall now apply it to two special choices of (H) to obtain the main results of this work.

Moreover, this is true for arbitrary value of g > 0. The interesting implication here is that, unlike system where sustained oscillation is only attainable for certain n1 (n1 must be greater than 4), the inclusion of g, even small, has enabled the system to attain oscillation at any n1.

Since the above inequality is true for any and is arbitrary, we find from (4.17) that.

Since the inequality (3.12) is true for any, and is arbitrary, we find from (3.8) that (3.13).

Since the inequality (20) is true for any x ∈ W and arbitrary λ > 0, then φ ( r ) d B ( T ( h 1 ), h 1 ) ≤ d B ( h 1, h 2 ).

Since (3.11) is true for all u, we can take an arbitrary function that is even with respect to all variables in C ( 2 ) ( K R + ).