iosr-Jm   Volume-20 ~ Issue-1 ~ Jan. – Feb. 2024

Abstract : The article is a review work of the strong Liouville's theorem based conjecture on nonelementary integrals using computer software Mathematica. The fast growing applications of computer software has opened a new scope of research in Mathematics and its allied sciences. It is being used in justifying theorems, conjectures, properties, examples and applications in many fields of sciences, arts and commerce. Mathematica provides the best computational techniques, which works like a calculator and solve many problems of mathematics in a single step. Its direct use makes the work easier and time saving. In the present paper, the proof of the conjecture on nonelementary integrals has been justified by applying.....

Keywords: Conjecture, Elementary Integral, Elementary Function, Nonelementary Integral, Nonelementary Function, Hypergeometric Function, Mathematica.

[1]. Abbott, P. (1997). Teaching Mathematics Using Mathematica. In Proceedings Of The 2nd Asian Technology Conference In Mathematics (Pp. 24-40). [2]. Abell, M. L., & Braselton, J. P. (2021). Mathematica By Example. Academic Press.
[3]. Chaudhary, M. K. & Yadav, D. K. (2024). Strong's Liouville Theorem Based Conjecture On Nonelementary Integrals, IOSR Journal Of Mathematics (IOSR-JM), 20 (1), Ser.1 (Jan. – Feb.), 35-44.
[4]. Fitelson, B. (1998). Using Mathematica To Understand The Computer Proof Of The Robbins Conjecture. Mathematica In Education And Research, 7, 17-26. [5]. Hardy, G. H. (2018). The Integration Of Functions Of A Single Variable, Hawk Press, 1-12.

Abstract : In this paper the concept of perfect codes to Quadratic Residue Cayley graph modulo an odd prime p, is introduced. Let p be an odd prime & let S be the set of quadratic residue modulo p. Consider.....

Keywords: Cayley Graph, Quadratic residue Cayley Graph, Symmetric set, Perfect code

[1]. P. Berrizbeitia And R.E. Giudici, Counting Pure K -Cycles In Sequences Of
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[3]. P. Berrizbeitia And R.E. Giudici, On Cycles In The Sequences Unitary Cayley
[4]. Graphs, To Appear. (Reporte Techico No.01–95, Universidad Simon Bolovar, Dpto. De Mathematicas, Caracas, Venezuela,1995)
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Abstract : This paper is a response of three articles: Saaty and Vargas, [published in International Journal of Management and Decision Making, 2006, 180], Liberatore and Nydick [published in Computers & Operations Research, 2004, 889], and Finan and Hurley [published in Computers & Operations Research, 2002, 1025]. Finan and Hurley (2002) claimed that their paper forms a serious challenge to Analytic Hierarchy Process. Saaty and Vargas (2006), and Liberatore and Nydick (2004) both pointed out that after wash criterion being deleted, then the weights for the upper level criteria should be re-evaluated. We provide a patch work for re-evaluation to show that the four level hierarchy decision....

Keywords: Analytic Hierarchy Process; Wash Criteria

[1]. Finan Js, Hurley Wj. The Analytic Hierarchy Process: Can Wash Criteria Be Ignored? Computers & Operations Research 2002;29:1025-30.
[2]. Liberatore Mj, Nydick Rl. Wash Criteria And The Analytic Hierarchy Process. Computers & Operations Research 2004;31:889-92.
[3]. Lin Jsj, Chou Sy, Chouhuang Wt, Hsu Cp, Note On ''Wash Criterion In Analytic Hierarchy Process''. European Journal Of Operational Research 2008;185: 444–447.
[4]. Saaty Tl, Vargas Lg. 2006. The Analytic Hierarchy Process: Wash Criteria Should Not Be Ignored. International Journal Of Management And Decision Making 2006;7:180-8.
[5]. Yao Jff, Yao Js. 2001. Fuzzy Decision Making For Medical Diagnosis Based On Fuzzy Number And Compositional Rule Of Inference. Fuzzy Sets And Systems 2001;120:351-66.

Abstract : Background: Despite the importance of good wealth and financial planning for the future, Malaysians' decisions to save money aside for their retirement are still a big issue. The uncertainty and unawareness of future risks such as inflation, income instability, and critical illness may lead to this decision. It is believed that a person's behaviour or reaction to money influences their decision to save for retirement. One's love of money, money anxiety, number of desires, or materialistic inclinations are just a few examples of how one's view towards money might be converted into subjective and emotional functions. As a result, each person views and behaves differently toward money and....

