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Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
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Volume 6 Issue 1 January - March 2017

Research Paper

Triology: A Novel, Innovative, and in–Depth Science Concerned with the Mathematical Triadic, Tripartite, and Triplex Components, Content, and Cycles of Life, Learning, Logic, and the Universal Aspects of Nature

James Edward Osler II*

Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.

Osler, J. E., II. (2017). Triology: A Novel, Innovative, and in–Depth Science Concerned with the Mathematical Triadic, Tripartite, and Triplex Components, Content, and Cycles of Life, Learning, Logic, and the Universal Aspects of Nature. i-manager’s Journal on Mathematics, 6(1), 1-17. https://doi.org/10.26634/jmat.6.1.11398

Abstract

This monograph provides an epistemological rational for a novel science grounded in trichotomous statistical analysis metrics. Triology is the study of the trifold nature of phenomena. It has its foundation in the mathematical “Law of Trichotomy”. Triology is measured using the Tri–Squared Statistic. Advanced post hoc measurement of Triology is conducted using Triostatistics (or more simply “Triostat”) is the application of Post Hoc measures to the statistically significant outcomes of the Trichotomous Squared Test. Triology involves a variety of concepts that are defined using robust and rigorous calculations provided in this paper. It uses its computations to provide further insight on the inner workings of the threefold aspects of nature. The topology and taxonomy of the triology are covered in detail along with Tri–Squared and Triostatistics procedures.

References

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[2]. Kant, I., (2007). Critique of Pure Reason (based on Max Müller's Translation). P. Classics a Division of Pearson PLC. New York, NY

[3]. Osler, J.E., (2010). Visualus™ © Visioneering Volumetrically: The Mathematics of the Innovative Problem–Solving Model of Inventive Instructional Design (First edition). OSI: Publishing Division. Lulu, Morrisville NC.

[4]. Osler, J.E., (2012). “Trichotomy – Squared – A novel mixed methods test and research procedure designed to analyze, transform, and compare qualitative and quantitative data for education scientists who are administrators, practitioners, teachers, and technologists”. i-manager's Journal on Mathematics, Vol.1, No.3, pp.23–31, ISSN Print: 2277-5129, ISSN Online: 2277-5137.

[5]. Osler, J.E., and Waden, C., (2012). “Using innovative technical solutions as an intervention for at risk students: A meta–cognitive statistical analysis to determine the impact of ninth grade freshman academies, centers, and center models upon minority student retention and achievement”. i-manager's Journal on School Educational Technology, Vol.7, No.3, pp.11–23, ISSN Print: 0973-2217, ISSN Online: 2230-7133.

[6]. Osler, J.E., (2013a). “Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining the Application Process of the Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.2, No.2, pp.10–16, ISSN Print: 2277-5129, ISSN Online: 2277-5137.

[7]. Osler, J.E., (2013b). “The Triangulation Algorithmic: A Transformative Function for Designing and Deploying Effective Educational Technology Assessment Instruments”. i-manager's Journal of Educational Technology, Vol.10, No.1, pp.46–54, , ISSN Print: 0973-0559, ISSN Online: 2230-7125.

[8]. Osler, J.E., (2013c). “Transformational Research Engineering: Research Design Metrics for In–Depth and Empowering K–12 Teacher Professional Development”. i-manager's Journal on School Educational Technology, Vol.9, No.1, pp.43–60, ISSN Print: 0973-2217, ISSN Online: 2230-7133.

[9]. Osler, J.E., (2013d). “The Psychometrics of Educational Science: Designing Trichotomous Inventive Investigative Instruments for Qualitative and Quantitative for Inquiry”. i-manager's Journal on Educational Psychology, Vol.8, No.3, pp.15–22, ISSN Print: 0973-8827, ISSN Online: 2230-7141.

[10]. Osler, J.E., (2013e). “The Psychological Efficacy of Education as a Science through Personal, Professional, and Contextual Inquiry of the Affective Learning Domain”. i-manager's Journal on Educational Psychology, Vol.6, No.4, pp.36–41, ISSN Print: 0973-8827, ISSN Online: 2230-7141.

