Advances in Mathematics Research" presents original studies on the leading edge of mathematics. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Topics discussed herein include recent advances in the periodicity in dynamical systems; non-linear differential equations and Fucik Spectrum; matrix theory; column and row determinants in quaternion linear algebra; elliptic perturbations of parabolic and hyperbolic problems and a discrete time (s,S) inventory system with service facility.