| 1 |
Author(s):
Anongo D.O., Awari Y.S..
Page No : 1-11
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Solution of One-dimensional Partial Differential Equation with Higher-Order Derivative by Double Laplace Transform Method
Abstract
Many problems in natural and engineering sciences such as heat transfer, elasticity, quantum mechanics, water flow, and others are modelled mathematically by partial differential equations. Some of these problems may be linear, nonlinear, homogeneous, non-homogeneous, and order greater or equal one. Finding the theoretical solution to these problems with less cumbersome techniques is an active area of research in the aforementioned field. In this research paper, we have developed a new application of the double Laplace transform method to solve homogeneous and non-homogeneous linear partial differential equations (pdes) with higher-order derivatives (i.e order n where n≥2) in science and engineering. We discussed a brief theory of double Laplace transforms that helped in its application. The main advantage of our method is the reduction of computational effort in finding solution to pdes. Another major benefit of our method is solving problems in the form of (21) directly by transforming to an algebraic equation where the inverse double Laplace transform is implemented for analytical solution, unlike other integral transform methods that would first transform to a system of ODEs before they are solved, is it also very effective in solving linear high-order partial differential equations and yield fast convergence. We present a well-simplified solution for easier comprehension by upcoming researchers.
| 2 |
Author(s):
Anthony Usoro, Emediong Udoh.
Page No : 12-31
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Multivariate Time Series Modelling of Nigerian Gross Domestic Product (GDP) and Some Macroeconomic Variables
Abstract
This paper focused on modelling Nigeria’s Gross Domestic Product and some macroeconomic variables, which include, Agriculture, Crude Oil/Mineral Gas and Telecommunication using different classes of multivariate time series models. Multi-Dependent Linear Regression Model (MLRM), Vector Autoregressive Model (VARM) and Multivariate Autoregressive Distributed Lag Models (MARDLM) have been fitted to the multivariate time series. The basic statistics of the estimates and errors reveal the competitiveness of VARM and MARDLM. This was also evidently using the model selection criteria. But the mean square error of forecast places VARM on a higher comparative advantage than MARDLM. The results of the Granger causality tests showed that Crude Oil/Mineral Gas granger causes Gross Domestic Product and also granger causes Agriculture, but not vice versa in each case. This paper establishes the fact that Crude Oil/Mineral Gas is a good predictor of Gross Domestic Product and Agriculture as a major contributor to the nation’s economic development. The need to consistently juxtapose causal relationships between major economic sectors and Gross Domestic Product is vehemently advocated for proper evaluation of sectorial contributions and formulation of economic driven policy in the country.
| 3 |
Author(s):
Sallah Emmanuel Kwadzo, Joshua Kofi Sogli, Alex Owusu.
Page No : 32-46
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Use of Maple Software to Reduce Student Teachers’ Errors in Differential Calculus
Abstract
The study was conducted on the use of Maple software to reduce student teachers’ errors in Differential Calculus at Evangelical Presbyterian College of Education, Volta Region - Ghana. The research design for the study was quasi-experimental non-equivalent control group design. Convenience and simple random sampling techniques were employed to obtain a sample of 104 student teachers, which comprised 53 student teachers in the control group and 51 in the experimental group. Test items were the instruments used for data gathering. Descriptive, paired samples t-test and independent samples t-test were used in analyzing data. Descriptive content error analysis revealed that student teachers committed many conceptual, procedural and technical errors when solving tasks in the differential calculus. The results also indicated that there was a statistically significant difference between student teachers’ of the experimental group exposed to the use of Maple software in learning differential calculus to control groups exposed to traditional methods. Consequently, it was recommended that Maple assisted instruction be incorporated in the teaching and learning of differential calculus in the school; and also there is the need for the mathematics teachers in the school to employ blended teaching approaches, in which Maple software are used simultaneously to enhance teaching of mathematics concepts.
| 4 |
Author(s):
P. S. Owhondah, D. Enegesele, O.E. Biu, D.S.A. Wokoma.
Page No : 47-63
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Discriminating Between Second-Order Model With/Without Interaction Base on Central Tendency Estimation
Abstract
The study deals with discriminating between the second-order models with/without interaction on central tendency estimation using the ordinary least square (OLS) method for the estimation of the model parameters. The paper considered two different sets of data (small and large) sample size. The small sample size used data of unemployment rate as a response, inflation rate and exchange rate as the predictors from 2007 to 2018 and the large sample size was data of flow-rate on hydrate formation for Niger Delta deep offshore field. The〖 R〗^2, AIC, SBC, and SSE were computed for both data sets to test for adequacy of the models. The results show that all three models are similar for smaller data set while for large data set the second-order model centered on the median with/without interaction is the best base on the number of significant parameters. The model’s selection criterion values (R^2, AIC, SBC, and SSE) were found to be equal for models centered on median and mode for both large and small data sets. However, the model centered on median and mode with/without interaction were better than the model centered on the mean for large data sets. This study shows that the second-order regression model centered on median and mode are better than the model centered on the mean for large data set, while they are similar for smaller data set. Hence, the second-order regression model centered on median and mode with or without interaction are better than the second-order regression model centered on the mean.
| 5 |
Author(s):
Emmanuel Kwadzo Sallah, Joshua Kofi Sogli, Alex Owusu, Leonard Kwame Edekor.
