International Journal of Mathematical Research

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Online ISSN: 2306-2223
Print ISSN: 2311-7427
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No. 2

Consistency of a Mixture Model of Two Different Distributions Approach to the Analysis of Buying Behaviour Data

Pages: 179-187
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Consistency of a Mixture Model of Two Different Distributions Approach to the Analysis of Buying Behaviour Data

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DOI: 10.18488/journal.24/2016.5.2/24.2.179.187

Akomolafe Abayomi. A

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  1. A. A. Akomolafe, "Analysis of consumer depth of repeat purchasing pattern: An exploratory study of beverages buying behaviour data," Journal of Business and Organisational Development, vol. 3, pp. 1-8, 2011.
  2. M. G. Kendall and S. Alan, The advanced theory of statistics, 3rd ed. New York: Hafner, 1977.
Akomolafe Abayomi. A (2016). Consistency of a Mixture Model of Two Different Distributions Approach to the Analysis of Buying Behaviour Data. International Journal of Mathematical Research, 5(2): 179-187. DOI: 10.18488/journal.24/2016.5.2/24.2.179.187
A four-parameter probability distribution, which includes a wide variety of curve shapes, is presented. Because of the flexibility, generality, and simplicity of the distribution, it is useful in the representation of data when the underlying model is unknown. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies and Monte Carlo sampling studies of the robustness of statistical procedures. This research centered on combining these two distributions that will simultaneously capture the rate of occurrence of a phenomenon, especially buying behaviour and the actual performance of that phenomenon as well as tracking and forecasting future purchasing pattern based the data. Further important applications of the distribution include the modeling and subsequent generation of random variates for simulation studies of the robustness of statistical procedures. To do this, specification of the hybrid model named Exponential- Gamma mixture model is given and followed by its derivation. The concluding part of the paper depicts an example of the areas of its application.
Contribution/ Originality
This study contributes to the existing literature by combining exponential-gamma mixture as a hybrid model to see its rate of tracking and forecasting purchasing pattern. This is carried out by using our newly arrived formula in analyzing both the real life and simulated data in other to ascertain the uniqueness of combined probability distribution in forecasting future customer buying behavior data for producers effective planning and administration.

Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation

Pages: 166-178
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Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation

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DOI: 10.18488/journal.24/2016.5.2/24.2.166.178

Joshua Ikechukwu Nwamba

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  1. J. I. Nwamba, "Delayed Mathieu equation with fractional order damping: An approximate analytical solution," International Journal of Mechanics and Applications vol. 3, pp. 70-75, 2013.
  2. E. Mathieu, "Memoire sure le mouvement vibratiore d’une membrane de forme Elliptique," Journal de Mathématiques Pures et Appliquées, vol. 13, pp. 137-203, 1868.
  3. A. Nayfeh and D. T. Mook, Nonlinear oscillations. New York: Wiley, 1979.
  4. R. H. Rand, "Lecture notes on nonlinear vibrations (version 53). Ritriveved from http//audiophile.tam.cornell," 2012.
  5. R. H. Rand, S. M. Sah, and M. K. Suchorsky, "Fractional mathieu equation," Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 3254-3262, 2010.
  6. A. Ebaid, D. M. M. Elsayeed, and M. D. Aljoufi, "Fractional calculus model for damped Mathieu equation: Approximate analytical solution," Applied Mathematical Sciences, vol. 6, pp. 4075-4080, 2012.
  7. O. A. Taiwo and O. S. Adetunde, "Approximation of multi-order fractional differential equations by an iterative decomposition method," American Journal of Engineering Science and Technology Research, vol. 1, pp. 10-18, 2013.
  8. I. K. Hanan, "The homotopy analysis method for solving multi-fractional order integro-differential equations," J. Al-Nahrain Univ., vol. 14, pp. 139-143, 2011.
  9. R. L. Bagley and P. J. Torvik, "A theoretical basis for the application of fractional calculus to viscoelasticity," Journal of Rheology, vol. 27, pp. 201-210, 1983.
  10. I. N. Joshua, "Joshua Ikechukwu Nwamba: Exact and explicit approximate solutions to the multi-order fractional burgers-poisson and fractional burgers-poisson equations," Applied and Computational Mathematics, vol. 2, pp. 78-85, 2013.
  11. H. M. Srivasta and R. K. Saxena, "Operators of fractional integration and their applications," Applied Mathematics and Computation, vol. 118, pp. 1-52, 2001.
  12. R. Hilfer, "Applications of fractional calculus in physics." Retrieved from http://cict.umcc.cu/repositorioinstitucional/Matem%C3%A1tica/16-Medida%20e%20Integraci%C3%B3n/Fractional%20Calculus/Applications%20of%20Fractional%20Calculus%20in%20Physics.pdf, 2000.
  13. I. Podlubny, Fractional differential equations. San Diego, California: Academic Press, 1999.
  14. J. H. He, "Homotopy perturbation technique," Computer Methods in Applied Mechanics and Engineering, vol. 178, pp. 257-262, 1999.
  15. J. H. He, "An elementary introduction to the homotopy perturbation method," Computers and Mathematics with Applications, vol. 57, pp. 410-412, 2009.
  16. J. H. He, "The homotopy perturbation method for nonlinear oscillators with discontinuities," Applied Mathematics and Computation, vol. 151, pp. 287-292, 2004.
  17. J. H. He, "Homotopy perturbation method: A new nonlinear analytical technique," Applied Mathematics and Computation, vol. 137, pp. 73-79, 2003.
  18. J. H. He, "Recent development of the homotopy perturbation method," Topological Methods in Nonlinear Analysis, vol. 31, pp. 205-209, 2008.
  19. B. Raftari, "Application of he’s homotopy perturbation method and variational iteration method for nonlinear partial integro-differential equations," World Applied Sciences Journal, vol. 7, pp. 399-404, 2009.
  20. C. Chum and R. Sakthivel, "Homotopy perturbation technique for solving two-point boundary value problems-comparison with other methods," Computer Physics Communications, vol. 181, pp. 1021-1024, 2010.
  21. M. M. Ghasemi, "Numerical solution of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method," Applied Mathematics and Computation, vol. 188, pp. 450-455, 2007.
Joshua Ikechukwu Nwamba (2016). Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation. International Journal of Mathematical Research, 5(2): 166-178. DOI: 10.18488/journal.24/2016.5.2/24.2.166.178
This paper presents an investigation of the behavior of the multi-order fractional differential equation (MFDE). We derive expressions for the transition curves separating regions of stability from instability for the MFDE generally and the particular case K=2. Employing the harmonic balance technique, we obtained approximate expressions for the n=1 and n=2   transition curves of the MFDE and particularly for the case k=2. We also obtained an approximate analytical solution to the multi-order fractionally damped and forced Duffing-Mathieu equation as well as some special cases computationally using the Homotopy Perturbation Method (HPM).
Contribution/ Originality

