Our approach relied upon the use of fermionic worldline fields to represent the additional spin and color information of the particle multiplets
, and associated worldline gauge fields to project onto appropriate sectors of the Hilbert space.
In this paper, we describe the method for estimating the critical pore-pressure distribution by using the orientations of subsurface fractures derived form AE multiplets
and the regional stress field.
Both fields are embedded together with the [q.sub.1] and [q.sub.2] doublets into the SU(5) multiplets
: [mathematical expression not reproducible].
analysis or clustering analysis must be done to confirm it, because it has been proved that these methods are effectively used to estimate phenomenon of AE sources .
It has been envisaged that various properties of these ionomers may be influenced profoundly by the presence of the so-called clusters and multiplets
. Thus, introduction of ionic groups onto hydrophobic backbone chains results in a dramatic increase in mechanical properties such as modulus, tensile strength, impact resistance, and stiffness characteristics (bending modulus) (17-19).
In choosing the SO(10) multiplets
for breaking the symmetries (by acquiring appropriate VEVs), we follow the common tradition in the literature as follows.
We have pointed out that this model is simpler than that of [S.sub.3] and our previous [S.sub.4] model, since fewer Higgs multiplets
are needed in order to allow the fermions to gain masses and to break the gauge symmetry.
As for literature data, due to interaction of polymeric chains in physical gels, such microstructures as aggregates, micelles, multiplets
and crystallites are formed.
Znojil, "A generalized Morse asymmetric potential and multiplets
of its non-numerical exact bound states," Journal of Physics A, vol.
For complex 2, the terminal methyl protons of butyl group emerge as a clear triplet at 0.93 ppm while multiplets
are observed at 1.48-1.21 ppm for methylene protons.
We shall systematically study the chiral structure of light scalar mesons through local tetraquark currents which belong to the "nonexotic" [([bar.3], 3) [direct sum] (3, [bar.3])] chiral multiplets
. This chiral multiplet
only contains flavor singlet and octet mesons, and it does not contain any meson having exotic flavor structure.
In each case, the ligand protons appeared as three sets of signals as expected; two multiplets
due to the piperazine moiety and a singlet due to the aldehydic proton.