[11]. Osler, J.E., (2013f). “Tri–Squared Mean Cross Comparative Analysis: An Advanced Post Hoc Qualitative and Quantitative Metric for a More In–Depth Examination of the Initial Research Outcomes of the Tri–Square Test”. i-manager's Journal of Educational Technology, Vol.10, No.3, pp.35–41, ISSN Print: 0973-0559, ISSN Online: 2230-7125.

[12]. Osler, J.E., (2014a). “Triostatistics: The Application of Innovative In–Depth Advanced Post Hoc Statistical Metrics for the Assessment and Analysis of Statistically Significant Tri–Squared Test Outcomes”. Kentucky Journal of Excellence in College Teaching and Learning, Vol.12, No.3, pp.27–39.

[13]. Osler, J.E., (2014b). “Introducing TRINOVA: ‘Trichotomous Nomo graphical Variance’ A Post Hoc Advanced Statistical Test of Between and within Group Variances of Trichotomous Categorical and Outcome Variables of a Significant Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.3, No.4, pp.1–14, ISSN Print: 2277-5129, ISSN Online: 2277-5137.

[14]. Osler, J.E., (2014c). “Trichotomous Progression Analysis: An Advanced Comprehensive Statistical Post Hoc Measure of the Tri–Squared Test”. i-manager's Journal on Mathematics, Vol.3, No.3, pp.7–20, ISSN Print: 2277-5129, ISSN Online: 2277- 5137.

[15]. Osler, J.E., (2014d). “The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test designed to Statistically determine Construct Validity”. i-manager's Journal on Mathematics, Vol.3, No.2, pp.27–35, ISSN Print: 2277-5129, ISSN Online: 2277- 5137.

[16]. Osler, J.E., (2014e). “Tri–Center Analysis: Determining Measures of Trichotomous Central Tendency for the Parametric Analysis of Tri–Squared Test Results”. i-manager's Journal of Educational Technology, Vol.11, No.1, pp. 23–30, ISSN Print: 0973- 0559, ISSN Online: 2230-7125.

[17]. Osler, J.E., (2014f). “Calculating Tri–Symmetrical Analytics: A Guide into the In–Depth Processes associated with the Post Hoc Advanced Statistical Metrics used to determine the Value of Significant Tri–Squared Tests”. i-manager's January– March Journal on Mathematics, Vol.3, No.1, pp.14–26, ISSN Print: 2277-5129, ISSN Online: 2277-5137

[18]. Osler, J.E., (2015a). “TRICOM: ‘Trichotomous Comparative Oneness of Measurement’ The Functional Analysis of Trichotomous Squared Single Case Research for the Application of the Tri–Squared Test to Single Subject Research Designs”. i-manager's Journal on Mathematics, Vol.4, No.2, pp.11–21, ISSN Print: 2277-5129, ISSN Online: 2277-5137.

[19]. Osler, J.E. (2015b). “Introducing MULTICOVA: ‘Multiple Trichotomous Coefficient of Variation Analysis’ The Advanced Post Hoc Test of the Tri–Squared Coefficient of Variation”. i-manager's Journal on Mathematics, Vol.4, No.1, pp.11–31, ISSN Print: 2277-5129, ISSN Online: 2277-5137 .

[20]. Rust, J., and Golombok, S., (1989). Modern Psychometrics: The Science of Psychological Assessment, (2^nd ed.). Florence, KY, US: Taylor & Frances/Routledge.

[21]. Sensagent, (2012). Trichotomy (Mathematics). Retrieved: http://dictionary.sensagent.com/trichotomy%20 (mathematics)/ en–en/

[22]. Singh, S., (1997). Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. A. Books - A Division of Random House. New York, NY.

[23]. Stevens, J.P. (2002). Applied Multivariate Statistics for the Social Sciences. Mahwah, NJ: Lawrence Erblaum.