Dx-Schemes and Jets in Conformal Gravity Using Integral Transforms

Pages: 154-165
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Dx-Schemes and Jets in Conformal Gravity Using Integral Transforms

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DOI: 10.18488/journal.24/2016.5.2/24.2.154.165

Francisco Bulnes , Sergei Fominko

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  1. F. Bulnes, "Geometrical langlands ramifications and differential operators classification by Coherent D-modules in field theory," Journal of Mathematics and System Sciences, vol. 3, pp. 491-507, 2013.
  2. F. Bulnes, "Integral geometry methods on deformed categories in field theory II," Pure and Applied Mathematics Journal, vol. 3, pp. 1-5, 2014.
  3. S. Sämman and O. Lechtenfeld, "Matrix models and D-branes in twistor string theory," Journal of High Energy Physics, vol. 2006, p. 002, 2006.
  4. F. Bulnes, "Mathematical electrodynamics: Groups, cohomology classes, unitary representations, orbits and integral transforms in electro-physics," American Journal of Electromagnetics and Applications, vol. 3, pp. 43-52, 2015.
  5. S. G. Gindikin, "Generalized conformal structures," Twistors in Mathematics and Physics, vol. 156 p. 36, 1990.
  6. R. J. Baston and J. L. Mason, "Conformal gravity, the einstein equations and spaces of complex null geodesics," Class Quantum Gravity, vol. 4, pp. 815-826, 1987.
  7. I. Verkelov, "Moduli spaces, non-commutative geometry and deformed differential categories," Pure and Applied Mathematics Journal, vol. 3, pp. 12-19, 2014.
  8. F. Bulnes, "Integral geometry methods on deformed categories to geometrical langlands ramifications in field theory," Ilirias Journal of Mathematics, vol. 3, pp. 1-13, 2014a.
  9. S. Fominko, "Approaching by DX- schemes and jets to conformal blocks in commutative moduli schemes," Pure and Applied Mathematics Journal, vol. 3, pp. 38-43, 2014.
  10. C. R. LeBrun, Twistors, ambitwistors and conformal gravity. Cambridge, UK: Twistor in Physics, 1981.
  11. M. Eastwood, "Notes on conformal differential geometry," in Proceedings of the 15th Winter School Geometry and Physics (Srni 1995). Rend. Circ Mat. Palermo (2) Suppl. 43, 1996, pp. 57-76.
  12. F. Bulnes, "Derived categories in langlands program ramifications: Approaching by penrose transforms," Journal of Advances in Pure Mathematics, vol. 4, pp. 253-260, 2014b.
  13. F. Bulnes, "Electromagnetic gauges and Maxwell lagrangians applied to the determination of curvature in the space-time and their applications," Journal of Electromagnetic Analysis and Applications, vol. 4, pp. 252-266, 2012a.
  14. F. Bulnes, "Integral transforms and opers in the geometrical langlands program," Journal of Mathematics, vol. 1, pp. 6-11, n.d.
  15. F. Bulnes, Integral geometry methods in the geometrical langlands program. USA: Scientific Research Publishing Books, 2016.
  16. J. L. Verdier, "A duality theorem in the etale cohomoloy of schemes, Springer-Verlag, Tonny Albert (Ed)," in Proceedings of a Conference on Local Fields: NUFFIC Summer School held at Driebergen, Netherland-66, Berlin, New York, 1967, pp. 184-198.
  17. A. Grothendieck, "On the de rham cohomology of algebraic varieties," Publications Mathématiques de l'Institut des Hautes Études Scientifiques, vol. 29, pp. 95-103, 1966.
  18. F. Bulnes, "Penrose transform on D-modules, moduli spaces and field theory," Journal of Advances in Pure Mathematics, vol. 2, pp. 379-390, 2012b.
Francisco Bulnes , Sergei Fominko (2016). Dx-Schemes and Jets in Conformal Gravity Using Integral Transforms. International Journal of Mathematical Research, 5(2): 154-165. DOI: 10.18488/journal.24/2016.5.2/24.2.154.165
A  scheme is a scheme equipped with a flat connection over a smooth scheme on a base field. The flat connection equipment is a characterization of this scheme to construct through isomorphisms between commutative algebras and formal moduli problems the conformal images of the space-time that are solutions in conformal field theory. If are considered the  schemes and their particular tools, the jets, these determine conformal blocks of space-time pieces that are invariant under conformal transformations. These conformal block of space-time pieces determine a homogeneous degree factor that characterizes the solutions in a complex Riemannian model of the space-time of the field equations to certain tensors of the Weyl curvature. Finally, is demonstrated that the algebra belonging to the  schemes to the mentioned formal moduli problem is the image under a generalized Penrose transform that in the conformal context of many pieces of the space-time, has a structure as objects in commutative rings of CAlgk each one.

