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i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 12 Issue 2

Statistical Analysis on Job Satisfaction of Academic Staff at College of Natural Science in Jimma University, Ethiopia: A Cross-Sectional Study
Tolerance Based Rough Algebras Induced by Blocks
Significance of Thermal Boundary Layer Analysis of MHD Chemically Radiative Dissipative Casson Nanofluid Flow over a Stretching Sheet with Heat Source
Transient Analysis of M/M/1 Fractional Queue
A Novel Multi-Viewpoints Based Cosine Similarity Visual Technique for an Effective Assessment of Clustering Tendency

Most Cited

Volume 3 Issue 4 October - December 2014

Research Paper

Introducing Trinova: “Trichotomous Nomographical 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

James Edward Osler II*

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

Osler, J. E., II. (2014). Introducing Trinova: “Trichotomous Nomographical 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, 3(4), 1-14. https://doi.org/10.26634/jmat.3.4.3184

Abstract

This monograph provides an epistemological rational for the Trinova Post Hoc test methodology. Trinova is an in–depth [Trichotomous Nomographical Variance] statistical procedure for the internal testing of the transformative process of qualitative data, into quantitative outcomes through the Tri–Squared Test first introduced in i-manager’s Journal on Mathematics, and further detailed in the Journal on Educational Technology, Journal on School Educational Technology, and in Journal on Educational Psychology. Trinova is an advanced statistical measure that is designed to check the validity and reliability of a Tri–Squared Test. This is a novel approach to advanced statistical post hoc Tri–Squared data analysis. It adds considerable value to the mixed methods approach of research design that involves the holistic combination and comparison of qualitative and quantitative data outcomes. A sequential Trinova mathematical model is provided, that illustrates the entire process of advanced statistical Trichotomous inquiry.

References

[1]. Apostol, T. M. (1967). Calculus: One–variable calculus, with an introduction to linear algebra, Second edition, Waltham, MA: Blaisdell, Vol.1,pp.1-686.

[2]. Hamilton, G. F. (1944). The cranial capacity of the living, calculated automatically by a nomographical instrument, Journal of Anatomy, Vol.78, pp.200.

[3]. Kant, I. (2007). Critique of pure reason (based on Max Müller's translation). P. Classics Division of Pearson PLC. New York, NY

[4]. Morita, K. ????. (1952). Nomographical Determination of the Complex and Real Roots of the Stability Biquadratic Equations,3 rd Report, Full-nomographic method. ?????????, Vol.18(75), pp. 123–126.

[5]. Ojalvo, M. (1965). The Use of Nomography in the Solution of Beam-column Problems (No. TSS-15). Princeton University New Jersey Department of Graphics and Engineering Drawing.

[6]. James Edward Osler (2012). Introducing: 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(3) Print ISSN 2277- 5129, E-ISSN 2277-5137, pp. 23-32.

[7]. James Edward Osler and Carl Waden (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.8(2), Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 11-23.

[8]. James Edward Osler (2013). The Psychometrics Of Educational Science: Designing Trichotomous Inventive Investigative Instruments For Qualitative And Quantitative Inquiry. i-manager's Journal on School Educational Technology, Vol.8(3), Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 15-22.

[9]. James Edward Osler (2013). 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(4) Print ISSN 0973-8827, E-ISSN 2230-7141, pp. 36-41.

[10]. James Edward Osler II (2013). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining The Application Process of The Tri–Squared Test. i-manager's Journal on Mathematics, Vol.2(2) Print ISSN 2277-5129, E-ISSN 2277- 5137, pp. 10-16.

[11]. Rust, J. & Golombok, S.(1989). Modern psychometrics: The science of psychological assessment(2nd ed.). Florence, KY, US: Taylor & Frances/Routledge.

[12]. Searle, S. R., Casella, G., & McCullock, C. E. (1992).Variance components, New York: Wiley. Sensagent: Retrieved, http://dictionary.sensagent.com/trichotomy+(mathematics)/en–en/

[13]. 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.

