The volatility of equity returns for two beverages traded on the Nigerian stock exchange is the subject of this study. The ARCH effect test demonstrated that the two beverages disprove the claim that there is no ARCH effect. According to the preliminary analysis, both beverages were volatile. CGARCH and EGARCH were chosen as the best volatility models for Guinness Nigeria Plc returns and Nigeria Breweries returns, respectively, based on model selection criteria. The EGARCH model, on the other hand, rejected the idea that Guinness Nigeria Plc’s equity returns respond equally to negative and positive shocks of similar magnitude. This study’s findings suggest that the government should be cautious about how it manages inflation and foreign direct investment because they affect the rising stock price. Financial stability will likely be a more direct and explicit part of the macroeconomic responsibilities of central banks in the coming years.

Numerical solution of ordinary differential equations is the most important technique which is widely used for mathematical modelling in science and engineering. The differential equation that describes the problem is typically too complex to precisely solve in real-world circumstances. Since most ordinary differential equations are not solvable analytically, numerical computations are the only way to obtain information about the solution. Many different methods have been proposed and used is an attempt to solve accurately various types of ordinary differential equations. Among them, Runge-Kutta is a well-known and popular method because of their good efficiency. This paper contains an analysis for the computations of the modified Runge-Kutta method for nonlinear second order initial value problems. This method is wide quite efficient and practically well suited for solving linear and non-linear problems. In order to verify the accuracy, we compare numerical solution with the exact solution. We also compare the performance and the computational effort of this method. In order to achieve higher accuracy in the solution, the step size needs to be small. Finally, we take some examples of non-linear initial value problems (IVPs) to verify proposed method. The results of that example indicate that the convergence, stability analysis, and error analysis which are discussed to determine the efficiency of the method.

It has been shown that Ranked Set Sampling (RSS) is highly beneficial to the estimation based on Simple Random Sampling (SRS). There has been considerable development and many modifications were done to this method. The problem of estimating the population means is an integral aspect of a scientific survey. The estimators were examined for cum-dual products under Ranked Set Sampling (RSS), while the first-order approximation to the bias and Mean Square Error (MSE) of the proposed estimators were obtained. The numerical illustration of the comparisons was carried out to support the claim that the proposed estimators are more efficient than some existing estimators. Data were simulated for study variable y and auxiliary variable x using R software for the analysis to support the claim. The result shows that MSE of the proposed estimators, y ̅_(pd,RSS)^* is smaller than the MSE of the existing estimators y ̅_pd^*,y ̅_Rd^*, y ̅_(R,RSS)^*,y ̅_(RSS,MM1)^* and y ̅_(RSS,MM2)^* and y ̅_(RSS,MM3)^* at ρ = −0.1,−0.2,0.1,0.2, hence, the proposed estimator performed better than the existing estimators. While the MSE of the proposed estimator yy ̅_(pd,RSS)^* is greater than the MSE of the existing estimators y ̅_pd^* and y ̅_Rd^* at ρ = -0.3 and 0.3. However, the proposed estimator y ̅_(pd,RSS)^* does not perform better than the estimators, y ̅_pd^*,and y ̅_Rd^* at ρ = -0.3 and 0.3. It was concluded that the proposed estimator was more efficient than a class of regression estimators and four existing ratio-type estimators based on RSS.

In this study, linear Volterra-Fredholm integral equations are approximatively solved in terms of Lucas polynomials about any point in this study using a practical matrix approach. This technique uses collocation points and Lucas polynomials to transform the aforementioned linear Volterra-Fredholm integral problem into a matrix equation. Lucas coefficients are unknown in the system of linear algebraic equations. With the use of an error estimation, some illustrated examples are also provided. The outcomes demonstrate how effective and practical the suggested methodology is. Code was created in MATLAB to acquire the matrix equations and answers for the chosen issues.