Contribution/ Originality

MHD Flow of a Nanofluid at the Forward Stagnation Point of an Infinite Permeable Wall with a Convective Boundary Condition

Pages: 138-153
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MHD Flow of a Nanofluid at the Forward Stagnation Point of an Infinite Permeable Wall with a Convective Boundary Condition

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DOI: 10.18488/journal.24/2016.5.2/24.2.138.153

Siti Hidayah Muhad Saleh , Norihan Md Arifin , Roslinda Mohd Nazar , Ioan Pop

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  1. K. Hiemenz, Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Berlin: Weber, 1911.
  2. F. Homann, "Der Einfluß großer Zähigkeit bei der Strömung um den Zylinder und um die Kugel," ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol. 16, pp. 153-164, 1936.
  3. T. R. Mahapatra and A. S. Gupta, "Stagnation-point flow towards a stretching surface," Canadian Journal of Chemical Engineering, vol. 81, pp. 258-263, 2003.
  4. R. Nazar, "Stagnation point flow of a micropolar fluid towards a stretching sheet," International Journal of Non-Linear Mechanics, vol. 39, pp. 1227-1235, 2004.
  5. A. Ishak, "MHD mixed convection flow near the stagnation-point on a vertical permeable surface," Physica A: Statistical Mechanics and its Applications, vol. 389, pp. 40-46, 2010.
  6. T. R. Mahapatra, S. K. Nandy, and A. S. Gupta, "Analytical solution of magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface," Applied Mathematics and Computation, vol. 215, pp. 1696-1710, 2009.
  7. T. Ray Mahapatra, S. K. Nandy, and A. S. Gupta, "Magnetohydrodynamic stagnation-point flow of a power-law fluid towards a stretching surface," International Journal of Non-Linear Mechanics, vol. 44, pp. 124-129, 2009.
  8. S. U. S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. Medium: ED; Size, n.d.
  9. A. V. Kuznetsov and D. A. Nield, "Natural convective boundary-layer flow of a nanofluid past a vertical plate," International Journal of Thermal Sciences, vol. 49, pp. 243-247, 2010.
  10. W. A. Khan and I. Pop, "Boundary-layer flow of a nanofluid past a stretching sheet," International Journal of Heat and Mass Transfer, vol. 53, pp. 2477-2483, 2010.
  11. M. Mustafa, "Stagnation-point flow of a nanofluid towards a stretching sheet," International Journal of Heat and Mass Transfer, vol. 54, pp. 5588-5594, 2011.
  12. M. Hassani, "An analytical solution for boundary layer flow of a nanofluid past a stretching sheet," International Journal of Thermal Sciences, vol. 50, pp. 2256-2263, 2011.
  13. N. Bachok, A. Ishak, and I. Pop, "Stagnation-point flow over a stretching/shrinking sheet in a nanofluid," Nanoscale Research Letters, vol. 6, pp. 1-10, 2011.
  14. N. Bachok, A. Ishak, and I. Pop, "Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet," International Journal of Heat and Mass Transfer, vol. 55, pp. 2102-2109, 2012.
  15. W. Ibrahim, B. Shankar, and M. M. Nandeppanavar, "MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet," International Journal of Heat and Mass Transfer, vol. 56, pp. 1-9, 2013.
  16. W. A. Khan and A. Aziz, "Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux," International Journal of Thermal Sciences, vol. 50, pp. 1207-1214, 2011.
  17. A. Alsaedi, M. Awais, and T. Hayat, "Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions," Communications in Nonlinear Science and Numerical Simulation, vol. 17, pp. 4210-4223, 2012.
  18. A. Aziz and W. A. Khan, "Natural convective boundary layer flow of a nanofluid past a convectively heated vertical plate," International Journal of Thermal Sciences, vol. 52, pp. 83-90, 2012.
  19. M. A. A. Hamad and M. Ferdows, "Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A lie group analysis," Communications in Nonlinear Science and Numerical Simulation, vol. 17, pp. 132-140, 2012.
  20. P. Rana and R. Bhargava, "Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study," Communications in Nonlinear Science and Numerical Simulation, vol. 17, pp. 212-226, 2012.
  21. F. Labropulu, J. M. Dorrepaal, and O. P. Chandna, "Oblique flow impinging on a wall with suction or blowing," Acta. Mechanica, vol. 115, pp. 15-25, 1996.
  22. M. Katagiri, "Magnetohydrodynamic flow with suction or injection at the forward stagnation point," Journal of the Physical Society of Japan, vol. 27, pp. 1677-1685, 1969.
  23. R. Kandasamy, K. Gunasekaran, and S. b. H. Hasan, "Scaling group transformation on fluid flow with variable stream conditions," International Journal of Non-Linear Mechanics, vol. 46, pp. 976-985, 2011.