[14]. Stang, P. L., & Taylor, C. A. (1961). The Prediction of Thermal Hazards in Propellants by a Nomographical Technique (No.NOTS-TP-2755), Naval Ordnance Test Station China Lake, CA.

[15]. Agresti, Alan (1996). An Introduction to Categorical Data Analysis. New York: Wiley.

[16]. Morrison, D. F. (1990). Multivariate statistical methods,(3rd Ed.). New York: McGraw-Hill.

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Research Paper

Magneto-Nanofluid Over an Exponentially Stretching Permeable Sheet with Viscous Dissipation

K. Lakshmi Narayana* , K.Gangadhar**

*-** Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh, India.

Narayana, K.L., and Gangadhar, K. (2014).Magneto-Nanofluid Over an Exponentially Stretching Permeable Sheet with Viscous Dissipation. i-manager’s Journal on Mathematics, 3(4), 15-26. https://doi.org/10.26634/jmat.3.4.3185

Abstract

This paper analyzes the steady boundary layer flow of magneto-nanofluid, due to an exponentially permeable stretching sheet with viscous dissipation. In this paper, the effect of viscous dissipation on heat transfer and nanoparticle volume friction is considered. The similarity ordinary differential equations were then solved by MATLAB bvp4c solver. This study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, Eckert number, Brownian motion parameter, and thermophoresis parameter have major effects on the flow field. The heat transfer, and the nanoparticle volume friction as well as skin friction, local Nusselt number and local Sherwood number have been discussed in detail.

References

[1]. Choi, S. U. S. (1995). “Enhancing thermal conductivity of fluids with nanoparticles in developments and applications of non-Newtonian flows,” ASME, FED-Vol. 231/MD, Vol.66, pp.99- 105.

[2]. Eastman, J. A., Choi, S. U. S., Li, S., Yu, W., and Thompson, L. J. (2001). “Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles,” Applied Physics Letter, Vol.78, pp.718-720.

[3]. Puneet Rana and Bhargava, R. (2011). “Flow and Heat Transfer Analysis of a Nanofluid along a Vertical Flat Plate with Non-Uniform Heating Using Fem: Effect of Nanoparticle Diameter”, International Journal of Applied Physics and Mathematics, Vol. 1, No. 3, pp.171-176.

[4]. Sakiadis, B.C. (1961). “Boundary-layer behaviour on continuous solid surfaces: Boundary-layer equations for twodimensional and axisymmetric flow”, AIChE J., Vol.7, pp.26-28.

[5]. Crane, L.J. (1970), “Flow past a stretching sheet”. Z.Angew.Math. Phys, Vol.21, pp.645–647.

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[7]. Mahapatra,T.R., and Gupta.A.S. (2002). Heat transfer in stagnation-point flow towards a stretching sheet, Heat and Mass Transfer, Vol.38, pp.517–521.

[8]. Sohail Nadeem., and Changhoon Lee. (2012). Boundary layer flow of nanofluid over an exponentially stretching surface, Nanoscale Research Letters, 7:94, pp.1-6.

[9]. Alam, M.S., Rahman, M.M., and Sattar, M.A. (2008). Effect of variable suction and thermophoresis on steady MHD combined free-forced convective heat and mass transfer flow over a semi- infinite permeable inclined plate in the presence of thermal radiation, International Journal of Thermal Sciences, Vol.47, pp.758-765.

[10]. Jyothi, P., Viswanatha Reddy, G., and Vijaya Kumar Varma, S. (2013). Thermo diffusion and chemical reaction effects on unsteady free mhd convection flow past a vertical porous plate in slip-flow regime, International Journal of Advanced Engineering Technology, pp.33-36.

[11]. Iswar Chandra Mandal, Swati Mukhopadhyay. (2013). Heat transfer analysis for fluid flow over an exponentially stretching porous sheet with surface heat flux in porous medium, Ain Shams Engineering Journal, Vol. 4, pp.103-110.

