Sentence examples for is suitably large from inspiring English sources
Szemerédi's theorem extends this claim to any subset of the positive integers that is suitably large.
In this section, by discussing the bifurcations of positive solutions by using a and c as the main bifurcation parameters, respectively, we establish the multiplicity of positive solutions when γ is suitably large.
In fact, making use of bifurcation theory and degree theory, we can solve this problem and further establish the multiplicity of positive solutions to (1.1) when γ is suitably large.
More precisely, a sufficient and necessary condition for the existence of positive solutions is given when c ≤ λ 1, and when c > λ 1, the multiplicity of positive solutions is obtained under the assumption that γ is suitably large.
Denote γ ˜ = ∫ Ω ψ ˜ 1 q m ( x ) d x and δ ˜ = min x ∈ Ω ¯ ψ ˜ 1 ( x ) > 0. Set w ( x, t ) = k ψ ˜ 1 1 m ( x ), then we shall show that w ( x, t ) is a super-solution of (1.1) provided that k > 0 is suitably large.
In Section 3, by investigating the bifurcation of positive solutions emanating from the semi-trivial solution ( θ a, 0 ; c ), we give a sufficient and necessary condition for the existence of positive solutions to (1.1) and establish the multiplicity result of positive solutions when γ is suitably large.
Statistical checks confirmed the sample was adequate for factor analysis (Kaiser Meyer Olkin measure = 0.9) and correlations between questions were suitably large [Bartlett's test of sphericity, χ (210) = 2168.1, P < 0.001].
Implementations of segmentation-based approaches applied to B allele frequency (BAF) and log R ratio (LRR) values, including BAFsegmentation [ 8] and MAD [ 9], are proficient at detecting abnormalities, including mosaicism, when there are suitably large percentages of abnormal cells.
if K is sufficiently large and ε 0 is suitably small.
Guardiola is suitably expansive.