  24. W. Ibrahim and B. Shankar, "MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions," Computers & Fluids, vol. 75, pp. 1-10, 2013.
  25. M. A. A. Hamad, I. Pop, and A. I. Md Ismail, "Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate," Nonlinear Analysis: Real World Applications, vol. 12, pp. 1338-1346, 2011.
  26. P. Rana, R. Bhargava, and O. A. Bég, "Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium," Computers & Mathematics with Applications, vol. 64, pp. 2816-2832, 2012.
  27. A. Aziz, "A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition," Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 1064-1068, 2009.
  28. E. Magyari, "The moving plate thermometer," International Journal of Thermal Sciences, vol. 47, pp. 1436-1441, 2008.
  29. A. Ishak, "Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition," Applied Mathematics and Computation, vol. 217, pp. 837-842, 2010.
  30. O. D. Makinde, W. A. Khan, and Z. H. Khan, "Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet," International Journal of Heat and Mass Transfer, vol. 62, pp. 526-533, 2013.
  31. N. Bachok, A. Ishak, and I. Pop, "Stagnation point flow toward a stretching/shrinking sheet with a convective surface boundary condition," Journal of the Franklin Institute, vol. 350, pp. 2736-2744, 2013.
  32. S. K. Nandy and T. R. Mahapatra, "Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions," International Journal of Heat and Mass Transfer, vol. 64, pp. 1091-1100, 2013.
  33. N. S. Akbar, "Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition," Chinese Journal of Aeronautics, vol. 26, pp. 1389-1397, 2013.
  34. M. A. A. Hamad, M. J. Uddin, and A. I. M. Ismail, "Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable flat plate with thermal convective surface boundary condition, temperature dependent viscosity and thermal conductivity," Nuclear Engineering and Design, vol. 242, pp. 194-200, 2012.
  35. J. H. Merkin and I. Pop, "The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition," Communications in Nonlinear Science and Numerical Simulation, vol. 16, pp. 3602-3609, 2011.
  36. A. M. Rashad, A. J. Chamkha, and M. Modather, "Mixed convection boundary-layer flow past a horizontal circular cylinder embedded in a porous medium filled with a nanofluid under convective boundary condition," Computers & Fluids, vol. 86, pp. 380-388, 2013.
  37. O. D. Makinde and A. Aziz, "MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition," International Journal of Thermal Sciences, vol. 49, pp. 1813-1820, 2010.
  38. O. D. Makinde and A. Aziz, "Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition," International Journal of Thermal Sciences, vol. 50, pp. 1326-1332, 2011.
  39. O. D. Makinde, T. Chinyoka, and L. Rundora, "Unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions," Computers & Mathematics with Applications, vol. 62, pp. 3343-3352, 2011.
Siti Hidayah Muhad Saleh , Norihan Md Arifin , Roslinda Mohd Nazar , Ioan Pop (2016). MHD Flow of a Nanofluid at the Forward Stagnation Point of an Infinite Permeable Wall with a Convective Boundary Condition. International Journal of Mathematical Research, 5(2): 138-153. DOI: 10.18488/journal.24/2016.5.2/24.2.138.153
The steady magnetohydrodynamic (MHD) flow of a nanofluid at the forward stagnation point of an infinite permeable wall is investigated in this study. A mathematical model has been constructed and the governing partial differential equations are converted into ordinary differential equations by similarity transformation. The similarity equations are solved numerically by a shooting technique. Results for the surface shear stresses, surface heat transfer, and velocity, nanoparticle fraction and temperature profiles are presented in tables and in some graphs. Effects of the magnetic parameter  , constant mass flux   Biot number  , Brownion  motion parameter  thermophoresis parameter   and Lewis number   are examined. The present results are compared with previously available numerical results obtained using other methods of solution, and they are found to be in good agreement.
Contribution/ Originality
This study documents important features of MHD stagnation point flow with the effect of convective boundary condition also suction and injection. The paper's contribution is finding that the development of skin friction, heat flux and mass flux, with the velocity, temperature and nanoparticle fraction profiles, in tables and graphs.

Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers

Pages: 131-137
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Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers

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DOI: 10.18488/journal.24/2016.5.2/24.2.131.137

Kirtiwant P. Ghadle , Priyanka A. Pathade

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  1. M. Gaspard, Optimal transportation. USA: American Society (AMS) AMS Press, 2003.
  2. F. L. Hitchcock, The hitchcock transportation problem. Nerlin Heidelberg: Springer, 1988.
  3. P. Pandian and G. Natrajan, "A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problem," Applied Mathematical Sciences, vol. 4, pp. 79-90, 2010.
  4. A. Thamaraiselvi and R. Santhi, "Optimal solution of fuzzy transportation problem using hexagonal fuzzy numbers," International Journal: Scientific and Engineering Research, vol. 6, pp. 2229-5518, 2015.
  5. L. A. Zadeh, "Fuzzy sets," Information and Control, vol. 8, pp. 338-353, 1965.
  6. R. Anandhi, "An optimum solution for solving fuzzy pentagonal transportation problem," International Journal: Scientific Research and Development, vol. 11, pp. 2321-0613, 2016.
  7. S. Chandrasekaran, "Fuzzy transportation problem of hexagon number with alpha cut and ranking technique," International Journal: Scientific Engineering and Applied Science, vol. 5, pp. 2395-3470, 2015.
  8. S. Chandrasekaran, "Ranking of heptagon number using zero suffix method," International Journal: Science and Research, vol. 4, pp. 2319-7064, 2013.
  9. R. J. Timothy, Fuzzy logic with engineering applications. New Mexico, USA: John Wiley & Sons, 2004.
  10. K. Khadhirvel and K. Balamurugan, "Method for solving the transportation problem using trapezoidal fuzzy numbers," International Journal: Engineering and Applications, vol. 5, pp. 2154-2158, 2012.
  11. B. Thangaraj and M. Priyadharsini, "Fuzzy transportation problem with the value and ambiguity indices of trapezoidal intutionistic fuzzy number," International Journal: Mathematical Science with Computer Applications, vol. 3, pp. 427- 437, 2015.
  12. S. Poonam, "Unbalanced fuzzy transportation problem with robust ranking technique," Asian Journal: Current Engineering and Math’s, vol. 1, pp. 94-97, 2012a.
  13. S. Poonam, "Fuzzy transportation problem of triangular numbers with alpha cut and ranking technique," IOSR Journal: Engineering, vol. 2, pp. 1162-1164, 2012b.
  14. R. Deepika, "A method for unbalanced transportation problem in fuzzy environment," Indian Academy of Sciences, vol. 3, pp. 573-581, 2014.
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Kirtiwant P. Ghadle , Priyanka A. Pathade (2016). Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers. International Journal of Mathematical Research, 5(2): 131-137. DOI: 10.18488/journal.24/2016.5.2/24.2.131.137
A fuzzy transportation problem (FTP) includes cost, supply and demand of transportation problems. Its numbers are fuzzy numbers. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Present research paper points out a technique with an alpha cut, optimal solution for solving transportation problem. We suggest a technique to find the fuzzy optimal solution on scales of transportation problem and propose a new hexagonal representation of fuzzy numbers. In general, the comparison of balanced fuzzy transportation problem (BFTP) and unbalanced fuzzy transportation problem (UFTP) shows that the optimal transportation cost of UFTP is less than BFTP.
Contribution/ Originality
This study contributes in networking for transportation. This study uses new estimation methodology. This study originates optimal solution and comparison between BFTP and UFTP. This study investigated comparatively. This paper contributes the first logical analysis that is minimizes or maximizes objective solution is an optimal solution in hexagonal fuzzy numbers.

The Hartman-Wintner Law of the Iterated Logarithm for Noncommutative Martingales

Pages: 123-130
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The Hartman-Wintner Law of the Iterated Logarithm for Noncommutative Martingales

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DOI: 10.18488/journal.24/2016.5.2/24.2.123.130