[12]. Gangadhar, K., and Bhaskar Reddy, N. (2013). Chemically Reacting MHD Boundary Layer Flow of Heat and Mass Transfer over a Moving Vertical Plate in a Porous Medium with Suction, Journal of Applied Fluid Mechanics, Vol. 6, No. 1, pp. 107-114.

[13]. Rushi Kumar, B., and Gangadhar, K. (2012). Heat generation effects on mhd boundary layer flow of a moving vertical plate with suction, Journal of Naval Architecture and Marine Engineering, Vol.9, pp.153-162.

[14]. Bandaris Shankar, Yohannes Yirga. (2013). Unsteady Heat and Mass Transfer in MHD Flow of Nanofluids over Stretching Sheet with a Non-Uniform Heat Source/Sink, World Academy of Science, Engineering and Technology International Journal of Mathematical, Computational Science and Engineering, Vol:7, No:12, pp.943-951.

[15]. Liu, I.C. (2004). Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to a transverse magnetic field, Int J Heat Mass Transf., Vol.47, pp.4427-4437.

[16]. Jing zhu, Liancun Zheng, Xinxin Zhang. (2010). Flow and Heat Transfer In a Power-law Fluid with Variable Conductivity over a Stretching Sheet, Proceedings of the World Congress on Engineering, Vol III WCE 2010, June 30 - July 2, 2010, London, U.K.

[17]. Van Rij, J., Ameel, T., Harman, T. (2009). The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer. Int. J. Therm. Sci. 2009, Vol.48, pp.271–281.

[18]. Koo, J., Kleinstreuer, C. (2004). Viscous dissipation effects in microtubes and microchannels, Int. J. Heat Mass Transf., Vol. 47, pp.3159-3169.

[19]. Mohammad H. Yazdi., Shahrir Abdullah., Ishak Hashim., and Kamaruzzaman Sopian. (2011). Effects of Viscous Dissipation on the Slip MHD Flow and Heat Transfer past a Permeable Surface with Convective Boundary Conditions, Energies, Vol.4, pp.2273-2294.

[20]. Khan, S.K., Subhas Abel, M., and Sonth Ravi, M. (2003). Viscoelastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work, Int J Heat Mass Transf., Vol.40, pp.47-57.

[21]. Md Shakhaoath Khan., Ifsana Karim., Lasker Ershad Ali., and Ariful Islam. (2012). Unsteady MHD free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation and viscous dissipation effects, International Nano Letters, 2:24,pp.1-9.

[22]. MAKINDE, O. D. (2012). Analysis of Sakiadis flow of nanofluids with viscous dissipation and Newtonian heating, Appl. Math. Mech. -Engl. Ed., Vol.33(12), pp.1545-1554.

[23]. Chandrasekar, M., and Baskaran, S. (2007). Thermodynamical modelling of viscous dissipation in magnetohydrodynamic Flow, Theoret. Appl. Mech., Vol.34, No.3, pp. 197- 219.

[24]. Fekry M Hady, Fouad S Ibrahim, Sahar M Abdel-Gaied and Mohamed R Eid. (2012). Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet, Nanoscale Research Letters, Vol.7, No.229.

[25]. Bhattacharyya Krishnendu and Layek, G. C. (2014). Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet, Hindawi Publishing Corporation, Physics Research International, Article ID 592536, 12 pages.

[26]. Khan, W. A. and Pop, I. (2010). Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, Vol. 53, No. 11-12, pp. 2477–2483.

[27]. Bhattacharyya, K., and Pop, I. (2011). MHD boundary layer flow due to an exponentially shrinking sheet, Magnetohydrodynamics, Vol. 47, pp. 337-344.

[28]. Ishak, A. (2011). MHD boundary layer flow due to an exponentially stretching sheet with radiation effect, SainsMalaysiana, Vol. 40, No. 4, pp. 391-395.

