Abstract We generalize the greedy and lazy $\beta $ -transformations for a real base to setting of alternate bases ${\boldsymbol {\beta }}=(\beta _0,\ldots ,\beta _{p-1})$ , which were recently introduced by first second authors as particular case Cantor bases. As in case, these new transformations, denoted $T_{{\boldsymbol }}}$ $L_{{\boldsymbol respectively, can be iterated order generate digi...

Let $\alpha>0$, $\beta>\alpha$, and let $X_1,\ldots, X_q$ be $\mathscr{C}^{\alpha}_{\mathrm{loc}}$ vector fields on a $\mathscr{C}^{\alpha+1}$ manifold which span the tangent space at every point, where $\mathscr{C}^{s}$ denotes Zygmund-H\"older of order $s$. We give necessary sufficient conditions for when there is $\mathscr{C}^{\beta+1}$ structure manifold, compatible with its structure, resp...

Sclerotinia sclerotiorum is a phytopathogenicfungus that attacks more than 400 plant species of them medicinal plant. In this study the extract obtained from basal stalk rot of Helianthus annuus L., attacked by S. sclerotiorum, was subjected to the analysis of FTIR to identify the presence of beta-glucan. FT-IR spectrum showed four ranges of bands in 890 cm-1, two overlap band in 1047 and 1078 ...