Open Access Original Research Article

Population Dynamics in Optimally Controlled Economic Growth Models: Case of Cobb-Douglas Production Function

S. Opuni-Basoa, F. T. Oduro, G. A. Okyere

Journal of Advances in Mathematics and Computer Science, Page 1-24
DOI: 10.9734/JAMCS/2017/36753

In this paper, we discuss optimally controlled economic growth models with Cobb-Douglas aggregate production function, comparing real per capita income performance in scenarios where the labour (population) growth dynamics range from purely exponential to strongly logistic. The paper seeks to ascertain, by means of analytical and qualitative methods, as well as numerical simulations, the causal factors and parameters, especially population related ones, which induce qualitative changes in the performance of real per capita income. The models use consumption per effective labour as their control variable, and capital per effective labour as the state variable. Income per effective labour is here used as the output variable. A time-discounted welfare functional is used as the objective functional, maximized subject to a differential equation in the state and control variables. Each system is found to be stable in the neighbourhood of its non-trivial critical value. The models are both locally controllable and observable. The models’ simulation values, in control, state and output, appear plausible and consistent with reality. It is found out that under R & D technological process, economies with exponential population growth consistently out-perform those with logistic population growth. On the contrary, in all other instances, economies with exponential population growth consistently perform worse than those with logistic population growth. These findings have far reaching inferences with regard to the running of economies.

Open Access Original Research Article

High Order Resolution in Reentry Flows in 3D

Edisson Sávio de Góes Maciel, Cláudia Regina de Andrade

Journal of Advances in Mathematics and Computer Science, Page 1-32
DOI: 10.9734/JAMCS/2017/36897

This work focuses on a numerical simulation of reentry 3D-flows using high order resolution schemes. Euler and Navier-Stokes equations are studied, on conservative and finite volume approaches, and employing structured spatial discretization. The ENO (Essentially Non-Oscillatory) procedure is presented to a conserved variable interpolation process, using either the Newton method, to second-, third-, fourth- and fifth-orders of accuracy, or the Hermite method, to third- and fifth-orders of accuracy. Furthermore, the WENO (Weighted Essentially Non-Oscillatory) procedure is also tested, using the Newton interpolation process, to generate third- and fifth-orders of accuracy solutions. Results applying the MUSCL scheme (Monotone Upstream-centered Schemes for Conservation Laws) are also presented and serve as TVD (Total Variation Diminishing) benchmark purpose. In this context, the “hot gas” hypersonic thermochemical non-equilibrium 3D-flow around a blunt body has been simulated. The convergence process is accelerated to steady-state condition through a spatially variable time step procedure, which has proved effective gains in terms of computational acceleration. The reactive simulations involve Earth atmosphere chemical models of five and seven species, based on the Saxena and Nair and Blottner models, respectively. Results showed that the ENO procedure using Newton 5th-order interpolation scheme presents better overall solutions.

Open Access Original Research Article

Comparison among Unstructured TVD, ENO and UNO Schemes in Two-dimensions

Edisson Sávio de Góes Maciel, Cláudia Regina de Andrade

Journal of Advances in Mathematics and Computer Science, Page 1-31
DOI: 10.9734/JAMCS/2017/36902

In this work, unstructured TVD, ENO and UNO schemes are applied to solve the Euler equations in two-dimensions. They are implemented on a finite volume context and cell centered data base. The algorithms of Yee, Warming and Harten 1982; Harten; Yee and Kutler; Yee Warming and Harten 1985; Yee; Yee and Harten; Harten and Osher; Yang; Hughson and Beran; and Yang and Hsu are implemented to solve such system of equations in two-dimensions. All schemes are flux difference splitting and good resolution is expected. This study deals with calorically perfect gas model and in so on the cold gas formulation is employed. Two problems are studied, namely: the transonic convergent-divergent symmetrical nozzle, and the supersonic ramp. A spatially variable time step is implemented to accelerate the convergence process. The results highlights the excellent performance of the Yang TVD scheme, yielding an excellent pressure distribution at the nozzle wall, whereas the Harten and Osher scheme yields accurate values to the angle of the oblique shock wave and the best wall pressure distributions in the ramp problem.

Open Access Original Research Article

Novel Technique for Utilizing Analogue Video Signal for IRFPA Raw Data Transfer for Calibration Purposes

Abdulaziz Mohammed Algamdi, Ahmad Abbas Ahmad Adas

Journal of Advances in Mathematics and Computer Science, Page 1-13
DOI: 10.9734/JAMCS/2017/37067

Infrared focal plane array (IRFPA) is a bi-dimensional array of micro scaled infrared detectors which become essential sensing devices in a wide range of applications. Due to the need for mobility and power saving, new uncooled IRFPA’s have become more suitable to substitute cooled IRFPA in many applications that require lighter weight and lower power consumption. Electronic Designers aim to reduce power consumption by integrating circuits inside high-density chips, invent new solid state components which consume less power and eliminate excess components when they are rare to use. This paper focuses on eliminating high speed digital data link channel from low profile portable IR camera and instead of that, it proposes manipulating bit arrangements by video processing unit to overcome video signal major issues like noise, clipping, and pixel resolution.

Open Access Review Article

Estimation in Step-stress Partially Accelerated Life Test for Exponentiated Pareto Distribution under Progressive Censoring with Random Removal

Amal S. Hassan, Marwa Abd-Allah, Hamdy G. A. El-Elaa

Journal of Advances in Mathematics and Computer Science, Page 1-16
DOI: 10.9734/JAMCS/2017/34691

Accelerated life testing or partially accelerated life testing is generally used in manufacturing industries since it affords significant minimization in the cost and test time. In this paper, a step-stress partially accelerated life test under progressive type-II censoring with random removals is considered. The lifetime of testing items under use condition follow the exponentiated Pareto distribution and the removals from the test are assumed to have binomial distribution. Maximum likelihood estimators for the model parameters and acceleration factor are obtained. Approximate confidence intervals for the parameters are formed via the normal approximation to the asymptotic distribution of maximum likelihood estimators. Simulation study is carried out to investigate the performance of estimators for different parameters values and sample size.