Bright O. Osu , Philip U. Uzoma

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  1. H. Bauer, Probability theory de Gruyter studies in mathematics vol. 23. Berlin: Walter de Gruyter & Co, 1996.
  2. W. F. Stout, "A martingale analogue of Kolmogonov’s law of the iterated logarithm  Z. Wahrscheinlichkeits theorie and verw," GEebiete, vol. 15, pp. 279 – 290, 1970.
  3. W. F. Stout, "The Hartman-wintner law of the iterated logarithm for martingales," Ann. Math. Statist., vol. 41, pp. 2158 – 2160, 1970.
  4. M. Ledoux and M. Talagrand, Probability in banach spaces, ergebnisse der mathematik und ihrer grenzgebiete (3) [Results in Mathematics and Related Area (3)] vol. 23. Berlin: Springer – Verlag, 1991.
  5. B. O. Osu and P. U. Uzoma, "A non-commutative martingale with a stochastic differential equation obeying the law of iterated logarithm LIL," International Journal of Applied Science and Mathematics, vol. 3, pp. 2394-2894, 2016.
  6. M. Junge and Q. Xu, "Non-commutative burkholoder/rosenthal inequalities," Ann. Probab., vol. 31, pp. 948 – 995, 2003.
  7. M. Konwerska, "The law of the iterated logarithm in non-commutative probability proquest LLC. Ann Arbor. MI," Thesis (Ph.D) University of Illinois of Urbana-Champaign MR2712889, 2008.
  8. T. Fack and H. Kosaki, "Generalized s- numbers of τ- measurable operators, pacific," J. Math, vol. 123, pp. 269 – 300, 1986.
  9. M. Konkwerska, "The law of the iterated logarithm in noncommutative probability preprint," ProQuest LLC, Ann Arbor, MI, 2008. Thesis (Ph.D.){University of Illinois at Urbana-Champaign, 2012.
  10. A. De Acosta, "A new proof of the Hartman-wintner law of the iterated Logarithm," Annals of Probability, vol. 11, pp. 270-276, 1983.
  11. M. Junge and Q. Xu, "Non-commutative maximal ergodic theorems," J. Amer. Math. Soc., vol. 20, pp. 385 – 439, 2007.
  12. M. Junge, "Doob’s inequality for non-commutative martingales," J. Reine Angew. Math, vol. 549, pp. 149 – 190, 2002.
  13. M. Junge and Q. Zeng, "Noncommutative martingale deviation and Poincar e type inequalities with applications," Probab. Theory Related Fields, pp. 1-59. Doi: 10.1007/s00440-014-0552-1, 2014.
  14. W. F. Stout, "A martingale analogue of Kolmogorov’s law of the iterated logarithm Z. Wahrscheinlickeits theorie and verw," Gebiete, vol. 15, pp. 279 – 290, 1970.
  15. Q. Zeng, "Kolmogorov’s law of the iterated Logarithm for noncommutative martingales," Ann. Inst. Henri Poincare Probab. Stat., pp. 1-9. Available: 1212.1504, 2014.
Bright O. Osu , Philip U. Uzoma (2016). The Hartman-Wintner Law of the Iterated Logarithm for Noncommutative Martingales. International Journal of Mathematical Research, 5(2): 123-130. DOI: 10.18488/journal.24/2016.5.2/24.2.123.130
In this study, we prove one of the fundamental strong laws of classical probability theory, the Hartman-Wintner’s law of the iterated logarithm for non-commutative martingale using a simple exponential inequality.

Contribution/ Originality
This study contributes in the existing literature by proving the Hartman-Wintner’s law of the iterated logarithm for non-commutative martingale using a simple exponential inequality as a counterpart of the Kolmogorov’s law of the law iterated logarithm.

A Simple Criterion for the Non-Existence of Limit Cycles of a Lienard System

Pages: 119-122
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A Simple Criterion for the Non-Existence of Limit Cycles of a Lienard System

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DOI: 10.18488/journal.24/2016.5.2/24.2.119.122

Makoto HAYASHI

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  1. J. Graef, "On the generalized Liénard equation with negative damping," Journal of Differential Equations, vol. 12, pp. 34-62, 1992.
  2. M. Cioni and G. Villari, "An extention of Dragilev’s theorem for the existence of periodic solution of the Liénard equation," Nonlinear Analysis, vol. 20, pp. 345-351, 2015.
  3. A. Gasull and A. Guillamon, "Non-existence of limit cycles for some predator-prey systems," Differential. Equations and Dynamical  Systems, vol. 3, pp. 345-366, 1995.
  4. M. Hayashi, "On uniqueness of the closed orbit of the Liénard system," Mathematica Japonicae, vol. 46, pp. 371-376, 1997.
  5. M. Hayashi, "Non-existence of homoclinic orbits and global asymptotic stability of FitzHugh-Nagumo system," Vietnam Journal of Mathematics, vol. 27, pp. 335-343, 1999.
Makoto HAYASHI (2016). A Simple Criterion for the Non-Existence of Limit Cycles of a Lienard System. International Journal of Mathematical Research, 5(2): 119-122. DOI: 10.18488/journal.24/2016.5.2/24.2.119.122
In this paper, as an application in our results, the non-existence of limit cycles for the Liénard system  x ̇ = y –F (x), y ̇=-g(x)  with F (x)=(x^2-x) e^(-x)  (x≥-1)  and 5(x^2+x) e^(x+2)+2e (x≤-1),g(x)=x is discussed by the simple criterion. Graef [1] in 1971 has studied the uniformly boundedness of the solution orbits under the condition (C1) and further proved the existence of limit cycles under the conditions (C1) and (C2) . Recently, Cioni and Villari [2] in 2015 gave the same result as in Graef [1] under the conditions (C1) and (C3) includes (C2). Our aim is to discuss on the case of which (C1) is satisfied, but (C3) is not satisfied. As the result, we shall give the simple criterion for the non-existence of limit cycles for a Liénard system with these conditions.

