On k-Gamma and k-Beta Distributions and Moment Generating Functions

The main objective of the present paper is to define k-gamma and k-beta distributions and moments generating function for the said distributions in terms of a new parameter k>0. Also, the authors prove some properties of these newly defined distributions

Solutions of k-Hypergeometric Differential Equations

We solve the second-order linear differential equation called the k-hypergeometric differential equation by using Frobenius method around all its regular singularities. At each singularity, we find 8 solutions corresponding to the different cases for parameters and modified our solutions accordingly

Kinetics Study of Extracellular Detergent Stable Alkaline Protease from Rhizopus oryzae

In this study, extracellular alkaline protease was produced from Rhizopus oryzae in submerged fermentation using dairy waste (whey) as a substrate. Fermentation kinetics was studied and various parameters were optimized. The strain produced maximum protease at initial medium pH of 6.0 medium depth of 26 mm, inoculum size of 2% at incubation temperature of 35ºC for 168 h of fermentation. Alkaline protease was purified to homogeneity by ammonium sulphate fractionation followed by sephadex G-100 chromatography. The molecular mass of alkaline protease was 69 kDa determined by 10% SDS-PAGE. The optimum pH and temperature of alkaline protease was 9.0 and 40ºC, respectively. Metal profile of the enzyme showed that the enzyme was non-metallic in nature. The Km , Kcat , Vmax and Kcat/Km values of purified protease were 7.0 mg/mL, 3.8 x102S-1, 54.30 µmol/min and 54.28 s-1mg -1.mL respectively, using casein as substrate. The purified alkaline protease had stability with commercial detergents