Keywords: Retirement, Saving Decisions, Money Attitudes, B40 Groups, Empirical Analyses

[1]. Shariff, N. S. M., Isah, N. A. M.: An Empirical Study On The Determinants Of Retirement Savings Attitude In Malaysia. Journal Of Physics: Conference Series, 1366 012110 (2019).
[2]. Nardi, M. De., French, E., Jones, J. B.: Saving After Retirement: A Survey. Annual Review Of Economics. 8, 177-204 (2016).
[3]. Mahdzan, N. S., Tabiani, S.: The Impact Of Financial Literacy On Individual Saving: An Exploratory Study In The Malaysian. Transformations In Business & Economics 12(1), 41-55 (2013).
[4]. Mansor, M. F., Hong, C. C., Abu, N. H., Shaari, M. S.: Demographic Factors Associated With Retirement Planning: A Study Of Employees In Malaysian Health Sectors. Asian Social Science 11(13), 108-116 (2015).
[5]. Talib, N. F. M., Manaf, H. A.: Attitude Towards Retirement Planning Behaviour Among Employees. Journal Of Business And Management 1(1), 15-21 (2017).

Abstract : An infectious viral disease called dengue fever (DF) is prevalent in urban and peri-urban areas of the tropics and subtropics. This disease continues to be a threat to global public health. In this study, a dengue virus transmission based on an equation system for ordinary differentials was developed to study the dynamics of DF as a measure to prevent epidemics in Kenya, quarantines during treatment and health education are used to prevent transmission. The next generation matrix approach determines the effective basic reproduction number (Ro). The model's equilibrium.....

Keywords: dengue fever, basic reproduction number, stability analysis, numerical stimulation

[1]. Abdiaziz Abdirashid (2021), Mathematical Model For The Dynamics Of Dengue Virus Disease Transmission In Mandera County In Kenya.
[2]. Afeez Adidemi, Nur Arina Bazilah Aziz. (2020); Optimal Control Strategies For Dengue Fever Spread In Johor Malaysia Computer Methods And Programs In Biomedicine.
[3]. Almutairi Km: Culture And Language Differences As A Barrier To Provision Of Quality Care By Health Workforce In Saudi Arabia. Saudi Med J.2015, 36:425, 31.10.15537/Smj.2015.4.10133
[4]. Dengue And Severe Dengue, World Health Organization 2020:
Https://Www.Who.Int/En/News- Room/Fact-Sheets/Detail/Dengue-And-Severe-Dengue.
[5]. Edith Chepkorir, Joel Lutomiah, James Mutisya, Francis Mulwa, Konongoi Limbaso, Benedict Orindi, Zipporah Ng'ang'a And Rosemary Sang Et Al. Vector Competence Of Aedes Aegypti Populations From Kilifi And Nairobi For Dengue 2 Virus And The Influence Of Temperature.,7(1); 1-8, 2014.

Abstract : The present paper investigates the effect of angular rotation of the solid on Rayleigh surface waves in a homogeneous, isotropic initially stressed Voigt-type viscoelastic layer in its gravity field. After solving the basic equations with harmonic solution method, the dispersion relations for initially stressed viscoelastic layer and free layer are derived in rotating solid in its gravity field. Symmetric and anti-symmetric modes of Raleigh waves are studied in the special cases. Rayleigh waves in symmetric modes are independent of gravity and influenced.....

Keywords: Rayleigh Wave; Rotation; Gravity; Voigt-type; Initial stress; Viscoelastic layer.

[1]. Ewing, W.M., Jardetzky, W.S. And Press, F, "Elastic Waves In Layered Media", Mc Graw-Hill,Newyark,(1957).
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[3]. Ezzin, H., Amor, M.B. And Ghozlen, M.H.B., "Propagation Behaviour Of Sh Waves In Layered Piezoelectric/Piezomagnetic Plates", Acta Mathematica 228(3), (2017), Pp.1071-1081.
[4]. Zhao, X., Qian, Z.H., Zhang, S. And Lui. J. X., "Effect Of Initial Stress On Propagation Behaviors Of Shear Horizontal Waves In Piezoelectric/Piezomagnetic Layered Cylinders",Ultrasonics, 63, (2015), Pp.47-53.
[5]. Kolahchi, R., "A Comparative Study On The Bending, Vibration And Bucking Of Viscoelastic Sandwich Nano-Plates Based On Different Nonlocal Theories Using Dc, Hdq And Dq Methods", Aerospace Science And Technology, 66, (2017), Pp.235-248..

