Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations

Raymond, Dominic, Skwame, Yusuf, Adiku, Lydia

Journal of Advances in Mathematics and Computer Science, Page 1-10
DOI: 10.9734/jamcs/2021/v36i330343

We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.

Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

G. R. Al-Dayian, A. A. El-Helbawy, R. M. Refaey, S. M. Behairy

Journal of Advances in Mathematics and Computer Science, Page 11-32
DOI: 10.9734/jamcs/2021/v36i330344

Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

Prediction for Modified Topp Leone-Chen Distribution Based on Progressive Type-II Censoring Scheme

G. R. AL-Dayian, A. A. EL-Helbawy, N. T. AL-Sayed, E. M. Swielum

Journal of Advances in Mathematics and Computer Science, Page 33-57
DOI: 10.9734/jamcs/2021/v36i330345

Prediction of future events on the basis of the past and present information is a fundamental problem of statistics, arising in many contexts and producing varied solutions. The predictor can be either a point or an interval predictor. This paper focuses on predicting the future observations from the modified Topp-Leone Chen distribution based on progressive Type-II censored scheme. The two-sample prediction is applied to obtain the maximum likelihood, Bayesian and E-Bayesian prediction (point and interval) for future order statistics. The Bayesian and E-Bayesian predictors are considered based on two different loss functions, the balanced squared error loss function; as a symmetric loss function and balanced linear exponential loss function; as an asymmetric loss function. The predictors are obtained based on conjugate gamma prior and uniform hyperprior distributions. A numerical example is provided to illustrate the theoretical results and an application using real data sets are used to demonstrate how the results can be used in practice.

Effect of Variable Viscosity and Thermal Conductivity on MHD Natural Convection Flow along a Vertical Flat Plate

Sree Pradip Kumer Sarker, Md. M. Alam

Journal of Advances in Mathematics and Computer Science, Page 58-71
DOI: 10.9734/jamcs/2021/v36i330347

Free convection flow around a heated vertical flat plate in the presence of a magnetic field is very important from the technical standpoint, and several researchers have studied this issue. The effects of variable viscosity and thermal conductivity on Magneto-Hydrodynamics (MHD) free convection flow over an isothermal vertical plate immersed in a fluid with heat conduction will be studied in this study. The two-dimensional, laminar, and unsteady boundary layer equations are considered in this paper. Using relevant variables, simple governing equations are transformed into non-dimensional governing equations. The implicit finite difference scheme, also known as the Crank-Nicolson scheme, is used to solve these equations numerically. This research looks at viscous incompressible fluids with temperature-dependent viscosity and thermal conductivity. The effect of various parameters on velocity, temperature, local skin friction, and local heat transfer coefficient profiles will be shown in this study, and the results will be compared to those of other researchers. The current numerical results will be compared to the results of previously published works. Figures from the current thesis will be compared to those from previously published works. The outcomes result will be shown in graphs for various values of relevant physical parameters.

Epidemic Model and Mathematical Study of Impact of Vaccination for the Control of Malware in Computer Network

Titus Ifeanyi Chinebu, Ikechukwu Valentine Udegbe, Adanma Cecilia Eberendu

Journal of Advances in Mathematics and Computer Science, Page 72-96
DOI: 10.9734/jamcs/2021/v36i330348

Malware remains a significant threat to computer network.  In this paper, we consideredthe problem which computer malware cause to personal computers with its control by proposing a compartmental model SVEIRS (Susceptible Vaccinated-Exposed-infected-Recovered-Susceptible) for malware transmission in computer network using nonlinear ordinary differential equation. Through the analysis of the model, the basic reproduction number  were obtained, and the malware free equilibrium was proved to be locally asymptotical stable if  is less than unity and globally asymptotically stable if Ro is less than some threshold using a Lyapunov function. Also, the unique endemic equilibrium exists under certain conditions and the model underwent backward bifurcation phenomenon. To illustrate our theoretical analysis, some numerical simulation of the system was performed with RungeKutta fourth order (KR4) method in Mathlab. This was used in analyzing the behavior of different compartments of the model and the results showed that vaccination and treatment is very essential for malware control.