[29]. Shampine, L. F. and Kierzenka, J. (2000). “Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c,” Tutorial Notes.

[30]. Gangadhar, K. (2012). Similarity solution for natural convection over a moving vertical plate with internal heat generation and viscous dissipation, Int. J. of Appl. Math and Mech., Vol. 8 (18), pp. 90-100.

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Research Paper

Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux

R.Chandra Sekhar Reddy* , K.Jayarami Reddy, M.S.N. Reddy*

* Department of Mathematics, Priyadarshini Institute of Technology, Tirupati, A.P, India.

Department of Mathematics, K.L University, Guntur, A.P, India.

* Department of Mathematics, JNTUA College of engineering, Pulivendula, A.P, India.

Reddy, R.C.S., Reddy, K.J., and Reddy, M.S.N. (2014). Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux. i-manager’s Journal on Mathematics, 3(4), 27-41. https://doi.org/10.26634/jmat.3.4.3186

Abstract

The analytical results are investigated for an unsteady MHD free convection heat and mass transfer flow of a viscous, dissipative incompressible fluid past an infinite vertical plate through porous medium. The presence of thermal radiation, chemical reaction, joules heating are considered along with aligned magnetic field effect and constant heat and mass flux. The non dimensional governing equations are reduced to a set of ordinary differential equation by using a multiple parameter perturbation technique. The expansion for the velocity, the temperature and the concentration are obtained with reference to the assumed boundary conditions. The expressions for Skin friction, Nusselt number and Sherwood number are also derived. The consequences of varied physical parameters like magnetic parameter (M), Radiation parameter (R), Grashof number (Gr), Sharewood number (Gm), Prandtl number (Pr), Eckert number (Ec), and heat source parameter on the flow quantified are studied numerically with the help of tables and graphs.

References

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[13]. Krishna, P. M., Sandeep, N. & Sugunamma, V. (2014). Effects of radiation and chemical reaction on MHD convective flow over a permeable stretching surface with suction and heat generation, Walailak Journal of Science and Technology, Vol. 11, No. 12, pp.141-148.

[14]. Kandasamy, R., Hayat, T. & Obaidat, S. (2011). Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heat source/sink, Nucl. Eng. Des., Vol. 241, No.6, pp.2155–2161.

[15]. Ravikumar, V. Raju, M.C. Varma, S.V.K. & Chamkha, A.J. (2013). MHD double diffusive and chemically reactive flow through porous medium bounded by two vertical plates, International Journal of Energy & Technology, Vol.5

[16]. Joneidi, A.A., Domairry, G. & Babaelahi, M. (2010). Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction, J. Taiwan Inst. Chem. Eng., Vol. 41, No.1, pp.35–43.

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[19]. Mohamed, R.A., Osman, A-N.A. & Abo-Dahab, S.M. (2013). Unsteady MHD double-diffusive convection boundarylayer flow past a radiate hot vertical surface in porous media in the presence of chemical reaction and heat sink, Meccanica, Vol. 48, pp.931-936.

[20]. Rajput, U. S. & Kumar, S. (2012). Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer, Int. J. of Appl. Math. and Mech., Vol. 8(1), pp.66-85.

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[26]. Umamaheswar, M., Varma, S. V. K. & Raju, M. C. (2013). Unsteady MHD Free Convective Visco-Elastic Fluid Flow Bounded by an Infinite Inclined Porous Plate in the Presence of Heat Source, Viscous Dissipation and Ohmic Heating, International Journal of Advanced Science and Technology, Vol.61, pp.39- 52.

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Research Paper

Mass Transfer Effects on MHD Viscous Flow Past an Impulsively Started Infinite Vertical Plate Through Porous Medium

J. Girish Kumar*

Lecturer, Department of Mathematics, Government Degree College, Jammalamadugu, Kadapa, A.P. India.

