This work develops novel rational Krylov methods for updating a large-scale matrix function $f(A)$ when $A$ is subject to low-rank modifications. It extends our previous in this context on pol...

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...

A new simple and reliable method for rapid and selective extraction and determination of trace levels of Zn(II) ion is developed. Zn(II) ions are adsorbed quantitatively during passage of aqueous samples through PET-AA/AAm nano fiber modified. Almost all matrix elements were found to pass through the nano fiber to drain. Modified Poly (ethylene terephthalate)-grafted-Acrylic acid/Acryl amide Na...

A new simple and reliable method for rapid and selective extraction and determination of trace levels of Zn(II) ion is developed. Zn(II) ions are adsorbed quantitatively during passage of aqueous samples through PET-AA/AAm nano fiber modified. Almost all matrix elements were found to pass through the nano fiber to drain. Modified Poly (ethylene terephthalate)-grafted-Acrylic acid/Acryl amide Na...

In order to decrease the self-agglomeration and improve the hydrophobic properties of type-II acetylated cellulose nanocrystals (ACNC II), various degree of substitution (DS) values of ACNCs were successfully prepared by a single-step method from microcrystalline cellulose with anhydrous phosphoric acid as the solvent, and acetic anhydride as the acetylation reagent, under different reaction te...