Open Access Original Research Article

Modelling Miraa Addiction like a Disease Incorporating Voluntary Quitting

Makembo George, Karanja Stephen, David Theuri

Journal of Advances in Mathematics and Computer Science, Page 1-19
DOI: 10.9734/JAMCS/2017/35953

This study presented a deterministic model of miraa addiction based on three compartmental classes incorporating miraa specific attributes as well as the aspect of voluntary quitting. Our model was based on SIS classical infectious model classes with Susceptible(S) and Infected (I) adopted as Light user (L) and Addicted (A) in our model. From the model flow chart, non linear differential equations are deduced. The basic reproduction number (R0) was determined using next generation method. Positivity and boundedness of the solution was investigated and the system of equations was found to lie in the feasible region. Miraa equilibrium points were determined and the condition necessary for the existence of miraa persistent equilibrium point was found to be R0 >1.  The conditions necessary for both local and global asymptotic stability of equilibrium points were determined. Sensitivity analysis of the  R0 was investigated using partial differentiation and then confirmed using normalized sensitivity analysis. Simulations were carried out using MATLAB ODE 45 inbuilt solver. Sensitivity analysis results revealed that the  R0 was directly proportional to the rate of quitting from addict to light user but inversely proportional to the rate of quitting from light user to susceptible. Therefore the rate of individuals moving from light user class to susceptible classes has higher impact on reducing the burden of miraa addiction than the rate of individuals moving from addict to light user. This study used theoretical data and parameters, future studies should consider fitting model to real data. The findings of this study will provide the stake holders including the government, NACADA, rehabilitation centres and general public with information of the spread of the addiction so that necessary measures may be taken to address the challenges. The model can find application in predicting future trends which is necessary for planning.  Control strategies can be instituted with the help of the model.

Open Access Original Research Article

Predictive Estimator for Simple Regression

Kunio Takezawa

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/JAMCS/2017/35869

The predictive estimator of the gradient in simple regression is assumed to be the product of the gradient given by least-squares fitting and a constant (ρ). The results of numerical simulations show that when generalized cross-validation is used to obtain the optimal ρ, the resultant predictive estimator is not of great use. However, when the parametric bootstrap method is applied for this purpose, the resulting predictive estimator is often superior to the maximum likelihood estimator in terms of prediction accuracy. Therefore, statistics reflecting the characteristics of data should be used to determine which estimator should be adopted.

Open Access Original Research Article

Open Access Original Research Article

Super Convergence Method for Solution of Higher Order Boundary Value Problems

Sh. Sharifi, J. Rashidinia

Journal of Advances in Mathematics and Computer Science, Page 1-24
DOI: 10.9734/JAMCS/2017/35804

A new O(h10) super convergence method based on B-spline of degree eight has been developed for solution of higher order boundary value problems. Our presented collocation method leads to optimal approximation, we describe the mathematical procedure in detail also analyze the convergence of the method. The obtained numerical results have been compared with results obtained by recent existing methods to verify the applicability and super convergence properties of the presented method numerically.

Open Access Original Research Article

Chiral Structure of Particles Bound by Magnetic Forces

Hans-Peter Morsch, Sudeep Ghosh

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/JAMCS/2017/35743

Aims/ objectives: Particle bound states exist only as microscopic systems in form of atomic and subatomic particles. An interesting class of these objects are particles bound by magnetic forces, which exhibit the particular property of chirality (handedness, which is not parity symmetric). These particles are discussed in quantum field theory based on a QED like Lagrangian with fermion and boson fields, in which about ten boundary conditions can be defined. With four (but effectively two) adjustable parameters only, this leads to a stringent test of the special mathematical structure of the underlying eld theory.

A first kind of these particles are leptons, e, μ, τ and neutrinos. With an additional quantum condition the radii of charged leptons can be deduced. Other systems of magnetic binding may be found in atoms, a first example being weakly bound H-atoms, which may be the origin of gravitation.