proper conditions for producing crude beta-galactosidase from waste materials were de-termined. this enzyme is to be used in the production of lactose-hydrolyzed milk. whey permeate was used as a basic medium. twenty seven treatments were developed by 3 vary-ing factors of: yeast extract (1, 2, and 3 %), wheat steep liquor (1, 2, and 3 %), and whey powder (0.5, 1, and 1.5 %). crude enzyme extra...

The aim of this paper is twofold. Firstly, we will investigate the link between condition for functions $\phi(s)$ from $(\alpha, \beta)$-metrics Douglas type to be self-concordant and k-self concordant, other objective continue recently new introduced \beta)$-metric ([17]): $$ F(\alpha,\beta)=\frac{\beta^{2}}{\alpha}+\beta+a \alpha where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ a Riemannian metric; $\b...

We study the cyclic vectors and spanning set of circle for $\ell^p\_\beta(\mathbb{Z})$ spaces all sequences $u= (u\_n ){n\in \mathbb{Z}}$ such that $(u\_n (1+|n|)^{\beta} \mathbb{Z}} \in \ell^p(\mathbb{Z})$ , with $p>1$ $\beta>0$. The uniqueness distribution on whose Fourier coefficients are in $\ell^q\_{-\beta}(\mathbb{Z})$ is spaces, where $q$ conjugate $p$. Our characterizations given terms ...