2-phosphonobutane-1,2,4-tricarboxylic acid is(pbtc) a member of phosphonate family, and used as corrosion and scale inhibitor in cooling water systems. phosphonocarboxylates as a member of organophosphorus compounds have c-p and p-o bonds in their structures. pbtc is mainly used as carbonate scale inhibitor (caco3), sulphate scale inhibitor (caso4), corrosion inhibitor of low alloyed steel, eff...

here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. for some special cases t...

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...