Each call to line 4 takes O(m) time, where m= j− i, and causes a strict decrease in Vec of 2 m units.
By the strict decreasing of μ ̄ ( a ( t ) ) with respect to a(t) (see [11]), where μ ̄ ( a ( t ) ) is the k th eigenvalue of (1.2) corresponding to the weight function a(t), we have μ ̄ ( a ( t ) ) < μ ̄ ( λ k ) = 1.
By the strict decreasing of μ k (f) with respect to weight function f (see [11]), where μ k (f) denotes the k th eigenvalue of (1.2) corresponding to weight function f, we can show that our condition c(t) ≤ λ k < ⋯ < λk+j≤ a(t) is equivalent to the condition f0 < μ k < · · · < μk+j< f∞.
We shall show C k ν crosses the hyperplane {1} × E in ℝ × E. By the strict decreasing of μ k (c(t)) with respect to c(t) (see [11]), where μ k (c(t)) is the k th eigenvalue of (1.2) corresponding to the weight function c(t), we have μ k (c(t)) > μ k (λ k ) = 1.
By the strict decreasing of μ k (f) with respect to weight function f (see [10]), where μ k (f) denotes the k th eigenvalue of (1.2) corresponding to weight function f, we can show that our condition c(t) ≤ λ k ≤ a(t) is equivalent to the condition μ k f ∞ < μ < μ k f 0. Similarly, our condition c (t) ≥ λk ≥ a (t) is equivalent to the condition μ k f 0 < μ < u k f ∞.
This makes it clear that the "LPS-tolerant" phenotype is not a strict definition of the phenotype that decreases production of the proinflammatory cytokines and increases production of anti-inflammatory cytokines in response to the M1-inductor LPS.
A strict version of this rule is a decrease in BMI SDS of -3 and a BMI SDS less than -1 between birth and 2.5 years of age.
The percentage in favor of making the laws governing the sale of firearms 'more strict' decreased from 78percentt in 1990, to 62percentt in 1995, and 51percentt in 2007.
The suppression of cell death in NbMAPKKKγ-silenced plants despite the slight decrease in its mRNA can be explained by a strict requirement of a high level of NbMAPKKKγ protein in cell death.
Instead, in case of very large matrices, saving more than one shortest tree per iteration and using a strict consensus tree of these yields decreased support compared to saving only one tree.
