This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.
Relationships between the structure characteristics of natural p-terphenyl com- pounds isolated from three edible mushrooms （Thelephora ganbajun, Thelephora aeronautical, and Boletopsis grisea） indigenous to China and their mechanism of antioxidant activity were studied. Geometry structures of terphenyl molecule and four corresponding radicals, bond dissociation energy （BDE）, frontier orbitals （HOMO and LUMO） and single electron density were calculated using DFT methods （B3LYP/6-311G＊＊）. The computational results which are consistent with the experimental data well show that terphenyl molecule scavenges DPPH radical by hydrogen abstract mechanism and the high antioxidant activity depends on the substitution position of hydroxyls. Two active 7-, 8-hydroxyls facilitate the hydrogen abstraction due to the intramolecular hydrogen bond and the resonance effect makes 4-hydroxyl radical more stable.
