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- "Sawdust particles soon after emission from the cutting machine usually move dynamically with transformation in some dimensions. This paper models the sawdust particle motion as a two dimensional transformation system of continuous time series. Cost could be saved using this approach instead of utilizing dynamic systems that depend on time history Two dimensional graphical representation of continuous time series of Duffing's dynamic system for sawdust particles was investigated with emphasis placed on application to sawdust particle motion and the saw machines. Pr~liminary studies were made using the harmonic functions, F(t) = Cos(wt) and F(t) = Sin(wt), for their familiarity in both science and technology communities. The solution to Duffing's model equation for the sawdust particles was sought from displacement and velocity perspectives, using the Runge-Kutta Algorithm. Linear transformation that guarantees non-negative values of time series was implemented. This was followed by the respective computation of the x- and y-components of the resulting time series values of the sawdust movement using a 21tmodulated time measured in radians. The graphical representations of the x- and y-components compared well quantitatively and qualitatively with the corresponding phase plots. The feasibility of modelling sawdust dynamics as emission from band saws was therefore demonstrated here, in approaches that thus advance knowledge of sawdust emission studies. " 1 results 1
- "Simulation of reliable solutions of nonlinear engineering problems by means of stable numerical algorithms is a frequent and acceptable practice. This study focuses the development and investigation of Runge-Kutta coefficients dependent stability polynomial for the second, third and fourth orders Runge-Kutta schemes. The development utilized matrix inversion operation procedure that involves determinant and cofactors computation of relevant matrix. The validation was made referencing the standard result of [1] and extended to several cases. The resulting polynom ials obtained consist of combination of the scheme coefficients with increasing power of time step that follows a rhyme pattern.The validation test case result agreed perfectly with test standard result. Selected studied version of different schemes shows wide variation in the shape of stability curve and region bounded. It is interesting to note that the popular second, third and•fourth order schemes have stability curve that bounded larger region than their respective counterpart. It is concluded that the study results can be utilized as reliable platform for stability analysis for different versions of the second, third and fourth order schemes. " 1 results 1
- "This investigation derived its strong motivation in the adoption of versions of second-order Runge-Kutta methods where there is presently dearth of relevant literature to re-establish .the complicated nature of solution of buffing oscillator dynamics. The choice of second-order Runge-Kutta methods hinged On its simplest algebraic formulation of relevant coefficients based on Taylor series expansion comparing with its higher order counterpart. Validation of FORTRAN-90 codes of algorithms was achieved by phase plots comparison reference to Dowell (1988) as standard. The nature of simulated solutions were visually determined with scatter plot of phase variables obtained from simultaneous implementation of large number of versions of second-order Runge-Kutta methods in conjunction with the corresponding literature results. Validation results are acceptable to within the accuracy limit of Runge-Kutta methods adopted. The scatter plots on phase plane for cases investigated are well structured and bounded (strange) and compare correspondingly well with literature Poincare sections. This investigation re-establishes the complex nature of solution of Duffings oscillator dynamics. Its established procedures provide an alternative Poincare section method and can be utilised for preliminary verification of system dynamics behaviour subject to confirmation by additional dynamics tests. " 1 results 1
- "This study investigated the characterisation of the dynamic responses of 3-dimensional Lorenz and Rӧsler models by Lyapunov's exponents using popular but laborious to implement Grahm Schmidt orthogonal rules over wider range of models driven parameters. The study also verifies a new proposed model for the validation of Lyapunov's spectrum when the requisite matrix depends on positions on the model attractor. Models and the corresponding Lyapunov's spectrums were simulated by appropriately effecting Grahm Schmidt orthogonal rules and using three different detailed constant step Runge-Kutta algorithms. The FORTRAN-90 coded algorithms were validated using literature results reported by Vladimir Golovko (2003). The stability of Lyapunov's exponents estimate variation was studied in the range of estimate reset period of 2≤τ≤16 .The Lorenz model was characterized at δ = 10, ƿ =28, and 1≤β≤2.8. This range covers both square and rectangular geometries. Similarly, Rӧsler model was characterised at a=ᵞ=0.2 and 2≤µ≤6. This range has potential to drive the model both periodically and chaotically depending on the choices of µ .The validation