Browsing by Author "Bekele, Berhanu (PhD)"

Now showing 1 - 4 of 4
  • No Thumbnail Available
    Item
    Ideals of Lattice Ordered Monoid
    (Addis Ababa University, 2017-08) Baye, Alemu; Bekele, Berhanu (PhD)
    In this project the notion of an ideal of a lattice ordered monoid A is introduced. The notion of congruence relations on a lattice ordered monoid (l-monoid) A is also introduced and its relation with ideals of A is investigated. In addition, we will introduce the notion of normal ideals of lattice ordered monoid and dually residuated lattice ordered monoid (DRl-monoid) in order to study their connection with congruence relations. The ideal induced by congruence relations on an lmonoid need not be normal. By imposing additional conditions on the congruence relations on a DRl-monoid, we will prove that the induced ideal will be normal.
  • No Thumbnail Available
    Item
    perpendicu- larity in Abelian Group
    (Addis Ababa University, 2014-08) Bayafers, Habtu; Bekele, Berhanu (PhD)
    The main objective of the present Project is to address how to set axioms to establish a perpendicularity relation in Abelian Group and then study the existence of perpendicularity in(Zn; +) and (Q+; :) in certain other groups. This approach provides a justi_cation for the use of the symbol ? denoting relative primeness in number theory and extends the domain of this con- vention to some degree.Related to that we also consider parallelism from an axiomatic perspective.
  • No Thumbnail Available
    Item
    Primary Ideals in Noncommutative Semirings
    (Addis Ababa University, 2016-01) Tsegaberhan, Heanok; Bekele, Berhanu (PhD)
    From an algebraic point of view, semirings provide the most natural gener- alizations of the theory of rings. In this paper, the ring theoretic results of concerning the primary ideals and their radicals to noncommutative semir- ings are generalized. The derived results are further carried over to a Gel'fand semiring.
  • No Thumbnail Available
    Item
    Recurrent Neural Network
    (Addis Ababa University, 2011-01) Tesfaye, Kassahun; Bekele, Berhanu (PhD)
    The purpose of the study was to investigate Neural Networks in general and Recurrent Neural Network in particular. The investigation was to construct a model that shows the complex data processing of these Neural Networks and their functions in a simple way by using Artificial Neural Networks. Therefore, in order to carry out this task, Perceptron, Feed Forward and Recurrent Neural Networks, and the basic concept of Biological Neural Networks, which are among the contents of this paper, are very important. From a biological point of view, Neural Networks are networks of biological neurons. Basically, they are networks of sensory, motor and associative neurons functionally, and axon, cell body and dendrites structurally. Now, when an external or internal signal reaches the sensory neuron through the receptors, then it passes to the motor neuron through the associative neuron within the central nervous system. Since motor neuron has connection with the brain, then it immediately fires through the command that comes from the brain. This means that it gives response for that particular signal. In this paper we extend these concepts to mathematical model by using the concepts of mathematics. For instance, a Heaviside function is a simple mathematical model of Neural Network. On the other hand, Recurrent Neural Network consists of the graphG=(N,A)and a family of formal neuronsG=(V,E)-(X,Y,a,S) each associated to one of the Vertices IEVThis paper also provides details about the types of Neural Networks present in human being and also provides details about the Artificial Neural Networks. This paper also presents some Applications of Neural Networks