The phrase "field degree" is not commonly used in English and is likely to be confusing. Instead, you can use the term "field of study" in the same context. For example: "I graduated with a degree in Psychology, which is my chosen field of study."
After the code length and synchronization position estimation, the extension field degree m corresponding to the being recognized code can also be obtained.
In addition, to further optimize the sampling, we describe a preconditioning scheme, which permits to treat each field degree of freedom individually with regard to the evolution through the auxiliary field configuration space.
We assume that the estimated code length and extension field degree are l and m, the number of minimal polynomials over GF(2 m ) is q and m1 x), m2 x), …, m q (x) are the minimal polynomials over GF(2 m ).
All 2005 maps in Fig. 1 contain some small scale residuals, which correspond to unmod-elled crustal field (degrees larger than 40) or external field.
However, tests have also been performed extending the ({mathrm {SM}}_{{Gamma ^{(1)}}}) to include the static main field (degrees n = 1 15).
Turning to the higher degree static field in CHAOS-6 (from CHAOS-6h, see the section "CHAOS-6h: estimation of the high-degree lithospheric field"), Fig. 7 presents a map of the lithospheric part of the radial field (degrees 15 110) along with the power spectrum and degree correlation at the Earth's surface in comparison with MF7 (Maus 2010) and CHAOS-4.
The high-degree internal field (degrees 25 to 90) is taken from the same model CHAOS-4h, based on low-altitude CHAMP data, which was used in CHAOS-4.
For each code length l and synchronization position t, we traverse all the possible extension field degrees to calculate ∆H, and choose the maximum one as ∆H l,t).
Here the 'node fluxes' (Phi_{j}(t) = cint^{t} dt' V_{j}(t')) are related to the node voltages (V_{j}(t)) and completely describe the classical electromagnetic field degrees of freedom (the current-voltage distribution) in the system.
For the Hybrid Monte Carlo algorithm as well as for the field transformation we will need derivatives with respect to the field degrees of freedom.
Our study focused on the predator's point of view by comparing the visual fields, degree of eye movement, and orbit convergence between three diurnal raptors.