Kumar, J.G. (2014).Mass Transfer Effects on MHD Viscous Flow Past an Impulsively Started Infinite Vertical Plate Through Porous Medium. i-manager’s Journal on Mathematics, 3(4), 42-50. https://doi.org/10.26634/jmat.3.4.3187

Abstract

This work focused on the effects of mass transfer on an unsteady visco-elastic second order Rivin-Erickson fluid, past an impulsively started infinite vertical plate in the presence of foreign mass on taking into account of viscous dissipative heat, at the plate under the influence of a uniform transverse magnetic field. The dimensionless governing equations for this investigation are solved numerically by using the finite difference method. The effects of various parameters such as Pr (Prandtl number), Gr (Grashof number), Gc (solutal Grashof number), Ec (Eckert number), Sc (Schmidt nmber), M (Hartmann number) and k (permeable parameter), on the velocity profiles, the temperature profiles and the concentration profiles are presented graphically and discussed. The author have observed that, the velocity increases with increase in the value of Grashof number or solutal Grashof number. Also the temperature decreases with increase in the Prandtl number and Concentration is reduced with increase in Schmidt number. The study of visco-elastic fluid flows over vertical surfaces immersed in porous media in the presence of magnetic field has attracted the researchers due to its application in geophysical, astrophysics and biological system etc.

References

[1]. R. Saravana, S., Sreekanth, S., Sreenadh., and R. Hemadri Reddy, (2011). Mass Transfer Effects on MHD Viscous flow past an impulsively started infinite vertical plate with constant Mass flux, Advances in Applied Science Research, Vol.2(1), pp.221- 229.

[2]. J. Gireesh Kumar., S. Ramakrishna, (2010). MHD flow of viscous fluid past an impulsively moving isothermal moving vertical plate through porous medium with chemical reaction, Ultra Scientist, Vol. 22(3), pp.446-454.

[3]. G. Noushima, Human., M.V. Ramana Murthy., M. Chennakrishna Reddy., Rafiuddin, A. Ramu., and Rajender, (2010). Hydro Magnetic free convective Rivin-Erickson flow through a porous medium with variable permeability, International Journal of Comp. and Applied Mathematics, Vol.5(3), pp.267-275.

[4]. G.V. Ramana., Ch.V. Ramana Murthy., and N. Bhaskar Reddy, (2010). Mass transfer and radiation effects of unsteady MHD free convective fluid flow embedded in porous medium with heat generation/absorption, Journal of Applied Mathematics and Fluid Mechanics, Vol.2, No.1, pp.85-98.

[5]. H. Bararnia., A.R. Ghotbi., and G. Domairry, (2009). On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium, Nonlinear Sci. Numer. Simul., Vol.14, pp.2689-2701.

[6]. R.C. Choudhury., and S. Kumar Das, (2014). Visco-elastic MHD free convective flow through porous media in presence of radiation and chemical reaction with heat and mass transfer, Journal of Applied Fluid Mechanics, Vol. 7, No. 4, pp.603- 609.

[7]. Rita Choudhury., Madhumita Mahanta., and Debasish Dey, (2014). Visco-Elastic fluid flow with heat and mass transfer in a vertical channel through porous medium, Journal of Global Research in Mathematical Archive, Vol.2, No.1, pp.22-33.

[8]. M. Umamaheswar., S.V.K. Varma., and M.C. Raju, (2013). Unsteady MHD free convective visco-elastic fluid flow bounded by an infinite inclined porous plate in the presence of heat source, viscous dissipation and ohmic heating, International Journal of Advanced Science and Technology, Vol.61, pp.39-52

[9]. N. A. Reddy., M. C. Raju., and S. V. K. Varma, (2010). Unsteady free convective MHD non Newtonian flow through a porous medium bounded by an infinite inclined porous plate, International Journal of Emerging Technologies and applications in engineering, Technology and sciences, Vol. 3, No. 2, pp.238-244.

