Khintchine's singular Diophantine systems and their applications

Diophantine Approximations, Diophantine Equations, Transcendence and Applications

This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...

Singular constrained linear systems

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

Magentotactic bacteria and their applications

Magentotactic bacteria are the types of bacteria capable of orientation in an external magnetic field because of the ability to produce structures called magnetosomes. Magnetosomes, nanometer-scale structures, are present in most of the magnetotactice bacteria. They are intracellular organelles composed of magnetic iron mineral crystals individually surrounded by a phospholipid layer. Because o...

Sequential Methods and Their Applications

Iterative Solution of Singular Systems with Applications