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Research Paper

Convection Boundary Layer Flow and Heat Transfer in an Eyring - Powell Fluid Past a Horizontal Circular Cylinder in Porous Medium

L. Nagaraja* , A. Subba Rao, M. Sudhakar Reddy*, M. Suryanarayana Reddy****

* Research Scholar, Department of Mathematics, JNTU College of Engineering, Andhra Pradesh, India.

-* Assistant Professor, Department of Mathematics, Madanapalle Institute of Technology and Science, Andhra Pradesh, India.

**** Assistant Professor and Head, Department of Mathematics, JNTU College of Engineering, Andhra Pradesh, India.

Nagaraja, L., Rao, A.S., Reddy, M.S., and Reddy, M.S.N. (2017). Convection Boundary Layer Flow and Heat Transfer in an Eyring - Powell Fluid Past a Horizontal Circular Cylinder in Porous Medium. i-manager’s Journal on Mathematics, 6(1), 18-26. https://doi.org/10.26634/jmat.6.1.11399

Abstract

A mathematical model is developed to study laminar, nonlinear, non-isothermal, steady-state free convection boundary layer flow and heat transfer of a non-Newtonian Eyring - Powell fluid from a horizontal circular cylinder in porous media in the presence of a magnetic field. The transformed conservation equations for linear momentum, energy are solved numerically under physically viable boundary conditions using a finite difference scheme (Keller, Box method). The influence of dimensionless parameters, i.e. Eyring - Powell fluid parameter (ε), the local non-Newtonian parameter (δ), Prandtl number (Pr), dimensionless tangential coordinate (ξ), magnetic parameter (M), and temperature evaluation on velocity, temperature, skin friction, and Nusselt number are illustrated graphically, skin friction and Nusselt number are illustrated in tabular form. Validation of solutions with earlier published work is also included.

References

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[9]. Abdul Hakeem. A.K, Vishnu Ganesh., and N Ganga. B, (2015). “Heat transfer of non-Darcy MHD flow of nano-fluid over a stretching/shrinking surface in a thermally stratified medium with second order slip model”. Scientia Iranica F, Vol.22, No.6, pp.2766-2784.

[10]. Animasaun. I.L, Raju. C.S.K, and Sandeep. N, (2016). “Unequal diffusivities case of homogeneous–heterogeneous reactions within viscoelastic fluid flow in the presence of induced magnetic-field and nonlinear thermal radiation”. Alexandria Engineering Journal, Vol.55, No.2, pp.1595–1606.

[11]. Subba Rao. A, Ramachandra Prasad. V, Nagendra. N, Bhaskar Reddy. N, and Anwar Beg. O, (2016). “Non-Similar Computational Solution for Boundary Layer Flows of Non-Newtonian Fluid from an Inclined Plate with Thermal Slip”. Journal of Applied Fluid Mechanics, Vol.9, No.2, pp.795-807.

[12]. Bear, J., (1988). Dynamics of Fluids in Porous Media. Dover, New York.

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[20]. Zueco, J., and Anwar Bég. O, (2009). “Network simulation solutions for laminar radiating dissipative magneto-gas dynamic heat transfer over a wedge in non-Darcian porous regime”. Mathematical and Computer Modelling, Vol.50, No.3-4, pp.439-452.

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[22]. Bég, O.A., (2012b). “Numerical methods for multi-physical magneto hydrodynamics”. In Maximiano J. Ibragimov and Miroslava A. Anisimov Eds., New Developments in Hydrodynamics Research, Nova Science, New York, Ch. 1, pp. 1-110,

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[30]. Muhammad Raheel Mohyuddin, Jamshaid ul Rahman, Syed Zahoor, SV, and Amira, (2016). “Mathematical and Simulink Model for Paint Industry Effluent”. Journal of Engineering Chemistry and Fuel, Vol.1, No.2, pp.1-8.

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[33]. Muhammad R. Mohyuddin, and T. Gotz, (2005). “Resonance behavior of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field”. International Journal for Numerical Methods in Fluids, Vol.49, No.8,pp.837-847.

