Advances in Mathematics and Computer Science Vol. 3

A Numerical Study of Turbulent Natural Convection in a Square Enclosure Using a Two Equation Model

Mutili Peter Mutisya, Awuor Kennedy Otieno — Wed, 23 Oct 2019 00:00:00 +0000

In this study the performance of one numerical turbulence model, is accessed. In predicting heat transfer due to natural convection inside an air-filled square cavity. Turbulent natural convection in an enclosure plays an important role in the field of heat transfer and buildings environment. Natural turbulent convection is square air cavities having isothermal vertical and highly heat – conducting horizontal walls are compared with the experimental data obtained for these cavities at a varying Rayleigh numbers, 1.8 x 10⁹, 1.44 x 10¹⁰ and 1.15 x 10¹¹. In carrying out numerical investigations, a two – dimensional, low turbulence, two – parameter model known as the Low – Reynolds – number turbulence model was used. The vorticity – vector potential formulation was used to eliminate the need to solve the pressure terms. The vorticity, vector potential energy and two – equation model with their boundary conditions were solved using finite difference approximations. The results of the investigation are presented for the distribution of the velocity and temperature components. The non – linear terms and in the averaged momentum and energy equations respectively are modelled using the model to close the governing equations. The cavity is maintained at 313K on the hot wall and 293K on the opposite cold wall. The horizontal walls are adiabatic. The results obtained show that as the Rayleigh number increases, the values of the stream function increases. As the Rayleigh number increases, uniform distribution of heat inside the cavity is achieved.

Information Distances and Divergences for the Generalized Normal Distribution

T. L. Toulias, C. P. Kitsos — Wed, 23 Oct 2019 00:00:00 +0000

The study of relative measures of information between two distributions that characterizes an Input/Output System is important for the investigation of the informational ability and behaviour of that system. The most important measures of information distance and divergence are brieﬂy presented and grouped. In Statistical Geometry, and for the study of statistical manifolds, relative measures of information are needed that are also distance metrics. The Hellinger distance metric is studied, providing a “compact” measure of informational “proximity” between of two distributions. Certain formulations of the Hellinger distance between two generalized normal distributions are given and discussed. Some results for the Bhattacharyya distance are also given. Moreover, the symmetricity of the Kullback-Leibler divergence between a generalized normal and a t -distribution, is examined for this key measure of information divergence.

Vibrational Spectra of Linear Molecule: Carbonyl Sulphide

J. Vijayasekhar — Wed, 23 Oct 2019 00:00:00 +0000

In this chapter, vibrational spectra of Carbonyl sulphide (OCS) in fundamental level and at higher overtones calculated by Lie algebraic method. In this method Hamiltonian expressed in terms of invariant and Majorana operators, describe stretching vibrational frequencies. The Hamiltonian is an algebraic one and so far all the operations in this one dimensional Lie algebraic method, unlike the more well-known differential operators of wave mechanics.

Homotopy Analysis Method to Heat and Mass Transfer in Visco-Elastic Fluid Flow through Porous Medium over Exponential Stretching Sheet with Radiation and Chemical Reaction

Hymavathi Talla — Wed, 23 Oct 2019 00:00:00 +0000

This paper elucidates the radiation and chemical reaction in heat and mass transfer of steady incompressible visco- elastic fluid flow over an exponentially stretching sheet through porous medium. The flow and heat transfer governing equations are partial differential equations and are converted into nonlinear ordinary differential equation by using suitable similarity transformations. The converted non linear ordinary differential equations are solved analytically by Homotopy Analysis Method (HAM), which provides a convergent solution with the help of control and convergence non-zero auxiliary parameter ћ. The effect of Prandtl number, Eckert number, Reaction parameter and Schmidt number on temperature and concentration are represented through graphically. The obtained results are compared with existing results in the literature and seen in good agreement.