Contribution/ Originality

Finite Difference Method Applied to an Unsteady Magnetohydrodynamic Newtonian Fluid with Wall Slip in Darcy-Forchheimer Porous Medium

Pages: 111-118
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Finite Difference Method Applied to an Unsteady Magnetohydrodynamic Newtonian Fluid with Wall Slip in Darcy-Forchheimer Porous Medium

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DOI: 10.18488/journal.24/2016.5.2/24.2.111.118

Oyelami, Funmilayo H , Jimoh, Abdulwaheed , Saka-Balogun O.Y.

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  1. A. Mehmood and Ali, "The effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planer channel," Rom. Journal of Physics, vol. 52, pp. 85-91, 2007.
  2. M. K. Mazumdar and R. K. Deka, "MHD flow past an impulsively started infinite vertical plate in presence of thermal radiation," Rom. Journal of Physics, vol. 52, pp. 565-573, 2007.
  3. P. Sibanda and O. D. Makinde, A mathematical introduction to incompressible flow. Harare: University of Zimbabwe Publications 2000.
  4. O. D. Makinde, B. I. Olajuwon, and A. W. Gbolagade, "Adomian decomposition approach to a boundary layer flow with thermal radiation past a moving vertical porous plate," Int. Journal of Applied Maths and Mech, vol. 3, pp. 62-70, 2007.
  5. M. Yurusoy and M. Pakdemirili, "Exact solutions of boundary layer equations of a special non-Newtonian fluid over a stretching sheet," Mechanical Research Communication, vol. 26, pp. 171-175, 1999.
  6. J. W. Marques, G. M. Kremer, and F. M. Shapiro, "Coutte flow with slip and jump boundary conditions," Continumm Mech. Thermodynam, vol. 12, pp. 379-386, 2000.
  7. A. R. A. Khaled and K. Vafai, "The effect of the slip condition on stokes and coutte flows due to an oscillating wall exact solutions," Int. J. Nonlinear Mech, vol. 39, pp. 795–809, 2004.
  8. O. D. Makinde and E. Osalusi, "MHD steady flow in a channel with slip at the permeable boundaries," Rom. J. Phys., vol. 51, pp. 319-328, 2006.
  9. N. C. Sacheti, P. Chandran, and A. K. Singh, "An exact solution for unsteady magnetohydrodynamic free convection flow with constant heat flux," Int. Commun Heat Mass Transf., vol. 21, pp. 131–142, 1994.
  10. P. Chandran, N. C. Sacheti, and A. K. Singh, "Unsteady hydromagnetic free convection flow with heat flux and accelerated boundary motion," J. Phys. Soc. Jpn., vol. 67, pp. 124–129, 1998.
  11. P. Ganesan and G. Palani, "Natural convection effects on impulsively started inclined plate with heat and mass transfer," Heat Mass Transf., vol. 39, pp. 277–283, 2003.
  12. C. Samiulhaq, I. Fetecau , A. F. Khan, and S. Shafie, "Radiation and porosity effects on the magnetohydrodynamic flow past an oscillating vertical plate with uniform heat flux," Z Naturforsch, vol. 67a, pp. 572–580, 2012.
  13. P. Chandran, N. C. Sacheti, and A. K. Singh, "Natural convection near a vertical plate with ramped wall temperature," Heat Mass Transf., vol. 41, pp. 459–464, 2005.
Oyelami, Funmilayo H , Jimoh, Abdulwaheed , Saka-Balogun O.Y. (2016). Finite Difference Method Applied to an Unsteady Magnetohydrodynamic Newtonian Fluid with Wall Slip in Darcy-Forchheimer Porous Medium. International Journal of Mathematical Research, 5(2): 111-118. DOI: 10.18488/journal.24/2016.5.2/24.2.111.118
This study investigated the effects of magnetic field, thermal radiation and wall slip on a Newtonian, incompressible, viscous fluid flowing through a saturated porous medium. Boundary conditions for slip at the wall hold in the fluid. The governing equations are formulated, simplified and non-dimensionalised. The dimensionless equations were solved with the help of Crank Nicolson’s finite difference method. This method converges faster and it is unconditionally stable. Numerical results are presented with the aid of graph to account for the fluid parameters affecting the flow on velocity and temperature profiles.

Contribution/ Originality
This study contributes in the existing literature of Newtonian fluids. Series of practical problems involves either Newtonian or non-Newtonian fluids. This study uses new estimation methodology of analyzing the heat transfer properties of Newtonian fluids. This study originates new formula for solving non-linear partial differential equations using Crank Nicolson finite difference method. This study is one of very few studies which have investigated the heat transfer in a Darcy-Forchheimer porous medium. The paper's primary contribution is finding the effects of various thermo physical parameters affecting the flow. This study documents a less well-known Darcy-Forchheimer porous medium by finding the effects of magnetic field, thermal radiation and wall slip on a Newtonian fluid in the presence of viscous dissipation.

