Mathematics

Permanent URI for this collection

http://etd.aau.edu.et/handle/123456789/31

Browse

Now showing 1 - 20 of 421

Abundance, Distribution and Insecticide Resistance of Anopheles Mosquitoes (Diptera: Culicidae) and Malaria Transmission Intensity in Relation to Agro-ecology in Sekoru District, Southwestern Ethiopia
(Addis Ababa University, 2017-06) Ejeta, Desta; Tekie, Habte(PhD)
Malaria is a leading cause of morbidity and mortality in several sub-Saharan African countries. Environmental/ecological changes due to anthropogenic activities are among the determinant factors for malaria transmission. Agricultural practices are among anthropogenic activities that contribute to malaria incidence and transmission. Understanding association of ecological changes due to anthropogenic activities on mosquito species composition, abundance, distribution, dynamics, insecticide resistance and malaria transmission intensity is important to plan and implement effective vector control intervention strategies. Thus, the aim of this study was to investigate species composition, abundance, distribution and infectious rate of Anopheles mosquitoes and their knockdown resistance (kdr) status in relation to agricultural practices. A longitudinal entomological study was conducted from January to December 2015 in Sekoru District, southwestern Ethiopia. Anopheles mosquito larvae and adults were collected using different methods from villages with different agro-ecology. The mosquitoes were identified to species level using standard keys. Molecular identification of Anopheles gambiae complex and detection of knockdown insecticide resistance (kdr) was conducted using species-specific PCR and allele specific PCR techniques. Moreover, Plasmodium circumsporozoite protein was detected for both Plasmodium falciparum and P. vivax using Enzyme-linked Immunosorbent Assay (ELISA). Eight Anopheles mosquito species (Anophelesarabiensis,An. demeilloni, An. squamosus, An. garnhami, An. christyi, An. pretoriensis, An. longipalpis and An. marshallii) were identified, of which An. arabiensis was the predominant species (46.2%; n=715). The highest number of Anopheles mosquitoes (66%; n=1019) was collected from the irrigated village. The xvi infection rate of An. arabiensis was higher in the irrigated village (10.8 infective bites/person/month) as compared to rain fed agriculture practicing village (5.99 infective bites/person/month) and human settlement village (zero infective bite). Anopheles gambiaes.l. larvae were the predominant (57.4%) larval species identified. The highest larval density (2.12 larvae/dip) was recorded from the irrigated village. Only West African kdr mutation (L1014F) was detected with an allelic frequency of 83.88%. The distribution and frequency of kdr allele were significantly associated with study villages (X2=133.85, df=2, P <0.001). The kdr allele frequency was 95%in the irrigated village, 78.87%in village with rain fed agriculture, and 3.89% in the human settlement village. In conclusion, Anopheles mosquito abundance, distribution, infection rate and insecticide resistance were significantly associated with agro-ecology. Agro-ecological practices need to be considered in the management of Anopheles vectors of malaria. Keywords: Anopheles mosquitoes, Agro-ecology, Insecticide resistance, Irrigation, Larval habitats, Malaria, Sekoru District
Active Set Method for Solving Quadratic Programming
(Addis Ababa,University, 2010-06) Kajela, Diriba
Analysis of Boundary Integral Equations for Laplace Dirichlet Bvp In 2d
(Addis Ababa University, 2016-08-04) Fekade, Behailu; Gedif, Tsegaye (PhD)
Using an appropriate fundamental solution, Dirichlet boundary value problem is reduced to some direct Boundary Integral Equations (BIEs). Although the theory of BIEs in 3D is well developed, the BIEs in 2D need a special consideration due to their di_erent equivalence properties. Consequently, we need to set conditions on the domain for the invertibility of corresponding fundamental based integral layer potentials and hence the unique solvability of BIEs. The properties of corresponding potential operators are investigated. The equivalence of the original BVP and the obtained BIEs are analyzed and the invertibility of the BIE operators is proved.
Analysis of Boundary-Domain Integral Equations for Variable Coefficient (The Case of Dirichelet Bvp in 2d)
(Addis Ababa University, 2017-06) Aschale Shitaye; G.Tsegaye (PhD)
Using an appropriate parametrix (Levi function), Dirichlet boundary value problem is reduced to some direct segregated systems of Boundary- Domain Integral Equations (BDIEs). Although the theory of BDIEs in 3D is well developed, the BDIEs in 2D need a special consideration due to their different equivalence properties. Consequently, we need to set conditions on the domain or the spaces to insure the invertibility of corresponding parametrix-based integral layer potentials and hence the unique solubility of BDIEs. The properties of corresponding potential operators are investigated. The equivalence of the original BVP and the obtained BDIEs are analysed and the invertibility of the BDIE operators is proved.