Page No : 64-78
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Effective Application of Maple Software to Reduce Student Teachers’ Errors In Integral Calculus
Abstract
This study explored the effective application of Maple software to reduce student teachers’ errors in Integral Calculus at Evangelical Presbyterian College of Education, Volta Region – Ghana. The study employed the quasi-experimental non-equivalent group design. Convenience and simple random sampling techniques were employed to obtain a sample of 80 students, which consisted of 40 students in the control group and 40 in the experimental group. Teacher-made Pre, -Post-Calculus Achievement Tests (CAT), and questionnaires were used to collect quantitative and qualitative data respectively. Descriptive, Independent samples t-test and paired samples t-test were used in analyzing the data. Descriptive error analysis revealed that students committed many conceptual, procedural and technical errors when solving Integral Calculus tasks. The results also indicated that there was a statistically significant difference between students of the experimental group exposed to the use of Maple software in learning integral calculus to the control group exposed to traditional methods. The researchers recommend Maple assisted instruction in the teaching and learning of Integral Calculus and also the need to employ a blended teaching approach, in which Maple software is used simultaneously with traditional teaching strategy.
| 6 |
Author(s):
Confidence N. Woko, Isaac D. Essi, Anthony I. Wegbom.
Page No : 79-88
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Estimating the Predictors of Maternal Mortality in a Southern State of Nigeria using Logistic Regression Model
Abstract
The maternal mortality ratio (MMR) for Nigeria is 512 deaths per 100,000 live births, suggesting one of the highest in the world. Furthermore, disparities still exist between northern and southern Nigeria, and across the states of the country with varying contributing factors. This study therefore aimed to identify the predictors of maternal mortality in Rivers State, Southern Nigeria using the technique of logistic regression. Diagnostic study design was utilized for the study and data for women of childbearing age (15–49 years) were extracted from the Rivers State Hospital Management Board, Port Harcourt from January to December 2019. The association between the maternal mortality and selected maternal and health care related factors were tested using chi-square, and multivariate logistic regression was used to identify the effects of maternal and health care related factors on maternal mortality at 5% level of significance. The study identified maternal age, educational level, place of residence, marital status, delivery outcome, baby weight, ANC attendance and parity as the risk factors of maternal mortality in Rivers State. With the risks factors identified, policy makers will be better informed to plan intervention programmes to reduce maternal mortality in Rivers State and fast track the achievement of SDG goals on maternal health.
| 7 |
Author(s):
Iwundu M.P., Oko E.T..
Page No : 89-117
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Design Efficiency and Optimal Values of Replicated Central Composite Designs with Full Factorial Portions
Abstract
Efficiency and optimal properties of four varieties of Central Composite Design, namely, SCCD, RCCD, OCCD and FCCD and having r_f replicates of the full factorial portion, r_α replicates of the axial portion and r_c replicates of the center portion are studied in four to six design variables. Optimal combination,[r_f: r_α: r_c ] of design points associated with the three portions of each central composite design is presented. For SCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the center portion of the SCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For RCCD, the optimal combinations resulting in A- and D- efficient designs generally put emphasis on replicating the factorial and center portions of the RCCD. However, replicating the center and axial portions allows for G-optimal and efficient designs. For OCCD, the optimal combinations resulting in A- optimal and efficient designs generally put emphasis on replicating the axial and center portion of the OCCD. The optimal combinations resulting in G- optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the OCCD. To achieve designs that are D-optimal and D-efficient, the optimal combination of design points generally put emphasis on replicating the center portion of the OCCD. For FCCD, the optimal combinations of design points resulting in A-efficient designs put emphasis on replicating the axial portion of the FCCD. The optimal combinations resulting in G- optimal and efficient designs as well as G-optimal and efficient designs generally put emphasis on replicating the factorial and axial portions of the FCCD. It is interesting to note that for FCCD in five design variables, any r^th complete replicate of the distinct design points of the combination [r_f: r_α: r_c ] resulted in a D-efficient design. Many super-efficient designs having efficiency values greater than 1.0 emerged under the D-criterion. Unfortunately, these designs did not perform very well under A- and G-criteria, having some efficiency values much below 0.5 or just about 0.6.
| 8 |
Author(s):
Usoro Anthony E., John Eme E..