On the Local and Global stability analysis for the Typhoid Fever Disease incorporating Protection against Infection

J. K. Nthiiri, G. O. Lawi — Wed, 23 Oct 2019 00:00:00 +0000

A mathematical model for typhoid fever disease incorporating protection against infection is hereby analyzed. Specically, local and global Stability analysis of the model are carried out to determine the conditions that favour the spread of the disease in a given population. Numerical simulation of the model carried showed that an increase in protection leads to low disease prevalence in a population.

Study of Gegenbauer Matrix Polynomials Via Matrix Functions and their Properties

Virender Singh, Archna Sharma, Mumtaz Ahmad Khan, Abdul Hakim Khan — Wed, 23 Oct 2019 00:00:00 +0000

The present paper deals with a new kind of Gegenbauer matrix polynomials and some special cases. The paper contains a three term matrix recurrence relation, hypergeometric representation, their Rodrigues formula and orthogonal properties.

Investor’s Power Utility Optimization with Consumption, Tax, Dividend and Transaction Cost under Constant Elasticity of Variance Model

Silas A. Ihedioha — Wed, 23 Oct 2019 00:00:00 +0000

This work considered an investor’s portfolio where consumption, taxes, transaction costs and dividends are in involved, under constant elasticity of variance (CEV). The stock price is assumed to be governed by a constant elasticity of variance CEV model and the goal is to maximize the expected utility of consumption and terminal wealth where the investor has a power utility preference. The application of dynamic programming principles, specifically the maximum principle obtained the Hamilton-Jacobi-Bellman (HJB) equation for the value function on which elimination of variable dependency was applied to obtain the close form solution of the optimal investment and consumption strategies. It is found that optimal investment on the risky asset is horizon dependent.

Numerical Solution to Effect of Chemical Reaction on a Casson Fluid Flow over a Vertical Porous Surface

Hymavathi Talla — Wed, 23 Oct 2019 00:00:00 +0000

In this chapter we study the effect of chemical reaction by considering the flow of a casson fluid which is having lot of importance. The fluid flow is over a vertical porous surface. The governing partial differential equations are converted into ordinary differential equations by using similarity transformations. The reduced system of equations is then solved using an implicit FDM known as the Keller Box method. The velocity and concentration profiles are examined for various changes in the different governing parameters like the Casson parameter, suction parameter, Grashof number and the Schmidt number.

Parabolic Transform and Some Ill-posed Problems

Mahmoud M. El-Borai, Khairia El-said El-Nadi — Wed, 23 Oct 2019 00:00:00 +0000

A new transform is constructed, which is called parabolic. By using this transform, existence and stability results can be obtained for singular integro-partial differential equations and also for stochastic ill-posed problems. It is well known that the cauchy problem for elliptic partial differential equations is ill-posed. The question, which arises, how a priori knowledge about solutions and the set of initial conditions can bring about stability? With the help of the parabolic tranform, we can study, not only elliptic partial differential equations, but also a general stochastic partial differential equations and singular integro-partial differential equations without any restrictions on the charachtrestic forms of the partial differential operators. The cauchy problem of fractional general partial differential equations can be considered as a special case from the obtained results. In addition, Hilfer fractional differential equations can be solved also without any restrictions on the charachtrestic forms. Many physical and engineering problems in areas like biology, seismology, and geophysics require the solutions of ill-posed stochastic problems and general singular integro-partial differential equations.

Regularization Methods for Solving Ill-Posed Problems

Benedict Barnes, Francis Ohene Boateng — Wed, 23 Oct 2019 00:00:00 +0000

This chapter of the book present recent regularization methods for solving ill-posed equations.

On Markov Moment Problem and Related Inverse Problems

Octav Olteanu — Wed, 23 Oct 2019 00:00:00 +0000

Existence and construction of the solutions of some Markov moment problems are discussed. Starting from the moments of a solution, one recalls a method of recovering this solution, also solving approximately related systems with infinite many nonlinear equations and infinite unknowns. This is the first aim of this review paper. Extension of linear forms with two constraints is applied. Measure theory arguments play a central role. Other results in analysis and functional analysis are used tacitly, sending the reader to the references for unproved stated theorems. Secondly, in the end, existence of solutions of special Markov moment problems is studied.