Analysis of Constrained Optimal Control Prob- Lems"
(Addis Ababa University, 2013-07-02) Chalchisa, Mengistu; Mitiku, Semu (PhD)
This paper gives a review for optimal control problems with state variable inequality constraints. To solve the problem with pure state inequality constraint, we use different approaches such that: direct adjoint approach, the indirect adjoining approach with complementary slackness (first order constraints), the indirect adjoining approach for higher order constraints and the indirect adjoining approach with continuous adjoint functions. Furthermore, the application of optimal control problems conditions is demonstrated by solving illustrative examples. Keywords: Optimal control problems, pure state inequality constraint and mixed state inequality constraint
Analysis of Constrained Optimal Control Problem
(Addis Ababa University, 2015-10) Hundessa, Desta; Mitiku, Semu(PhD)
This paper gives a review for optimal control problems with state inequality constraints. To solve the problem with pure state inequality constraint, we use di_erent approaches with complementary slackness(_rst order constraints), the indirect adjoining approach for higher order constraints and the indirect adjoining approach with continuous adjoint functions. Furthermore, the application of optimal control problems conditions is demonstrated by solving illustrative examples
Analysis of Direct Segregated Boundary- Domain Integral Equations for Variable-Coefficient Mixed Bvps in Exterior Domains
(Addis Ababa University, 2012-02) Geremew, Shiferaw; Gedif, Tsegaye (PhD)
Direct segregated systems of boundary-domain integral equations are formulated from the mixed (Dirichlet-Neumann) boundary value problems for a scalar second order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in Weighted Sobolev spaces that are proved as well. Key words: Partial Differential Equation; Variable coefficient; Mixed problem; Parametrix; Levi function; Boundary-domain integral equations: Unbounded domain; Weighted Sobolev spaces.
Analysis of Elliptic Partial Differential Equaions
(Addis Ababa University, 2018-09-05) Wodajeneh, Terefe; Goa, Mengistu
Partial differential equations arise naturally as models for many physical phenomena. The unknown function u then describes the state of a physical system (for example, the temperature distribution or the shape of a soap film realizing the least surface area amongst all surfaces spanned by a wire) and the given function E describes the physical laws according to which the state evolves or behaves (possibly also including interaction with external forces). In this thesis elliptic boundary problems of the form { are analyzed. The main focus is obtaining the weak formulation of the problem, what is called the variational formation. The weak form of solution to the problem is obtained by applying the celebrated Lax-Milgram Theorem which is the generalization of Reisz Representation Theorem to the variational formulation of the problem.
Analysis of Fourier Transform in _L1 Space and its Inversion
(Addis Ababa University, 2012-01) Jenber, Dagnachew; Mohammed, Seid (PhD)
This project discusses the concept of Fourier transform of a function in Space with its properties theorem, inversion theorem, Fourier sine and cosine transforms theorem, Plancherel’s and Parseval’s identities theorem and the applications of Fourier transform in partial differential equations, Shannon’s sampling theorem and Heisenberg’s inequality. Therefore the purpose of this project is to solving certain problems in partial differential equations like for example Heat equation, Wave equation , and Laplace equation, to solve some complicated integrals shortly and simply, and it works in Shannon’s sampling theorem and Heisenberg’s inequality. This project uses some definitions and theorems as a preliminary from some real analysis and Fourier analysis books
Analysis of Heat Equation in Rn
(Addis Ababa University, 2020-06-16) Temesgen, Mehari; Biset, Tesfa (PhD)
This paper is concerned with Analysis of heat equation in Rn. Analysis of heat equation in Rn regarded as Fourier Transformation which has di erent properties and Inverse of Fourier Transformation that is important to solve heat equation in 0n0 spaces. using separation of variables for solving with boundary conditions like Dirichlet, Neumann and periodic conditions. By using these condition we solve heat equations in Rn is solved.
Analysis of Two-Operator Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems in 2D
(Addis Ababa University, 2020-10-24) Tesfaye, Solomon; Gedif, Tsegaye (PhD); Mikhailov, Sergey E. (Professor)