In the present study numerical solution for non linear equations have been studied. Ridders methodd have been discussed. An improvement of Ridders method with combination of Bisection and newton Raphson methods have been presented. An algorithm for the proposed method have been stated. Moreover, several examples are included to demonstrate the validity and applicability of the presented technique. Matlab program involved for numerical computations. The proposed method applied for given examples. The error analysis table presents the obtained numerical results. The numerical solutions which found by Matlab program has good results in terms of accuracy.

In this article, we construct an approximate series solution for the one-dimensional one-phase Stefan-like problems with a forcing term. An algorithm is proposed to represent the nonhomogeneous forcing term in a moving series form to incorporate it into the moving Taylor series method. Numerical examples are solved by the proposed algorithm and the results show that with a suitable number of terms in the utilized moving series, the approximate solution is in good agreement with the exact solution.

This study developed two to six multivariate regression equations that reliably predict global radiation in Jos (Latitude 9.87 °𝑁 and Longitude 8.75 °𝐸). Thirty-one years (1980 – 2010) observed monthly mean daily global solar radiation, sunshine hours, maximum and minimum temperatures, cloud cover, rainfall, relative humidity and wind speed data were used in this study with the clearness index as the response variable and other variables as predictors. The seven validation indices employed are the coefficient of determination (R2), Mean Bias Error (MBE), Root Mean Square Error (RMSE), Mean Percentage Error (MPE), t – test, Nash – Sutcliffe Equation (NSE) and Index of Agreement (IA) to determine the reliability, suitability and applicability of the developed models. The results in this study revealed that all the developed multivariate models were found reliable for global solar radiation estimation in Jos depending on the obtainable meteorological data measured in the location. The correlation between the measured and predicted (developed) global solar radiation shows a perfect correlation as depicted from the figures.

Linear programming is a mathematical method for choosing the best product combination to maximize profit or decrease cost within the limitations of available resources. In this article, we have proposed the linear programming application for profit Maximization of a Biscuit Factory in Bangladesh. For linear programming problems, the Simplex algorithm provides a powerful computational tool, able to provide fast solution to very large-scale application. The optimization principal examined unit cost of production, the selling price and the quantity of different raw materials used in production. A model for the problem was formulated and optimum results derived using software that employed simplex method. Our main goal is to emphasize the uniqueness of linear programming modeling at the business level as an optimization technique, and to encourage manufacturing companies to employ linear programming to determine their optimal profit.

The average run length (ARL) calculation of control charts (or Shewhart charts) is not a straightforward way as it measures and compares the performance of control charts like cumulative sum and exponentially weighted moving average (EWMA) to implement complex business analysis tools like six sigma. The cumulative sum charts plot the cumulative derivations between data point and the reference value. Like cumulative sum, the EWMA charts have also been used in detecting the small shifts in process mean. Such control charts monitor and detect the autocorrelated data. This paper presents the performance of standard and modified EWMA chart by investigating the two-sides of the exact average run length using explicit formula and analyses the detection of quick shift EWMA chart as one of the major components for monitoring the efficient industrial process. The ARL of explicit formula of is compared with standard and modified EWMA charts for different values of coefficient of the first order moving average process (MAP). The experimental results in standard EWMA control chart, the upper shift is detected in observations from 58 to 60 while in the modified EWMA the upper shift is detected in observations from 54 to 60 which shows the better performance of modified EWMA over standard form.

Hypha consists of two regions; cap (apex) and cylindrical shaft (subapex and mature combined). The hyphal-cap is the most critical part due to its dominant role in the hyphal-wall growth and mor- phogenesis. Just how the hyphal-wall growth is regulated in order to maintain its tubular shape has been the subject of much research for over 100 years. Here, we derived a formula of approximate idealized hyphal-contour based on gradients of secant lines joining a fixed coor- dinate at the starting hyphal-shaft to any coordinates on the contour. The formula is capable of being a control for experimental analysis in which it is not limited to one specific shape of the hyphal-like cell. Also, it potentially can play a role as built-in or ready-made hyphal-fitting profile that “best fits” microscopic images of various actual hyphal- like cells. In other words, given a microscopic image of hyphal-like cell, mycologists and microbiologists would not have to wonder about mathematical representation of its contour since the formula has pre- pared for it.