Browsing by Author "Solomon, Dawit"

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Determination of Transfer Coefficient through Mean Exit Time Method for Model Potentials
    (Addis Ababa University, 2006-07) Solomon, Dawit; Bekele, Mulugeta (PhD)
    The electrochemical oxidation of the Activated Complex (AC) has shown very low ( 0:1) values of Anodic Transfer Coe±cient (ATC) for conducting polymers such as Polypyrrole and Polyaniline [2-5] a particular model potential barrier. In order to explain the cause for such low values of ATC, Aoki used a speci¯c potential hill to estimate such low value for the ATC. He used Langevin dynamics to describe the motion of the AC. In our present work, using the method of ¯nding mean exit time, we are able to get expressions of the ATC for three model potential hills where one of the model we took is approximately that of Aoki's potential hill. Depending on the parameters of the model potentials, we have explored the conditions under which the ATC value goes from 0:5 to as small as 0:1 or less. Eventhough, the method we used to get the expression for the ATC is completely di®erent from that used by Aoki, we are able to get very low values of ATC under highly asymmetric conditions of the model potential hills
  • No Thumbnail Available
    Item
    The Minimum Cost Maximum Flow Problem
    (Addis Ababa University, 2012-01-01) Solomon, Dawit; Guta, Berhanu (PhD)
    The main objective of this project is to present different approaches to solve minimum cost maximum flow problem, which is one of the problems we face in "network flow problems." The first chapter of this paper gives us basic definition of different terms that we use in the chapters that follows and introduction to different network problems, and the second chapter shows how to solve maximum flow problems and since we also need the knowledge to solve minimum cost flow problem we present it in chapter three. After we presented the pre-requisite in three chapters our main problem of interest comes in chapter four which is the minimum cost maximum flow problem. It deals with finding the minimum possible cost of the maximum flow in the given network.
  • No Thumbnail Available
    Item
    A Sagbi Basis for Some Subalgebras of Polynomial Rings
    (Addis Ababa University, 2019-03-04) Solomon, Dawit; Tesemma, Mohammed (PhD)
    A SAGBI BASIS FOR SOME SUBALGEBRAS OF POLYNOMIAL RINGS Dawit Solomon Tadesse Addis Ababa University, 2018 The term \SAGBI" is an acronym for \Subalgebra Analogue to Gr obner Bases for Ideals". There exist _nitely generated subalgebras of |[x1; x2; :::; xn] which have no _nite SAGBI basis with respect to any monomial order. There are also subalgebras which may or may not have _nite SAGBI basis depending on the monomial order de_ned on |[x1; x2; :::; xn]. We know that, there are uncountably many monomial orders de_ned on |[x1; x2; :::; xn] for n _ 2. It is still an important open problem to classify subalgebras that have a _nite SAGBI basis. In addition to this, two or more generators of a subalgebra may not form a SAGBI basis. Torstensson et al. provide su_cient and necessary conditions for two generators form a SAGBI basis, in the case of univariate polynomial ring. An other important open problem is to provide a su_cient andnor necessary condition when three or more generators form a SAGBI basis in the univariate polynomial ring as well as two or more generators form a SAGBI basis in a multivariate polynomial ring. This thesis provides su_cient conditions when two generators of a subalgebra form a SAGBI basis in a multivariate polynomial ring. We also investigate su_cient and necessary condition when generators with consecutive degrees form a SAGBI basis in the univariate polynomial ring. Finally we conjecture that subalgebras generated by two polynomials have a _nite SAGBI basis with respect to any monomial order. We prove our conjecture in certain cases.