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Research Paper

Slip Effects of Viscous Dissipation on Steady MHD Flow Over a Stretching Sheet

Kuppala R. Sekhar* , G.Viswanatha Reddy**

* Research Scholar, Department of Mathematics, Sri Venkateswara University, Tirupati, India.

** Senior Professor, Department of Mathematics, Sri Venkateswara University, Tirupati, India.

Sekhar, K.R., and Reddy, G.V. (2017). Slip Effects of Viscous Dissipation on Steady MHD Flow Over a Stretching Sheet. i-manager’s Journal on Mathematics, 6(1), 27-34. https://doi.org/10.26634/jmat.6.1.11400

Abstract

Effects of slip at the boundary on steady MHD viscous dissipation flow over a stretching sheet in the presence of suction are investigated. Effectively a similarity variable, the governing partial differential equations is first transformed into ordinary ones, which are then solved numerically by applying shooting approximation. The results are presented for various values of the governing parameters. Comparison with capable results for reliable cases is excellent.

References

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[13]. M.R. Mohyuddin, and T. Gotz, (2015). “Resonance behaviour of visco-elastic fluid in Poiseuille flow in the presence of a transversal magnetic field”. International Journal for Numerical Methods in Fluids, Vol.49, No.8, pp. 837-847.

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[15]. Samra, Muhammad Raheel Mohyuddin, and Syed Mohammad Rizwan, (2015). “Similarity having perturbation in Newtonian fluid”. i-managers Journal on Mathematics. Vol.4, No.4, pp.22-27, ISSN Print: 2277-5129, ISSN Online: 2277-5137.

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Research Paper

Heat Transfer In MHD Viscoplastic Fluid Flow from a Vertical Permeable Cone with Convective Heating

CH. Amanulla* , N. Nagendra, M. Suryanarayana Reddy*

* Research Scholar, Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, India.

Assistant Professor, Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle, India.

* Assistant Professor and Head, Department of Mathematics, JNTUA College of Engineering, Andhra Pradesh, India.

Amanulla, Ch., Nagendra, N., and Reddy, M.S.N. (2017). Heat Transfer In MHD Viscoplastic Fluid Flow from a Vertical Permeable Cone with Convective Heating. i-manager’s Journal on Mathematics, 6(1), 35-42. https://doi.org/10.26634/jmat.6.1.11401

Abstract

A mathematical model is presented for the magneto-hydrodynamic flow and heat transfer in an electro-conductive Casson viscoplastic non-Newtonian fluid external to a vertical penetrable vertical cone under radial magnetic field and convective heating. The boundary layer conservation equations are parabolic in nature which can be transformed into a non-dimensional form via appropriate non-similarity variables and the emerging boundary value problem is solved computationally with the second order accurate implicit Keller-box finite-difference scheme. The influences of the emerging parameters, i.e. Magnetic parameter (M), Casson fluid parameter (β), Convective heating ( ), and Prandtl number (Pr) on velocity and temperature distributions are illustrated graphically. Validation of solutions with earlier published work is included.

References

[1]. S. Livescu, (2012). “Mathematical modeling of thixotropic drilling mud and crude oil flow in wells and pipelines - A review”. J. Petroleum Science and Engineering, Vol.98, No.99, pp.174–184.

[2]. J. Hron, J. Málek, P. Pustejovská, and K.R. Rajagopal, (2010). “On the modeling of the synovial fluid”. Advances in Tribology, Article ID 104957

[3]. F. Loix, L. Orgéas, C. Geindreau, P. Badel, P. Boisse, and J.F. Bloch, (2009). “Flow of non-Newtonian liquid polymers through deformed composites reinforcements”. Composites Science and Technology, Vol.69, No.5, pp.612–619.

[4]. V. Kechichian, G.P. Crivellari, J.A.W. Gut, and C.C. Tadini, (2012). “Modeling of continuous thermal processing of a non- Newtonian liquid food under diffusive laminar flow in a tubular system”. Int. J. Heat and Mass Transfer, Vol.55, No.21-22, pp.5783–5792 .

[5]. M. Ghannam, and N. Esmail, (2002). “Flow behavior of enhanced oil recovery Alcoflood polymers”. J. Applied Polymer Science, Vol.85, No.14, pp.2896 - 2904.

