Browsing by Author "Kirimi, Jacob"

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    Magnetic field and hall current effect on Mud free convection flow past a vertical rotating flat plate
    (2012-11) Kirimi, Jacob; Musundi, Sammy Wabomba*; Kinyanjui, Anthony Muthondu; Lunani, Murwayi Alice
    In this study, effects of Hall current and rotation on an electrically conducting rarefied gas are investigated . A constant , strong magnetic field is applied at an angle φ to both the electric field and the direction of flow of the fluid. The study seeks to find the effects of Hall current and angle of application of the magnetic field on velocity and temperature profiles . The flow of the gas is considered as unsteady and restricted to laminar domain. The set of equations which describe the flow are a combination of the Navier-Stokes equations of fluid dynamics, generalized Ohm’s law, Maxwell’s equations, equation of continuity and equation of energy. These equations are solved numerically using the finite difference method. Numerical results of velocity and temperature profiles are analyzed using tables and graphs for Hall current parameters m* ranging from 0.0 to 1.0 and parameter λ for angle of application of the magnetic field ranging from 0.0 to 1.0.
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    On Similarity and Quasisimilarity equivalence relations
    (2012-01) Sitati, Isaiah Nalianya; Musundi, Sammy Wabomba; Nzimbi, Benard Mutuku; Kirimi, Jacob
    Similarity and unitary equivalence can be shown to be of equivalence relations. We discuss a result showing that two similar operators have equal spectra (i.e. point and approximate point spectrum). More so, unitary equivalence results for invariant subspaces and normal operators are proved. For similar normal operators, we state the Fuglede – Putnam –Rosenblum theorem that makes proofs for similar normal operators more simplified. It is also noted that direct sums and summands are preserved under unitary equivalence. Furthermore, we show that the natural concept of equivalence between Hilbert Space operators is unitary equivalence which is stronger than similarity. By introducing the notion of quasisimilarity of operators which is the same as similarity in finite dimensional spaces, but in infinite dimensional spaces, it is a much weaker relation, we further show that quasisimilarity is an equivalence relation. We also link invariant subspaces and hyperinvariant subspaces with quasisimilarity where it is seen that similarity preserves nontrivial invariant subspaces while quasisimilarity preserves nontrivial hyperinvariant subspaces.