of the largest Lyapunov's exponents (λ)in Rosier model suffered the highest relative absolute percentage error of 14.29 while its absolute error is one of the lowest (0.01). The remaining five Lyapunov's exponents (three from Lorenz and two < from Rӧsier) suffered relative absolute percentage error of ≤ 2.00. Estimated Lyapunov's exponents stabilise for estimate reset period ≤ 10 .The most stable algorithms was found to be Butcher's modified fifth order followed respectively by fourth (RK4) and fifth (RK5) order. Estimation of Lyapunov's exponents' in Rӧsier model was found to be insensitive to algorithms due to its relative low degree of nonlinearity when compared with Lorenz model. It was established that the sum of Lyapunov's spectrum is the same as the average of trace of variation square matrix over large iteration regardless of dependence on position variable or not. This study demonstrated that the utility of Lyapunov's exponents as response characterising tool of dynamic systems driven by different parameters combination justify its laborious estimation by Grahm Schmidt method. " 1 results 1
- "This study utilised correlation and distribution analyses to investigate the acceptability of Parameters. selection sensitive simulation of the excited nonlinear pendulum waveforms was performed with the constant time step fourth order Runge-Kutta algorithm with codes developed in FORTRAN90. However, the waveforms validated by Gregory and Jerry (1990) and treated as time series were characterized using developed codes of Carlos (1998) and Hurst fractal dimension estimation procedures. The validation results compare. qualitatively well and the correlation coefficients between Carlos (1998)-based and Hurst's exponent based dimension estimate for the angular displacement and velocity are respectively R2 = 0.68 and R2 = 0.66. A higher correlation coefficient (R2 = 0.84) existed between the estimated Hurst's exponent of the angular displacement and velocity. The Hurst distribution exhibited both full spectrum and peak values range 0.04 to 1.00 and percentage probability range 2 to 12. The sum of this study results is the interchange possibility and utility of the two fractal dimension estimators as waveforms characterising tool. " 1 results 1
- "This study utilized coniJination of phase plots,time steps dstribution and adaptive time steps Runge-Kutta and fifth order algorfthms to investigate a harmonically duffing osciliator. The object is to visually compare fourth and fifth order Runge-Kutta algorithms performance as tools for seeking the chaotic solutions of a harmonically excited duffing oscillator. Though flth order algorithms favours higher time steps and as such faster to execute than fourth order for all studied cases.The reliability of results obtained with fourth order worth its higher recorded total computation time steps period. " 1 results 1
- "This work investigated the control of chaotic behavior of a harmonically perturbed Duffing Oscillator using vibration absorber. The systems of two degrees of freedom governing equations were simulated numerically using classical fourth order Runge-Kutta algorithm for a constant time step. The solution time history, phase plots and Poincare maps were used to validate the simulation. Essentially, the details of the' Poincare map were used numerically to determine the periodicity of Duffing oscillator for spectrum of mass ratio at a constant step of 0.001. The time history, phase plots and the Poincare at mass ratio (µ), absorber parameters (αa), and amplitude of excitation (Fo) are in agreement with what is obtained in open literature. The chaotic response of the Duffing-Absorber system at αa= 1.1, Fo = 0.21: and, taken respectively. The Duffing and the absorber initial conditions to be (1.0,0.0) and (0.0, 0.0), this chaotic response was rendered periodic for some selected mass ratio (0≤µ≤1.0) Specifically, periods 1, 2 and 4 were obtained at µ= 0.208; these periodic responses were obtained at respective values αa=1.1, αa=I.7803 and αa= 1.7595. In this work, eighty percent of the mass ratio selected did ensure that the chaotic behaviour of the Duffing-Absorber system is rendered periodic. This work demonstrated the practical utility of vibration absorber as a chaotic oscillations control tool by the mass ratio approach; and having a recorded success of about eighty percent. " 1 results 1
- "Though the major target of the HIV-virus is the immune system, the frequency of abdominal disorders in HIV/AIDS patients has been reported to be second only to pulmonary disease. These abdominal manifestations may be on the increase as the use of antlretroviral therapy has increased life expectancy and improved quality of life. Ultrasonography is an easy to perform, non invasive, inexpensive and safe imaging technique that is invaluable in Africa where AIDS is most prevalent and where sophisticated diagnostic tools are not readily available. Purpose: To describe the findings and evaluate the clinical utility of abdominal uitrasonography in HIV?AIDS patients in Ibadan. Methods:A Prospective evaluation of the abdominal ultrasonography of 391 HIV-positive patients as well as 391 age and sex- matched HIV-negative patients were carried out at the University College Hospital, Ibadan.Results: Of the 391 cases studied, 