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Research Paper

Thermal Diffusion and TGHS Effect on MHD Viscous Dissipative Kuvshinski´S Fluid Past an Inclined Plate Through Porous Medium with Thermal Radiation And Chemical Reaction

S. Rama Mohan* , G.Viswanatha Reddy, S.V.K. Varma*, Bala Krishna Sapparam****

*-**** Department of Mathematics, S.V. University, Tirupathi, Andra Pradesh, India.

Mohan, S.R., Reddy, G.V., Varma, S.V.K., and Krishna, S.B. (2017). Thermal Diffusion and TGHS Effect on MHD Viscous Dissipative Kuvshinski´S Fluid Past an Inclined Plate Through Porous Medium with Thermal Radiation And Chemical Reaction. i-manager’s Journal on Mathematics, 6(1), 43-56. https://doi.org/10.26634/jmat.6.1.11402

Abstract

The focus of the present investigation is to study the thermal diffusion and temperature gradient heat source effect on unsteady Magneto hydrodynamic viscous dissipative non-Newtonian fluid, namely Kuvshinski’s fluid past an inclined plate filled with a porous medium. Also the first order chemical reactions are taking into an account. At the same time, the plate temperature and concentration of the plate are raised to T * and C *.The set of partial differential equations is transformed to ordinary differential equations by using suitable similarity transformations and then solved analytically by using regular perturbation technique. The impact of various flow parameters on velocity, temperature and concentration as well as the friction factor coefficient, the local Nusselt number, and a local Sherwood number are analyzed and discussed through graphs and table.

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Convection Boundary Layer Flow and Heat Transfer in an Eyring - Powell Fluid Past a Horizontal Circular Cylinder in Porous Medium

L. Nagaraja* , A. Subba Rao**, M. Sudhakar Reddy***, M. Suryanarayana Reddy****

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Slip Effects of Viscous Dissipation on Steady MHD Flow Over a Stretching Sheet

Kuppala R. Sekhar* , G.Viswanatha Reddy**

* Research Scholar, Department of Mathematics, Sri Venkateswara University, Tirupati, India. ** Senior Professor, Department of Mathematics, Sri Venkateswara University, Tirupati, India.

Sekhar, K.R., and Reddy, G.V. (2017). Slip Effects of Viscous Dissipation on Steady MHD Flow Over a Stretching Sheet. i-manager’s Journal on Mathematics, 6(1), 27-34. https://doi.org/10.26634/jmat.6.1.11400

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Heat Transfer In MHD Viscoplastic Fluid Flow from a Vertical Permeable Cone with Convective Heating

CH. Amanulla* , N. Nagendra**, M. Suryanarayana Reddy***

Amanulla, Ch., Nagendra, N., and Reddy, M.S.N. (2017). Heat Transfer In MHD Viscoplastic Fluid Flow from a Vertical Permeable Cone with Convective Heating. i-manager’s Journal on Mathematics, 6(1), 35-42. https://doi.org/10.26634/jmat.6.1.11401

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Thermal Diffusion and TGHS Effect on MHD Viscous Dissipative Kuvshinski´S Fluid Past an Inclined Plate Through Porous Medium with Thermal Radiation And Chemical Reaction

S. Rama Mohan* , G.Viswanatha Reddy**, S.V.K. Varma***, Bala Krishna Sapparam****

*-**** Department of Mathematics, S.V. University, Tirupathi, Andra Pradesh, India.

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L. Nagaraja* , A. Subba Rao, M. Sudhakar Reddy*, M. Suryanarayana Reddy****

* Research Scholar, Department of Mathematics, Sri Venkateswara University, Tirupati, India.

** Senior Professor, Department of Mathematics, Sri Venkateswara University, Tirupati, India.

CH. Amanulla* , N. Nagendra, M. Suryanarayana Reddy*

S. Rama Mohan* , G.Viswanatha Reddy, S.V.K. Varma*, Bala Krishna Sapparam****