Sentence examples for pair formulation from inspiring English sources

It possesses bi-Hamiltonian and has a Lax pair formulation [2], [3].

Eq. (1) was shown to be bi-Hamiltonian and to have a Lax pair formulation.

by using asymptotic expansions directly in the Hamiltonian for Euler equations in the shallow water regime, and thereby it is shown to be bi-Hamiltonian and has a Lax pair formulation.

In [4], Holm and Ivanov generalized the Lax-pair formulation of system (1.1) to produce an integrable multi-component family, CH n, k), of equations with n components and 1 ≤ |k| ≤ n velocities.

None of the pair of formulations showed F1 lower than 15% or F2 higher than 50%, suggesting that all the release profiles are different from each other.

Lemma 5 The following pairs of formulations are incomparable with respect to the quality of lower bounds : (a) MTZ and SCF F, (b) MTZ and SCF R (SCF R +), (c) SCF F and SCF R (SCF + R ), (d) SCF R (SCF R +) and MCF F, (e) SCF R (SCF R +) and CF F, (f) MCF R and CF F. Proof (a) In Fig. 4 we have υ LP (SCF F ) = 11 < 16 = υ LP (MTZ ) and in Fig. 7 we have υ LP (MTZ ) = 9 < 10 = υ LP (SCF F ).

Since the optimal sub-channel set Opt C i is selected by each CR communication pair before Lagrange formulation, the optimal transmission power on each optimal channel set can be obtained by the similar procedure as (19) and (20) of Algorithm 1.

However, the lack of evidence of direct interaction for numerous other R-protein/cognate effector pairs led to formulation of the guard hypothesis, which states that R-proteins can indirectly recognize pathogen effectors by sensing perturbations they induce.

All Pearson's correlations between pairs reached unity, allowing formulation of two unbiased equivalence equations: (a) TRL-C = 97.8 * log[TG] - 181.9; and (b) TRL-C/apoA-I = 8.15 * (log[TG]/HDL-C) - 0.18.

The counting process formulation replaces the pair of variables (T i, δ i) with the pair of functions (N i(t), Y i(t)), where N i(t) = I T i⩽ t, δ i= 1) and Y i(t) = I T i⩾ t).

We will use the above formulation for a pair of distributions F x) and G x), where G x) is a submodel or the baseline distribution of F x).