Page No : 118-134
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Modelling Covid-19 Pandemic in Nigeria using Multivariate Autoregressive Distributed Lag-Moving Average Models
Abstract
The aim of this paper was to study the trend of COVID-19 cases and fit appropriate multivariate time series models as research to complement the clinical and non-clinical measures against the menace. The cases of COVID-19, as reported by the National Centre for Disease Control (NCDC) on a daily and weekly basis, include Total Cases (TC), New Cases (NC), Active Cases (AC), Discharged Cases (DC) and Total Deaths (TD). The three waves of the COVID-19 pandemic are graphically represented in the various time plots, indicating the peaks as (June–August, 2020), (December–February, 2021), and (July–September, 2021). Multivariate Autoregressive Distributed Lag Models (MARDLM) and Multivariate Autoregressive Distributed Lag Moving Average (MARDL-MA) models have been found to be suitable for fitting different categories of the COVID-19 pandemic in Nigeria. The graphical representation and estimates have shown a gradual decline in the reported cases after the peak in September 2021. So far, the introduction of vaccines and non-pharmaceutical measures by relevant organisations are yielding plausible results, as evident in the recent decrease in New Cases, Active Cases and an increasing number of Discharged Cases, with fewer deaths. This paper advocates consistency in all clinical and non-clinical measures as a way towards the extinction of the dreaded COVID-19 pandemic in Nigeria and the world.
| 9 |
Author(s):
Oni O.V., Oni O.A., Akanle Y.O., Ogunleye T.B..
Page No : 135-144
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Modelling Annual Cocoa Production Using ARIMA Time Series Model
Abstract
Cocoa is the most valuable tropical agricultural commodity, comes next to oil; a major target in Nigeria’s export diversification strategies. Cocoa production forecasting is important to the Nigerian agricultural transformation agenda. This study attempts to forecast Nigerian cocoa production between 2019 and 2025 using the ARIMA model. The automated analytical procedure implemented in the R software package indicated that ARIMA (0, 1, 1) is the combination with the least Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) and hence, the most appropriate for forecasting. The results revealed that cocoa production would fall by more than 20% in 2025 in comparison with 2018. Thus, to guard against the fall, cocoa farmers in the country should be incentivized through adequate financial and technical assistance.
| 10 |
Author(s):
Serge Manituo Aymar Somda, Eric Bernard Agodio Dabone, Moussa Doulougou, Cedric Stéphane Bationo, Kenneth Tiemoko Marie Galboni.
Page No : 145-156
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Early-Stage Modelling and Forecast of COVID-19 Outbreak in Burkina Faso using a Bayesian SIR Approach
Abstract
In this article, we propose a Bayesian approach for estimating and predicting the magnitude of the coronavirus epidemic in Burkina Faso in its early stage. Our approach is inspired by the work of Wang et al. but adapted to the Burkinabe context. Two models are presented: a simple Bayesian SIR approach and another Bayesian SIR which takes into account the public health measures undertaken by the government of Burkina Faso. The approach was implemented at the early stage of the COVID-19 pandemic in Burkina Faso, covering the period from March 9 to April 30, 2020. The results of the analyses will allow a good prediction of COVID-19 infections and deaths in the early days of the epidemic, considering government policies.
| 11 |
Author(s):
Etaga Harrison O., Okoro Ifeanyichukwu, Aforka Kenechukwu F., Ngonadi Lilian O..
Page No : 157-185
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Methods of Estimating Correlation Coefficients in the Presence of Influential Outlier(s)
Abstract
Correlation methods are indispensable in the study of the linear relationship between two variables. However, many researchers often adopt inappropriate correlation methods in the study of linear relationships which usually leads to unreliable results. Recurrently, most researchers ignorantly employ the Pearson method in a dataset that contained outliers, instead of more appropriate correlation methods such as Spearman, Kendall Tau, Median and Quadrant which might be suitable in the calculation of correlation coefficient in the presence of influential outliers. It is noted that the accuracy of estimation of correlation coefficients under outliers has been a long-standing problem for methodological researchers. This is due to low knowledge of correlation methods and their assumptions which have led to inappropriate application of correlation methods in research analysis. Five different methods of estimating correlation coefficients in the presence of influential outlier (contaminated data) were considered: Pearson Correlation Coefficient, Spearman Correlation Coefficient, Kendall Tau Correlation Coefficient, Median Correlation Coefficient and Quadrant Correlation Coefficient.
| 12 |
Author(s):
Anggun Yuliarum Qur'ani, Subanar.
Page No : 186-198
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A Spatial Nonhomogeneous Poisson Process Model Using Bayesian Approach on a Space-Time Geostatistical Data
Abstract
In this research, we propose the nonhomogeneous Poisson process on geostatistical data by adding a time component to be applied in the study case of air pollution in the Special Region of Yogyakarta. We use the Bayesian approach to inference the model using the MCMC method. And to generate samples of the posterior distribution, we wield the Metropolis-Hastings algorithm, and we obtained it has good convergence for this case. And to show the goodness of fit of this model, we had the value of DIC.
