Thesis and Dissertations

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    OPTIMAL MAINTENANCE DECISIONS UNDER SOME UNCERTAIN AUTOMOBILE EQUIPMENT DETERIORATION
    (Mathematics depertment, nasarawa state university keffi, 2012-10-02) Obina, Nwaze, Nweze
    Two critical components (brainbox and axle) of a commercial bus fleet have been selected for study towards obtaining optimal maintenance decisions, under some uncertain automobile equipment deterioration. An interview-assisted questionnaire was used to obtain data for the project. Three prominent probability distributions were studied, namely the exponential, weibull and lognormal functions.The weibull and lognormal functions were optimal for the brainbox and axle components, respectively. Models obtained were y=0.06t1'43e't2'43/41 for brainbox and y=0.08fle(lm-|7-36)2/sl for axle, interchangeable, at same / value, with below 20% error margin. Equipment reliability of up to 70% was achievable. Bathtubs of the components exhibit similarity and this was supported by the Kolmogorov-Smirnov test (0.194), failure ratios (0.20 and 0.24) and correlation coefficients (0.823&0.816) for brainbox and axle respectively. The general linear models are 3.93810+7.85E-0.3*t, for brainbox and 13.3079+0.198069*1, for axle scatter plots. It is postulated that optimal (preventive) maintenance (drying, trouble-shooting and cleaning) of a brainbox every 7.5x104km and relightening ,greasing and change of lubricating oil in the axle, every 2.85xl05km, would reduce reactive, corrective (replacement) maintenance to less than 30%.
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    A GLOBAL ERROR ESTIMATION FOR LINEAR MULTISTEP METHODS FOR NUMERICAL SOLUTION OF NON - STIFF ORDINARY DIFFERENTIAL EQUATIONS
    (MATHEMATICAL SCIENCES, NASARAWA STATE UNIVERSITY, KEFFI., 2015-07-05) Ijausi, Matthew Ojo.
    This thesis is mainly concerned with the derivation and an analysis of error of a class of continuous Adains-Moulton schemes with application for a direct solution of non - stiff first order differential equations. The members of the continuous Adams- Moulton methods are constructed by making use of the integrand approximation process, whereby the integrand is left continuous during the integration process. Very high order methods are easily obtained by this approach in contrast to the other derivation approaches based on multistep collocation for this class of methods. We show that for a specified step number K, of finite difference formula can be generated from the continuous formula, by evaluating the latter at some grid points. It is also discovered that these schemes are of order at least K +1 with very close accuracy and stability properties to that of the conventional Adams - Moulton Method of the same step number, which is also a member of this new discrete set of formulae. The K discrete formula are applied simultaneously over successive blocks of meshes for a direct solution of non - stiff initial value problems for first order ordinary differential equations. This is achieved at very little extra computational effort.A global error estimate to the continuous approximation is discussed. We develop an analytical error estimation approach to the method for initial value problems. Numerical examples are included to illustrate the reliability and accuracy of the estimates.
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    MODELLING AND ANALYZING PREY HARVESTING OF ONE PREDATOR –TWO PREY DYNAMICS IN TROPICAL ZONE.
    (Department of Mathematics, Nasarawa State University, Keffi., 2017-06) Abegye, Shehu Yakubu.
    A two prey harvesting of Type II functional response of prey species model was proposed. The model was used to study the behaviors of ecological dynamics of Antelope – Zebra – Lion in the tropic. The stability of the equilibrium points of the system was then studied. The analysis shows that without harvesting the system can still co – exist which is showed with increase in population density of the prey species. The two prey can co – exist without the predator for very small inter – specific competition among the prey and shows that the dynamics are globally asymptotically stable. Both the qualitative and numerical analysis of the model indicated that if the harvesting rate of both Antelope and Zebra exceeds their intrinsic growth rate, their population densities would decline to extinction with time. The conditions for global stability of the system was derived using a Lyapunov function. The possibility of existence of the predator – prey system equilibrium was discussed. The numerical simulation of the model portrait that at low predator’s efficiency rate the predator decreases with increase in the population density of the prey species. Furthermore, a decrease in a specie intrinsic growth rate reduces the specie population and the population density of the predator specie will decrease. Also, when the capture rate is zero the prey population increases to its maximum population as the predator goes to extinction and on the other hand with high capture rate the prey suffers till extinction.
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    RINGS OVER WHICH A FREE MODULE IS GENERATED FROM FLAT MODULE
    (DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF NATURAL AND APPLIED SCIENCES, NASARAWA STATE UNIVERSITY, KEFFI. NIGERIA, 2017-06-11) Funmilayo, Emily, Akinwade
    The aim of this dissertation is to determine the rings over which a free module is generated from flat module. Modules are not always like vector spaces, Dylan (2010); therefore the purpose of this dissertation is to generate a module that behaves so much like vector spaces, that is a module with bases which are linearly independent. Over any rings, projective and flat modules are generated from free module but the reverse is not always true, Konrad (2012); rather, there are specific rings that need to be identified in order to generate free module from flat module. From the well-known fact that over a local ring a finitely generated flat module is free; therefore in order to generate free module from flat module, the elements of the local ring were mapped with the elements of an abelian group using the four module axioms. This dissertation considered rational number as a -module (which is also flat module), an induction argument showed that any number of elements greater than two in are linearly dependent and cannot form basis for , hence -module are not free. The dissertation also considered the ring of rational numbers with even numerator and odd denominator as a local ring whose maximal ideal is 2 over module (flat module); the result showed that, ring of rational numbers with even numerator and odd denominator formed basis for rational number and the ring of rational numbers is a subset of . An ideal was also identified as a subset of and the result showed that the set of generators formed basis for and is the principal ideal generated by single element subset of . Therefore, -module over ring of rational numbers with odd denominator and -module over an ideal have generating sets consisting of linearly independent elements. The ring of rational numbers and ideal formed the rings over which the free module is generated from flat module. Finally, a description of the Smith Normal Form algorithm and related examples were given; this provides ability to compute bases for -modules and these bases are linearly independent; also the modules generated are free.
