Sentence examples for by constructing a pair from inspiring English sources
By constructing a pair of ordered upper and lower solutions, we establish the existence of nontrivial nonnegative periodic solutions.
The existence of traveling waves connecting the zero equilibrium and the positive equilibrium is then established by constructing a pair of upper-lower solutions.
The existence and uniqueness of the solution to problem (1.1) can be ensured by constructing a pair of ordered upper and lower solutions of (1.1).
At last, by constructing a pair of ordered upper and lower solutions, we establish the existence of the nontrivial nonnegative periodic solutions and the attractivity of the maximal periodic solution.
In this section, we will establish the existence of the nontrivial nonnegative periodic solutions by constructing a pair of ordered upper and lower solutions and the method of monotone iteration technique.
In this paper, the stability of the equilibria is firstly investigated, and the existence of traveling wave solutions is then established by constructing a pair of upper-lower solutions and using the cross iteration method and Schauder's fixed point theorem.
Degasperis et al. [2] proved the formal integrability of Eq. (3), derived the infinite sequence of conserved quantities with a bi-Hamiltonian structure and obtained the existence of the non-smooth solutions by constructing a Lax pair.
The effects of PA on the pharmacokinetics of ritonavir were assessed by constructing a 90% CI, based on a paired sample t test, for the geometric mean ratio between the AUC0-12hr on Day 10 (during administration of ritonavir with PA) and the AUC0-inf on Day 1.
The PerPlot algorithm starts by constructing a histogram N s) of spacings between pairs of "A-tracts", which can be defined as various combinations of A and T nucleotides.
The efficiency of each primer pair was determined by constructing a standard curve from serial dilutions (Table 4).
PCR efficiency values for each primer pair was obtained by constructing a standard curve using threshold cycle (Ct) values derived from 6 data points, corresponding to 2-fold decrements of an original cDNA stock (duplicates were prepared for each dilution).
