Browsing by Author "Okaka, Colleta A."

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    Characterization of codes of ideals of the polynomial ring for control in computer applicatons
    (C o u n c i l f o r I n n o v a t i v e R e s e a r c h : J o u r n a l o f A d v a n c e s i n M a t h e m a t i c s, 2016-06-01) Olege, Fanuel; Owino, M.O.; Aywa, Shem; Okaka, Colleta A.
    The study of ideals in algebraic number system has contributed immensely in preserving the notion of unique factorization in rings of algebraic integers and in proving Fermat’s last Theorem. Recent research has revealed that ideals in Noetherian rings are closed in polynomial addition and multiplication.This property has been used to characterize the polynomial ring F_2^n[x] mod(xn-1) for error control. In this research we generate ideals of the polynomial ring using GAP software and characterize the polycodewords using Shannon’s Code region and Manin’s bound.
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    Derivation and solution of the heat equation in 1-D
    (International Journal of Engineering, Science and Mathematics, 2013-06-01) Kwach, Boniface Otieno; Ongati, Omolo; Alambo, David; Okaka, Colleta A.
    Heat flows in the direction of decreasing temperature, that is, from hot to cool. In this paper we derive the heat equation and consider the flow of heat along a metal rod. The rod allows us to consider the temperature, u(x,t), as one dimensional in x but changing in time, t.