In this dissertation, the boundary value problems (BVPs) for the second order elliptic partial differential equation with variable coefficient in two-dimensional bounded domain is considered. Using an appropriate parametrix (Levi function) and applying the two-operator approach (where the one operator approach fails ), the problems are reduced to some systems of boundary-domain integral equations (BDIEs). The two-operator BDIEs in 2D need a special consideration due to their different equivalence properties as compared to higher dimensional case due to the logarithmic term in the parametrix for the associated partial differential equation. Consequently, we need to set conditions on the domain or function spaces to insure the invertibility of the corresponding layer potentials, and hence the unique solvability of BDIEs. Equivalence of the two-operator BDIE systems to the original BVPs, BDIEs solvability, uniqueness/ non uniqueness of the solution, as well as Fredholm property and invertibility of the BDIEs are analysed. Moreover, the two-operator boundary domain integral operators for the Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators.
Application of Schauder’s Fixed Point Theorem for Semilinear Evolution Equations
(Addis Ababa University, 2018-09-03) Leikun, Abie; Goa, Mengistu (PhD)
This thesis is concerned with Semilinear evolution equations on a bounded Ω n
Applications of Banach Fixed Point Theorem to Differential Equations
(Addis Ababa University, 2018-08-03) H/Giorgis, Shewaseged; Bekeshie, Tadesse (PhD)
Banach fixed point theorem states sufficient conditions for the existence and uniqueness of a fixed point (point that is mapped onto itself). The applications of Banach fixed point theorem to differential equations arise in connection with certain class functions called contractions. The theorem also provides a constructive procedure (called iteration) by which we can obtain better and better approximation to the solution of a problem and error bounds. In this project we apply the existence, uniqueness and iterative properties of the theorem to Differential Equations.
Applications of Fixed Point Method to Semilinear Elliptic Equations
(Addis Ababa University, 2018-09-03) Zewdie, Chernet; Goa, Mengistu (PhD)
In the study of differential equations there are two fundamental questions: Is there a solution? And what is it? One of the most elegant was to prove that an equation has a solution is to pose it as fixed point problem that is to find a function such that x is a solution if and only if ( ) . Results from fixed point theory can then be employed to show that has a fixed point. However the results of fixed point theory are often non-constructive: they guarantee that a fixed point exists but do not help in finding the fixed point. Thus these methods tend to answer the first questions but not the second. One such result is Schauder's fixed point theorem. This theorem is broadly applicable in proving the existence of solutions to differential equations. In this thesis we present a selection of fixed point theorems with applications in semilinear elliptic equation. We begin with the Banach fixed point theorem. Then prove in succession the fixed point theorems of Brouwer Schauder and Schaeffer after which we conclude with applications for semilinear elliptic equation.
Approximate Solution of Linear Differential Equation
(Addis Ababa University, 2018-08-04) Aragaw, Getahun; Abathun, Addisalem (PhD)
This thesis presents an efficient approach for determining approximate solutions of ordinary linear differential equations at ordinary points, near regular singular points and near irregular singular points. Test examples demonstrate the effectiveness and inefficiency of a given method at different points.
Approximating Common Solutions of Variational Inequality, Equilibrium and Fixed Point Problems
(Addis Ababa University, 2017-04) Hadush, Tesfalem; Zegeye, Habtu(Professor)
Many of the most important problems arising in nonlinear analysis reduce to solving a given equation, which in turn may be reduced to finding the fixed points of a certain mapping or solutions of varia- tional inequality and equilibrium problems. Because of the relation between the fixed point problem, variational inequality and equilib- rium problems, finding common solutions of these problems is an important field of research. In this thesis, we introduce and study an iterative algorithm which converges strongly to a common element of the set of xed points of a more general class of Lipschitz hemicontractive-type multi-valued mappings and the set of solutions of variational inequality problem in real Hilbert spaces. In addition, we have obtained strong convergence theorems of an iterative process for finding a common solution of the fixed point problem for Lipschitz hemicontractive-type multi-valued mapping and the generalized equilibrium problem in the framework of real Hilbert spaces. We also extend this result to a finite family of generalized equilibrium problems. Furthermore, a viscosity-type approximation method is introduced for approximating a common element of the set of fixed points of a nonexpansive multi-valued mapping, the sets of solutions of a split equilibrium and a variational inequality problems.
Artinian Rings Graduate Seminar Report
(Addis Ababa University, 1985-05) Symengne, Berhanu
