Growth properties of modified α-potentials in the upper-half space

The aim of this paper is to discuss the behavior at infinity of modified ?-potentials represented by the modified kernels in the upper-half space of the n-dimensional Euclidean space, which generalizes the growth properties of analytic functions, harmonic functions and superharmonic functions.

Kernel modifications and tryptophan content in QPM segregating generations

Maize has poor nutritional value due to deficiency of two essential amino acids - tryptophan and lysine. Although recessive opaque2 (o2) mutation significantly increases their content in the endosperm, incorporation of opaque2 into high yielding cultivars was not commercially successful, because of its numerous agronomic and processing problems due to soft endosperm. Quality protein maize - QPM has lately been introduced as opaque2 maize with improved endosperm hardness and improved agronomic traits, but mostly within tropical and subtropical germplasm. The ongoing breeding project at MRI includes improvement of MRI opaque2 lines and conversion of standard lines to QPM germplasm. The main selection steps in QPM breeding involve assessing kernel modifications and tryptophan level in each generation. Herein, we present the results of the analysis for these traits on F3 and BC1F1 generations of QPM x opaque2, opaque2 x QPM and standard lines x QPM crosses. The results showed that the majority the genotypes had kernel types 2 and 3 (good modifications). The whole grain tryptophan content in F3 and BC1F1 genotypes of crosses between QPM and opaque2 germplasm was at the quality protein level, with a few exceptions. All BC1F1 genotypes of standard lines x QPM had tryptophan content in the range of normal maize, while majority of F3 genotypes had tryptophan content at level of QPM. The progeny (with increased tryptophan levels) of QPM and opaque2 crosses had significantly higher tryptophan content compared to the progeny of crosses between standard and QPM lines - 0.098 to 0.114 and 0.080, respectively. All genotypes that had poorly modified kernels and/or low tryptophan content will be discarded from further breeding.