The matrix of the transformation that will eliminate the Larmor term of (13) depends on the sign of the gyromagnetic ratio
. For both cases we can write the matrix as
On the other hand, nonlinear electrodynamics coupled to gravity and satisfying the weak energy condition (nonnegative density as measured along any timelike curve) predicts, for an arbitrary gauge invariant lagrangian, the existence of a spinning charged soliton (a regular finite-energy solution of the nonlinear field equations, localized in the confined region and holding itself together by its own self-interaction) asymptotically Kerr-Newman for a distant observer with the gyromagnetic ratio
g = 2 .
Also, application of [sup.15]N NMR spectroscopy to SOM studies may be difficult because of the extremely low natural abundance of [sup.15]N (about 0.366%) and a small gyromagnetic ratio
. Thus, sensitivity of a [sup.15]N NMR experiment without sample enrichment is approximately 1/50 of that for a [sup.13]C NMR spectrum (Knicker and Ludemann 1995).
H = DC magnetic field vector M = magnetization vector t = time variable [Gamma] = gyromagnetic ratio
[Alpha] = damping magnitude coefficient
where [omega]L = e/m[gamma] H is the frequency of Larmor precession, g is gyromagnetic ratio
, and [gamma] = (1 - [[beta].sup.2])-2.
where [alpha] is the damping constant, [[gamma].sub.0] is the gyromagnetic ratio
, [M.sub.s] is the saturation magnetization, [??] is the magnetization, and [[??].sub.eff] is the effective magnetic field,
The total cross section for this spin flip is on the order of [4[pi]([gamma][e.sup.2]/[m.sub.e][c.sup.2])] = 3.6b ([gamma] = -1.91 is the gyromagnetic ratio
of the neutron, e is the charge of the electron, and [m.sub.e][c.sup.2] is the electron mass), which gives a spin-flip scattering probability of order 6 X [10.sup.-6].
[[Gamma].sub.m] = gyromagnetic ratio
of the ferrite material
In this equation, [[??].sub.F] is the magnetization of the free layer, [[??].sub.P] is the magnetization of the fixed layer, [gamma] is the gyromagnetic ratio
, [[??].sub.eff] is the effective magnetic field, [[alpha].sub.G] is the Gilbert damping constant, Ms is the saturation magnetization, and [[??].sub.STT] is STT.
The same technique as used to measure a solenoid's field in the proton gyromagnetic ratio
experiment  is used to measure a mutual inductance at dc that is independent of frequency.