Assessing the Implementation of Group InteractionIn Teaching and Learning of Mathematics in Cheha District Secondary Schools
(Addis Ababa University, 2007-09) Woldesenbet, Alemayehu; Atnafu, Mulugeta(PhD)
The main purpose of this study was to assess the implementation of five in one, group work and pair work cooperative learning in Cheha District general secondary schools. To conduct the study, survey design was employed. And the sources of data are students, teachers and school principals. It was carried out in cheha District general and secondary schools. By using simple random sampling 168 students were selected and 12 teachers were used. The main instrument of data collection was questionnaire. It was also substantiated with interview and classroom observations. And to analyze the data’s both quantitative & qualitative method were used. The result of the study showed that the extent of practicing five in one, group work and pair work in cheha District general and secondary schools was moderate. The preference of students from five in one, group work, pair work and individual learning is five in one whereas the preference of teachers is group work. But they did not prefer learning individually. The extent of the participation of students in five in one, group work and pair work is moderate. The attitude of students and teachers to word five in one group work and pair work learning is encouraging. Whereas the attitude of them toward individual learning is discourage. And the top five challenges were shared by both teachers and students, these are: large class size, commitment of teachers, interest of students, time shortage and interest of teachers
Association Between Participation in Sport and Academic Achievement of Preparatory Students in Adama Town, Oromiya Regional State, Ethiopia
(Addis Ababa University, 2016-09) Tsige, Shewangzaw; Wolde, Bezabih (PhD)
The purpose of this study was to investigate the association between sport participation and academic performance of preparatory school students. Sports and academic performance of students has been a topic of study for years. On the one hand, supporters of sports program in educational institutions say that participation in sports improves students’ grades, academic achievement, raises their educational aspirations, and keep them in schools. On the other hand, others say that participation in sports distract time away from the classroom and divert students’ attention from study. It is not possible for students to achieve excellence in sports as well as in education. The study was conducted in two Government and two private preparatory schools of Adama Town, Oromiya Regional State, Ethiopia. An interview question and a structured questionnaire on five point Likert scale were developed and utilized for collection of data. 10 education officials, coaches, sport teachers and 204 students were selected through purposive and random sampling techniques respectively. The data derived from these likert scales were evaluated using Statistical Package for the Social Science (SPSS) 19.0 software through descriptive statistics (Mean), independent samples t-test (p<0.05) and Pearson Product Moment Correlation (p<0.01). The result of the study revealed that there is association between participation in sports and performance in education and participation in sports improves the Class Marks (Scores), ability of students to succeed academically, and mental or cognitive development. This study also confirmed that Sports activities are very useful and helpful for enhancing students’ capability to learning and development. Both teachers and sport coaches should consider ways to best foster sport capacity among students. Keywords: Preparatory school students, sports’ participation, academic achievement
Asymptotic Solutions of Ordinary Differential Equations Having an Irregular Singular Point
(Addis Ababa University, 2010-06-06) Yesuf Jemal; Abdi Tadesse (PhD)
The problem of finding a basis solution of linear homogeneous ordinary differential equations with variable coefficients is, in general difficult. Indeed a considerable effort was directed at constructing solutions of specific equations with non constant coefficients. The solutions of differential equations with analytic coefficients were obtained from a theory called the method of power series. Most importantly is the case in which the equation has a singular point. In the special case of a so called regular (weak) singular point we can apply the method of Frobenius to construct convergent series solutions in a neighborhood of this point. In general this cannot be done for an irregular (strong) singular point. Treatment of this case is the main aim of this seminar. The first chapter gives the background information about the problem under investigated. The second chapter constructs a method of approximating the solutions of differential equations in a neighborhood of an irregular singular point. The final chapter extends these approximations to asymptotic expansions.

Browse

Browsing Mathematics by Title

Results Per Page

Sort Options