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    INVESTIGATION OF THE SOLUBILITY BY RADICALS OF A SELECTED TRINOMIAL OF HIGHER ORDER (DEGREE 5 n 7) POLYNOMIALS USING GALOIS THEORY
    (DEPARTMENT OF MATHEMATICS, FACULTY OF NATURAL AND APPLIED SCIENCES, NASARAWA STATE UNIVERSITY KEFFI, NIGERIA, 2017-06-12) Gyam, Jeremiah, Gambo
    This dissertation extends the results of the work of Galois and his contribution to the development of modern algebra. The fact is that polynomials of higher degree (n 5) are not solvable by radicals. However, very few at that were later discovered to be solvable by radicals. In particular, we specifically identified some special polynomials which are irreducible but can be solve by radicals. These polynomials are in trinomial form ( ).Then using the quintic, sextic, and septic polynomial as case study, we finally deduced that such type of a trinomial polynomial can be generalized and a theorem was then put forward to support our argument
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    DETERMINATION OF THE MOTION OF AN INFINITESIMAL MASS FOR BOTH PRIMARIES RADIATING AND TRIAXIAL
    (2017-06-16) Ibrahim, Paul.
    This model has examined the motion of an infinitesimal particle when both primaries are radiating and triaxial in the framework of the Circular Restricted Three Body Problem (CR3BP). It was observed that the equations of motion were affected by perturbing forces (triaxiality and radiation pressures) of the primary bodies. Analytically, the locations of equilibrium points were obtained and applied to the binary systems Kruger 60 (AB) and Achird to obtain the numerical results with the help of Math Lab software. Numerical investigations reveal that locations of equilibrium points of this problem have been determined and the effect of increasing triaxiality on the position of equilibrium point were obtained with graphical result shown which reveal that the infinitesimal mass moves in the direction of the bigger primary towards the line joining the primary bodies. The linear stability of the equilibrium points has also been examined a numerical solution of the analytical result was applied to the binary stars Kruger 60. It was found that the triangular points are unstable which means that the instability is cause due to the presence of perturbation forces (Radiation and Triaxiality).
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    EXTRAPOLATION OF CONTINUOUS LINEAR MULTISTEP METHODS FOR THE NUMERICALSOLUTION OF INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
    (Department of Mathematics, Nasarawa State University, Keffi., 2019-11-20) Egwu, Bernard Anuga.
    ith initial value conditions using extrapolation of continuous linear multistep methods. By this we mean using the same numerical methods to approximate numerically the solution of an initial value problem (IVP). For example, a problem is to be solved in the interval say [a, b], our interest is to solve the problem / find the solution at a point outside the boundary of the interval to the right say without doing any further calculation with those methods. What we want to solve in this problem is using the continuous linear multistep methods for their evaluations outside their range of construction. If the solution is valid within the interval and you are interested in the validity of the solution outside the interval is called extrapolation. Our studies show that the continuous formula can be used to finding values outside the interval of consideration which the discrete formula cannot do. Our studies also compare the results of continuous linear multistep methods and the discrete scheme with the exact solution and discovered that the continuous scheme minimizes the error which is better.
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    DESIGN AND IMPLEMENTATION OF POST-SERVICE RETIREMENT PORTAL FOR CIVIL SERVANTS (A CASE STUDY OF FEDERAL CIVIL SERVICE OF NIGERIA)
    (Department of Mathematics, Nasarawa State University, Keffi., 2020-09-05) SADIQ, NAAFISATU
    The traditional system of using paper method of calculating the number of yearly retiring civil servants in the federal civil service has become slow, difficult, stressful, time consuming and subject to abuse. With the introduction of computer based personnel database management technique calculation can be done better, faster and accurately and it eliminates the mistakes in the calculation of number of yearly retiring civil servants in the federal civil service in Nigeria. This study found solution to the current challenges in determining the number of yearly retiring civil servants in the federal civil service. Determining the number of staff due for retirement either by mandatory length of service or attainment of mandatory retirement age of sixty (60) years is stipulated by the federal civil service rule. The methodology is that the developed database software can be query using age, when the age is sixty (60) the staff is due for retirement or if the number of service year is thirty five (35) the staff is due for retirement. Therefore, using these two parameters the retirement is determined. Software architectural design of a retirement web-based portal is implemented using PHP (hypertext preprocessor) and MYSQL (structural query language) database system. With this software automation method, the federal civil commission can now handle retirees activities more efficiently in well-structured and transparent manner. Furthermore, the system can generate various reports and information that can facilitate decision-making and strategic planning. One example of a recommendation would be to enhance the low knowledge of computer among the government employees. The software programs design would help in the effective and efficient management of human resources in the ministry department agency.