260 (66.5%) were females; the mean age was 38.02 years, (range 15-66 years). The disease was most prevalent in the 4th decade with an incidence of 40.4%. Compared with the HIV-negative individual group of patients had a significantly higher proportion of splenomegaly (13.5% vs. 7.7%; p < 0.01), lymphadenopathy (2.0% vs. 1.3%; p < 0.70), and renal abnormalities (8.4% vs. 3.8%; p < 0.02). There were no differences in hepatic and pancreatic abnormalities between the HIV+ and HIV- groups. There were significantly fewer gallstones in the HIV+ group (1.4% vs. 5.1%; p < 0.01). Conclusion:AIDS is a multi-systemic disease and its demographic and clinical pattern remains the same globally. Ultrasond optimally suited for its clinical management especially in Africa. Its accuracy and sensitivity may be much improved with clinico-pathologic correlation which may not be readily available in developing countries; further studies may provide much needed diagnostic algorithms. " 1 results 1
- :Johnson's hlgoritlim 1 results 1
- A system of power generation whereby the generating equipment is located close to the point of usage, thereby reducing losses and operation cost is called distributed generation (DG). However, it is imperative that DGs are sited such that the quality of power delivered is optimized and the total real power loss within the system minimized. This paper proposes an approach for optimum sizing and siting of DGs sizing in a power distribution system using Ant Colony Optimization (ACO) algorithm. To validate the algorithm the IEEE 30 bus standard test system was employed. A 92% decrease in real power loss within the system relative to the value before the connection of DGs was observed, while the minimum bus voltage increased from 0.656 per unit to 0.965 per unit. The results obtained from ACO are further verified by creating an ETAP model of the IEEE 30 bus system and simulating the impact of DG on the system. A significant reduction in total real power losses within the system and improvement in voltage profile was observed when the DGs are placed at the ACO derived sites relative to at other locations. Therefore, Ant Colony Algorithm can be used in deriving the optimum sites and sizes of DGs in a power distribution system. 1 results 1
- Academic journals are an important outlet for dissemination of academic research. In this study, Neural Networks model was used in the prediction of abstracts from The Institute of Electrical and Electronics Engineers (IEEE) Transactions on Computers. Simulation of results was done using the Polynomial Neural Networks algorithm. This algorithm, which is based on Group Method of Data Handling (GMDH) method, utilizes a class of polynomials such as linear, quadratic and modified quadratic. The prediction was done for a period of twenty-four months using a predictive model of three layers and two coefficients. The performance measures used in this study were mean square errors, mean absolute error and root mean square error. 1 results 1
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- Asides inventory cost, which is being used as the only inventory performance measure at the University of Ibadan bakery, a number of other criteria, such as inventory cost, service level, inventory turnover and delivery lead time which influence the performance of an inventory system have surfaced over the years. Hence, there is the need to examine all these criteria-objectives altogether. Therefore, this research was centred towards optimising the inventory system of University of Ibadan bakery, putting multiple criteria into consideration. Data on 17 raw materials: their costs, suppliers, usage rate, lead time, storage space and available capital were collected by means of interviews, past records and observations. The weighted goal program algorithm was adopted to find the best compromise between fulfilling the four objectives by minimising the sum of the deviation from the target values of the goals. Subsequently, Lingo 17.0 and Tora 1.0 optimisation software packages were used to solve and compare the model generated, while putting into consideration storage space constraint and budgeted capital. The developed model from the goal programming algorithm exhibited four goals (combined into one objective function). Same solutions were obtained from Lingo 17.0 and Tora 1.0. While Lingo 17.0 gave a uniform service level of 100% , a turnover ratio greater than 1(>1) for all the materials at a negligible increase (of < 0.0001%) in total inventory cost of the raw materials and available lead time duration of zero days (< 24 hours) for each material, Tora 1.0 gave a uniform service level of 100% a turnover ratio greater than 1 (> 1) for all the materials at a negligible increase (of < 0.0001%) in total inventory cost of the raw materials and available ead time duration of zero days (< 24 hours) for each material. Implementation of the developed model will eliminate unnecessary waiting time between production, thereby ensuring effective and efficient utilization of raw materials in production which will lead to reduced cost of holding inventory, elimination of unnecessary overall cost and wastages, and also improvement of the productivity and profit on the long run. 1 results 1
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