NMR data were collected upon sample preparation and were repeated after 4 weeks; changes in the spectrum were not observed, suggesting that the sample had achieved equilibrium with respect to the cis-5 R,6 S: trans-5 R,6 R equilibrium.
Pin(r) is the inertial (orientational) polarization field, and Pin,Ieq(r; R) is its equilibrium value with the proton at R and the transferring electron in its initial localized state.
If there are three alleles, A1, A2, and A3, with frequencies p, q, and r, the equilibrium frequencies corresponding to the six possible genotypes (shown in parentheses) will be calculated as follows: The figure shows how the law operates in a situation with just two alleles.
Red indicates equilibrium or limit cycle, stable manifolds are green, unstable manifolds are blue and orbits yellow.
Let q denote a general time-reversible (GTR) substitution rate matrix [ 25, 26] on nucleotides, i.e., for i ≠ j, with elements q i, j) = r i, j) π (j) for some symmetric matrix r and equilibrium distribution frequencies π.
The elastic force constant κ is conveniently derived from Φ(r) at the equilibrium interionic distance r 0 as of the following: κ = ∂ 2 Φ ∂ r 2 r 0, Open image in new window = Z e 2 s − 1 r 0 3, Open image in new window (14).
The left (right) chemical potential is given byμ L (μ R ).TL(R) denotes the equilibrium temperature of the left (right) electrode.
The equation R ˜ ( t + 1 ) = R ˜ ( t ) + γ ε − μ R ˜ ( t ) has a unique equilibrium R ˜ ∗ = γ ε μ, which is globally asymptotically stable.
For every i = 1, 2, …, N, S i : C → CB ( H ) be ℋ-Lipschitz continuous with coefficients μ i, Φ i : H × C × C → R be equilibrium-like function satisfying (H1 - H3).
where D, T : C → CB ( H ) are ℋ-Lipschitz continuous with constants μ 1, μ 2, respectively, Φ 1, Φ 2 : H × C × C → R are equilibrium-like functions satisfying (H1 - H3), A : C → H is an α-inverse strongly monotone mapping and B : C → H is a β-inverse strongly monotone mapping.