SIR Model Parameters Estimation with COVID-19 Data

Nilson C. Roberty, Lucas S. F. de Araujo

Journal of Advances in Mathematics and Computer Science, Page 97-117
DOI: 10.9734/jamcs/2021/v36i330349

Based on the SIR model that divides the population into susceptible, infected and removed individuals, data about the evolution of the pandemic compiled by the Johns Hopkins University Center for Systems Science and Engineering (JHUCSSE) are integrated into the numerical system solution. The system parameters Rate of Contact β, Basic Reproduction Number R0 and Removal Rate γ, also named Rate of Decay, are determined according to a ridge regression approach and a mobile statistical scheme with different averages. Data is automatically downloaded from https://raw.githubusercontent.com/CSSEGISandData/COVID-19. The main Python libraries used are Numpy, Pandas, Skit-Learn, Requests and Urllib.

Lepton Bound State Theory Based on First Principles

Hans-Peter Morsch

Journal of Advances in Mathematics and Computer Science, Page 118-131
DOI: 10.9734/jamcs/2021/v36i330350

A quantum field theory has been constructed, in which leptons are bound by electromagnetic forces. Using severe boundary conditions, in particular several constraints on the rotation velocity, a precision test has been possible, in which the needed 7 parameters are determined by many more constraints. Since arbitrary adjustment parameters are excluded, absolute values of radii, rotation velocities and binding energies are obtained, possible only in a fundamental theory, which must be close to the final lepton theory. The resulting masses are obtained with uncertainties much smaller than 1 %.

The results show a very special structure of charged and neutral leptons.

1. Charged leptons: The deduced radii due to electric and magnetic binding are different by many orders of magnitude. In particular, the large electric root mean square radius of the electron of about 103fm is almost of the same size as electron wave functions in light atoms, whereas the magnetic radius of 2.5 · 1010 fm is consistent with a ”point” particle needed to describe electron hadron scattering.

1. Neutrals: The acceleration term gives rise to dynamically generated neutral particles of ”hole” structure, which can be identified with neutrinos. Their masses are 2 · 108eV, 17 eV and 12 MeV for νe, νµ and ντ , respectively.

The full calculations together with the underlying fortran source code can be viewed at https://h2909473.stratoserver.net or https://leptonia-etc.de.

Principal Component Factor Analysis of Some Development Factors in Southern Nigeria and Its Extension to Regression Analysis

Nnaemeka Martin Eze, Oluchukwu Chukwuemeka Asogwa, Chinonso Michael Eze

Journal of Advances in Mathematics and Computer Science, Page 132-160
DOI: 10.9734/jamcs/2021/v36i330351

This study was conducted to evaluate some development factors in Southern Nigeria in order to ascertain common factors that explained the interrelationships among them and identify best cities for recommendation. A total sample of 250 cities from different states in three geopolitical zones in Southern Nigeria was used in this study and 11 development factors were considered. Kaiser-Meyer-Olkin (KMO) of (> 0.5) was computed to test the sampling adequacy; Bartlett’s Test of Sphericity (Significant at 0.001) was conducted to test whether the correlation between the variables are sufficiently large for factor analysis; correlation matrix was computed to confirm the inter-item correlation. In this analysis, principal component factor analysis was the factor extraction method. Varimax rotation technique was used for factor rotation. The result showed that three new factors with eigenvalues greater than 1 were successfully constructed. The three new factors accounted for 71.63% of total variance in the dataset and assigned as the common factors influencing sustainable development in Southern Nigeria. The communalities results ranging from 0.32-0.88 depicted that factor model was adequate. The results of factor analysis were extended to multiple regression analysis. The multiple regression model was fitted using development scores as dependent variable and rotated factors as independent variables. The coefficient of determination,, for the regression model was 99% and this shows that the model is adequate to evaluate the Southern Nigerian cities. The higher the estimated development scores, the better a city. Tolerance and VIF values showed that there was no multicollinearity in the regression model.