Semilocal convergence of a family of third-order methods in Banach spaces under Hölder continuous second derivative

In this paper, the semilocal convergence of a family of multipoint third-order methods used for solving F(x)=0$F\left(x\right)=0$ in Banach spaces is established. It is done by using recurrence relations under the assumption that the second Fréchet derivative of F$F$ satisfies Hölder continuity condition. Based on two parameters depending upon F$F$, a new family of recurrence relations is defined. Using these recurrence relations, an existence–uniqueness theorem is established to prove that the R$R$-order convergence of the method is (2+p)$(2+p)$. A priori error bounds for the method are also derived. Two numerical examples are worked out to demonstrate the efficacy of our approach.     

Studies on manganese nodule leached residue 4. Physicochemical characterization and catalytic activity of acetic acid treated manganese nodule leached residue

The catalytic activity of water-washed manganese nodule leached residue (WMNLR) samples improved by treating with acetic acid. The effects of acetic acid treatment on the physicochemical properties and catalytic activity of manganese nodule leached residue have been studied. The surface area, surface oxygen, surface hydroxyl groups, surface acidity, electron donating properties, etc., increase gradually with acid treatment up to 0.5 M and thereafter show a decreasing trend. The rate constant of H2O2 decomposition, catalytic activity of CO oxidation, and esterification of acetic acid also show a similar trend to that of surface properties.     

Studies on the Chemical Modification of Goat Liver Cystatin and the Effect on Its Anti-Papain Inhibitory Activity

Goat liver cystatin was subjected to various chemical modifications in order to ascertain the amino acid residues responsible for its structural and functional integrity. Modification of tryptophan by HNBB led to the complete inactivation of the protein. The inactivation was also accompanied by the complete loss of tryptophan fluorescence at 340 nm. The reaction of liver cystatin with HNBB yielded a characteristic decrease in absorbance at 280 nm. Acetylation of the amino groups of liver cystatin was carried out in the presence of acetic anhydride. The acetylated cystatin showed a decrease in fluorescence intensity at 335 nm which could be attributed to the modification of tyrosine residue due to side reaction.