On Markov Moment Problem and Related Inverse Problems | Chapter 11 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Octav Olteanu
Department of Mathematics-Informatics, Politehnica University of Bucharest, Splaiul Independenței 313, 060042 Bucharest, Romania.

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Regularization Methods for Solving Ill-Posed Problems | Chapter 10 | Advances in Mathematics and Computer Science Vol. 3

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

Author(s) Details

Dr. Benedict Barnes
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

Dr. Francis Ohene Boateng (Ph.D.)
Department of Mathematics Education, University of Education, Winneba, Kumasi, Ghana.

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Parabolic Transform and Some Ill-posed Problems | Chapter 09 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Professor Mahmoud M. El-Borai
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt.

Professor Khairia El-said El-Nadi
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt.

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Numerical Solution to Effect of Chemical Reaction on a Casson Fluid Flow over a Vertical Porous Surface | Chapter 08 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Hymavathi Talla
Department of Mathematics, Krishna University Dr. MRAR PG Centre, Nuzvid, A.P., 521201, India

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Investor’s Power Utility Optimization with Consumption, Tax, Dividend and Transaction Cost under Constant Elasticity of Variance Model | Chapter 07 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Silas A. Ihedioha
Department of Mathematics, Plateau State University, Bokkos, P.M.B. 2012, Jos, Plateau State, Nigeria.

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Study of Gegenbauer Matrix Polynomials Via Matrix Functions and their Properties | Chapter 06 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Dr. Virender Singh
Department of Applied Mathematics, Galgotia college of Engineering and Technology, Greater Noida{201306, India.

Dr. Archna Sharma
SOVSAS Department of Applied Mathematics, Gautam Buddha University, Greater Noida{201312, India.

Prof. Mumtaz Ahmad Khan
Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh{202002, India.

Prof. Abdul Hakim Khan
Department of Applied Mathematics, Faculty of Engineering and Technology, Aligarh Muslim University, Aligarh{202002, India.

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On the Local and Global stability analysis for the Typhoid Fever Disease incorporating Protection against Infection | Chapter 05 | Advances in Mathematics and Computer Science Vol. 3

A mathematical model for typhoid fever disease incorporating protection against infection is hereby analyzed. Specifically, 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.

Author(s) Details

Dr. Joyce Kagendo Nthiiri
Lecturer and Chairperson, Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.

Dr. George Owuor Lawi
Senior lecturer, Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.

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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 | Chapter 04 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

Hymavathi Talla
Department of Mathematics, Krishna University Dr.MRAR PG Centre, Nuzvid, A.P., 521201, India.

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Vibrational Spectra of Linear Molecule: Carbonyl Sulphide | Chapter 03 | Advances in Mathematics and Computer Science Vol. 3

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.

Author(s) Details

J. Vijayasekhar
Department of Mathematics, School of Science, GITAM Deemed to be University, Hyderabad, India.

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Information Distances and Divergences for the Generalized Normal Distribution | Chapter 02 | Advances in Mathematics and Computer Science Vol. 3

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

Author(s) Details

Thomas L. Toulias
University of West Attica, Ag. Spyridonos Str. 28 (Campus 1), 12243 Egaleo, Athens, Greece.

Christos P. Kitsos
University of West Attica, Ag. Spyridonos Str. 28 (Campus 1), 12243 Egaleo, Athens, Greece.

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