[10]. G.N. Humera., M. V. Ramana Murthy., M. C. K. Reddy, Rafiuddin., A. Ramu., and S. Rajender, (2010). Hydromagnetic free convective Revlin-Ericksen flow through a porous medium with variable permeability, International Journal of computational and Applied Mathematics, Vol.5(3), pp.267-275.

[11]. R.M. Sonth., S. K. Khan., M. S. Abel., and K. V. Prasad, (2002). Heat and mass transfer in a visco-elastic flow over an accelerating surface with heat source/sink and viscous dissipation. Heat and Mass Transfer., Vol.38(3), pp.213-220.

[12]. S. Mohammed Ibrahim., and N. Bhaskar Reddy, (2012). Radiation and mass transfer effects on MHD free convection flow along a stretching surface with viscous dissipation and heat generation, Int. J of Appl. Math and Mech., Vol.8(8), pp.1- 21.

[13]. V. Ramachandra Prasad., and N. Bhaskar Reddy, (2008). Radiation and mass transfer effects on an unsteady MHD convection flow past a semi-infinite vertical permeable moving plate embedded in a porous medium with viscous dissipation, Indian Journal of Pure and Applied Physics, Vol.46, pp.81-92.

[14]. Hemanth Poonia., and R.C. Chaudhary, (2010). MHD free convection and mass transfer flow over an infinite vertical porous plate with viscous dissipation, Theoret. Appl. Mech., Vol.37, No.4, pp.263–287.

[15]. A.S. Idowu., M.S. Dada and A. Jimoh, (2013). Heat and mass transfer of magnetohydrodynamic and dissipative fluid flow past a moving vertical porous plate with variable suction, Mathematical Theory and Modeling, Vol.3, No.3, pp.80-102.

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Research Paper

Antiflexible Rings with Commutators in the Left Nucleus

M.Hema Prasad* , D. Bharathi**

* Assistant Professor in Mathematics, Department of Science & Humanities, SITAMS, Chittoor, A.P. India.

** Associate Professor in Mathematics, Department of Mathematics, S.V. University, Tirupati, A.P. India.

Prasad, M.H., and Bharathi, D. (2014). Antiflexible Rings with Commutators in the Left Nucleus. i-manager’s Journal on Mathematics, 3(4), 51-56. https://doi.org/10.26634/jmat.3.4.3188

Abstract

In this paper, the authors have assumed that 'R' is an antiflexible ring with commutators and (a, b, c) in the left nucleus. Using this, they have proved that the commutators are in the middle of the nucleus. Next they have proved that an antiflexible ring R cannot be simple. They assumed T = {t∈ N_l / t (R, R, R) = 0}and proved that T is an ideal of R and T (R, R, R)= 0 and then they have proved that T∩A = 0, ((a, b, a), R) = 0. Finally using these results they conclude that, if R is a prime antiflexible ring of characteristic ≠ 3, then R is associative.

References

[1]. A. A. Albert. (1948). “Power Associative Rings”, Trans. Amer. Math. Soc., Vol.64, pp.552-593.

[2]. C.T. Anderson and D. L. Outcalt. (1968). “On Simple Antiflexible Rings”, J. Algebra, Vol.10, pp.310 - 320.

[3]. A. Thedy. (1971). “On Rings satisfying ((a, b, c), d) = 0”, Proc. Amer. Math. Soc., Vol.29, pp.250–254.

[4]. A. Thedy. (1971). “On rings with commutators in nuclei”, Math. Z., Vol.119, pp.213 - 218.

[5]. A. H. Boers. (1971). “The nucleus in the associative ring”, Proc. Kon. Ned. Akad. Vanwet. Vol 74 et Indag. Math. 33, pp.464 - 470.

[6]. H. A. Celik. (1972). “On primitive and prime Antiflexible Rings”, Journal of Algebra, Vol.20, pp.428 - 440.

[7]. A. Thedy. (1975). “Right alternative rings”, Journal of Algebra, Vol.37, pp.1 - 43.