Abstract : This research work investigates the nonlinear dissemination of electrostatic ion acoustic solitary waves (IASWs) for weakly relativistic regime by considering the thermal ions speed is comparable with the speed of light and degenerates electrons, positrons. It is assumed that the densities of electrons and positrons follow the Fermi law. The Korteweg-de Varies (KdV) equation is derived to analyze the solation solution for both cases of ultra-relativistic and non-relativistic degenerated electrons and positrons by using the well known reductive perturbation technique. It is the angsts method which is employed to carry out the integration of this equation. The amplitude,.....

Keywords: Electrostatic propagations; Solution; Fermi-type electrons and positrons; The angsts method.

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Abstract : A two-dimensional natural convection flow of a viscous incompressible and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equations by introducing appropriate coordinate transformations. We have solved that ordinary differential equations and we have shown the velocity profiles, temperature profile, the skin friction.

Keywords:velocity profiles, temperature profile, the skin friction, nusselt number, Grashof number (Gr), Hartmann number (M), Prandtl number(Pr).

[1]. Acheson, D. J., Elementary Fluid Dynamics. Clarendon Press.ISBN 0 19 859679 0, (1990).
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[4]. Andersson, H. I., An Exact Solution oF THe Navier-Stokes Equations fOr Magnetohydrodynamic Flow, Acta Mechanica, 113, 241-244 (1995).
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Abstract : This article presents the numerical approximations for solving singularly perturbed parabolic convection- diffusion problems (SPPCDP) with discontinuous initial conditions. The scheme uses backward- Euler for temporal derivatives on a uniform mesh and classical upwind finite difference for spatial derivatives on a piecewise-uniform (Shishkin) mesh. This scheme provides almost a first-order con- vergence solution in space and time variables. The method employs an upwind finite difference operator on a piecewise....

Keywords: Singularly perturbed parabolic convection-diffusion problems, Upwind finite difference scheme

[1] L. BOBISUD, Parabolic Equations With A Small Parameter And Discontinuous Data, Journal Of Mathematical Analysis And Applications, 26 (1969), Pp. 208–220.
[2] C. CLAVERO, J. GRACIA, AND J. JORGE, High-Order Numerical Methods For One-Dimensional Parabolic Singularly Perturbed Problems With Regular Layers, Numerical Methods For Partial Differential Equations: An International Journal, 21 (2005), Pp. 149–169.
[3] C. CLAVERO, J. L. GRACIA, AND F. LISBONA, High Order Methods On Shishkin Meshes For Singular Perturbation Problems Of Convection–Diffusion Type, Numerical Algorithms, 22 (1999), Pp. 73–97.
[4] C. CLAVERO, J. L. GRACIA, G. I. SHISHKIN, AND L. P. SHISHKINA, An Efficient Numerical Scheme For 1d Parabolic Singularly Perturbed Problems With An Interior And Boundary Layers, Journal Of Computational And Applied Mathematics, 318 (2017), Pp. 634–645

Abstract : The present paper is a review work of the Laplace's theorem based conjecture on elementary integrals using advanced computer software Mathematica. The introduction of many computer software and its applications in Mathematics and allied sciences has replaced the research methodology from traditional theoretic processes to computational techniques. Previously to find antiderivative, a lengthy process were followed but now the computer software programming languages and technique find that in a second by using their predefined codes. So it now saves both time and energy. The software Mathematica is such a tool providing technique which is used in many.....

Keywords: Conjecture, Elementary Function, Elementary Integral, Nonelementary Function, Nonelementary Integral, Mathematica Software.

[1]. Abbott, P. (1997). Teaching Mathematics Using Mathematica. In Proceedings Of The 2nd Asian Technology Conference In Mathematics (Pp. 24-40).
[2]. Abell, M. L., & Braselton, J. P. (2021). Mathematica By Example. Academic Press.
[3]. Chaudhary, M. K. & Yadav, D. K. (2024). Strong Liouville's Theorem Based Conjecture On Nonelementary Integrals, IOSR Journal Of Mathematics (IOSR-JM), 20 (1), Ser. 1 (Jan.-Feb.), 35-44.
[4]. Fitelson, B. (1998). Using Mathematica To Understand The Computer Proof Of The Robbins Conjecture. Mathematica In Education And Research, 7, 17-26.
[5]. Hardy, G. H. (2018). The Integration Of Functions Of A Single Variable, Hawk Press, 1-12..