Browsing by Author "Bekele, Berhanu(PhD)"

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    Groebner Basis and its Applications
    (Addis Ababa University, 2012-06) Belete, Solomon; Bekele, Berhanu(PhD)
    In this thesis we present the basic concepts and results of Groebner basis for a polynomial ideal over a field and introduce an algorithm for computing and then present an improvement of Buchberger's algorithms for computing Groebner basis by reducing number of S-polynomials without computing them. This paper deals with Groebner basis for a polynomial ideal over a ring by defining the module of a solution of a homogenous linear equation with polynomial coeffcients (called the syzygy module). And finally, we will see the application of Groebner basis in detail.
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    Transfer Matrices
    (Addis Ababa University, 2017-06) Abate, Wossenu; Bekele, Berhanu(PhD)
    The transfer function of a linear time-invariant system describes the input output behavior of the system when all initial conditions are zero. Hence, it should be independent of the state variables used in a state space description of the system. A state space description of an input-output system can be regarded as a time-domain description. For linear time-invariant systems, transfer functions provide another way of describing inputoutput systems; this description is sometimes called a frequency domain description. To discuss transfer functions of continuous-time systems, we need the Laplace transform