[8]. M. Mahivee. (1975). “On prime right alternative rings”, (Russian) Algebra I logika Vol.14, pp.56 - 60.

[9]. H.A. Celik and D. L. Outcalt. (1975). “Power – Associativity of Antiflexible rings”, Proceedings of the American Mathematical Society, Vol.53(1), pp.19 - 23.

[10]. E. Kleinfeld. (1988). “Rings with (x, y, x) and commutators in the left nucleus”, Comm. Algebra, Vol.16, pp.2023-2029.

[11]. Y. Paul. (1990). “Prime rings satisfying (x, y, z) = (x, z, y)”, Proc. Symposium of Algebra and Number Theory, Kochi, Kerala, India, pp.91-95.

[12]. Kosier. F, (1962). “On a class of nonflexible algebras”. Trans. Am. Math. Soc. Vol.102, pp.299-318.

[13]. Kleinfeld, E (1957). “Assosymmetric rings”, Proc. Amer. Math. Soc., Vol. 8, pp.983-986.

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Introducing Trinova: “Trichotomous Nomographical 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

James Edward Osler II*

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

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Magneto-Nanofluid Over an Exponentially Stretching Permeable Sheet with Viscous Dissipation

K. Lakshmi Narayana* , K.Gangadhar**

*-** Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh, India.

Narayana, K.L., and Gangadhar, K. (2014).Magneto-Nanofluid Over an Exponentially Stretching Permeable Sheet with Viscous Dissipation. i-manager’s Journal on Mathematics, 3(4), 15-26. https://doi.org/10.26634/jmat.3.4.3185

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Aligned Magnetic Field Effect on Unsteady MHD Natural Convection Flow of a Chemically Reacting, Radiative and Dissipative Fluid Past a Porous Vertical Plate in the Presence of Constant Heat and Mass Flux

R.Chandra Sekhar Reddy* , K.Jayarami Reddy**, M.S.N. Reddy***

* Department of Mathematics, Priyadarshini Institute of Technology, Tirupati, A.P, India. ** Department of Mathematics, K.L University, Guntur, A.P, India. *** Department of Mathematics, JNTUA College of engineering, Pulivendula, A.P, India.

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Mass Transfer Effects on MHD Viscous Flow Past an Impulsively Started Infinite Vertical Plate Through Porous Medium

J. Girish Kumar*

Lecturer, Department of Mathematics, Government Degree College, Jammalamadugu, Kadapa, A.P. India.

Kumar, J.G. (2014).Mass Transfer Effects on MHD Viscous Flow Past an Impulsively Started Infinite Vertical Plate Through Porous Medium. i-manager’s Journal on Mathematics, 3(4), 42-50. https://doi.org/10.26634/jmat.3.4.3187

Abstract

References

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Antiflexible Rings with Commutators in the Left Nucleus

M.Hema Prasad* , D. Bharathi**

* Assistant Professor in Mathematics, Department of Science & Humanities, SITAMS, Chittoor, A.P. India. ** Associate Professor in Mathematics, Department of Mathematics, S.V. University, Tirupati, A.P. India.

Prasad, M.H., and Bharathi, D. (2014). Antiflexible Rings with Commutators in the Left Nucleus. i-manager’s Journal on Mathematics, 3(4), 51-56. https://doi.org/10.26634/jmat.3.4.3188

Abstract

References

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R.Chandra Sekhar Reddy* , K.Jayarami Reddy, M.S.N. Reddy*

* Department of Mathematics, Priyadarshini Institute of Technology, Tirupati, A.P, India.

Department of Mathematics, K.L University, Guntur, A.P, India.

* Department of Mathematics, JNTUA College of engineering, Pulivendula, A.P, India.

* Assistant Professor in Mathematics, Department of Science & Humanities, SITAMS, Chittoor, A.P. India.

** Associate Professor in Mathematics, Department of Mathematics, S.V. University, Tirupati, A.P. India.