Cubic Dual Ideals in BCK-Algebras

Pages: 103-110
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Cubic Dual Ideals in BCK-Algebras

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DOI: 10.18488/journal.24/2016.5.2/24.2.103.110

B. Satyanarayana , A.A.A. Agboola , U. Bindu Madhavi

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  1. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning," I, Information Sci. and Control, vol. 8, pp. 199-249, 1975.
  2. Y. Imai and K. Iseki, "On axioms systems of proposition calculi XIV," Proc. Japan Acad., vol. 42, pp. 19-22, 1996.
  3. Y. B. Jun, C. S. Kim, and K. O. Yang, "Cubic sets," Annals of Fuzzy Mathematics and Informatics, vol. 4, pp. 83–98, 2012.
  4. B. Satyanarayana, D. Ramesh, and P. R. Durga, "On interval-valued intuitionistic fuzzy dual ideals of BF-algebras," Annals of the Constantin Brancusi University of Targu Jiu. Eng. Series, vol. 3, pp. 116-126, 2011.
  5. J. Meng, "Some results on dual ideals in BCK-algebras," J. Northwest, Univ., vol. 16, pp. 12-16, 1986.
  6. J. Meng and Y. B. Jun, "Fuzzy dual ideals in BCK-algebras," Comm. Korean Math. Soc., vol. 8, pp. 225-231, 1993.
  7. R. Biswas, "Rosenfeld’s fuzzy subgroups with interval-valued membership function," Fuzzy Sets and Systems, vol. 63, pp. 87-90, 1994.
  8. Y. B. Jun, C. S. Kim, and J. G. Kang, "Cubic q-ideals of BCI algebras," Annals of Fuzzy Mathematics and Informatics, vol. 1, pp. 25–34, 2011.
B. Satyanarayana , A.A.A. Agboola , U. Bindu Madhavi (2016). Cubic Dual Ideals in BCK-Algebras. International Journal of Mathematical Research, 5(2): 103-110. DOI: 10.18488/journal.24/2016.5.2/24.2.103.110
In this paper we introduce the concept of cubic set to dual sub algebras and dual ideals in BCK-algebras and investigate some of its properties. The relationship between dual sub algebras and cubic dual sub algebras are given.

Contribution/ Originality
The primary contribution of this paper is application of cubic set to dual ideals in BCK-algebras and investigates some of its properties. This study originates new definition cubic dual ideal in BCK-algebras.

Retracted: Applications of Mathematical Modeling for Sensitivity and Sustainability in Supply Chain Flexibility

Pages: 75-102
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Retracted: Applications of Mathematical Modeling for Sensitivity and Sustainability in Supply Chain Flexibility

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DOI: 10.18488/journal.24/2016.5.1/24.1.75.102

G. M. G Farok , M. I.M. Wahab

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  1. L. K. Duclos, R. J. Vokurka, and R. R. Lummus, "A conceptual model of supply chain flexibility," Industrial Management & Data Systems, vol. 103, pp. 446-456, 2003.
  2. H. Y. H. R. Choi, "A sales agent for part manufacturers," VMSA, Decision Support System, vol. 28, pp. 333-346, 2000.
  3. F. C. H. K. Chan, "Comparative study of adaptability and flexibility in distributed manufacturing supply chains," Decision Support Systems, vol. 48, pp. 331-341, 2010.
  4. S. D. Grigore, "Supply chain flexibility," Romanian Economic and Business Review, vol. 2, pp. 66-70, n.d.
  5. K. Sanchoy and L. A. M. Das, "Modeling the flexibility of order quantities and lead-times in supply chains," Int. J. Production Economics, vol. 85, pp. 171-181, 2003.
  6. L. J. R. Zhiying, "A multi-objective supplier selection model under stochastic demand conditions," Int. J. Production Economics, vol. 105, pp. 150-159, 2007.
  7. C. Tang and T. Brian, "The power of flexibility for mitigating supply chain risks," Int. J. Production Economics, vol. 116, pp. 12-27, 2008.
  8. A. S. Sethi, "Flexibility in manufacturing," A Survey International Journal of Flexible Manufacturing Systems, vol. 2, pp. 289-328, 1990.
  9. K. H. Wathne and J. B. Heide, "Relationship governance in a supply chain network," Journal of Marketing, vol. 68, pp. 73-89, 2004.
  10. K. A. K. Saadettin Erhan, "Evaluating supply chain flexibility with order quantity constrains and lost sales," Int. J. Production economics, vol. 126, pp. 181-188, 2010.
  11. M. Abrahamsson, N. Aldin, and F. Stahre, "Logistics platforms for improved strategic flexibility," International Journal of Logistics Research and Applications, vol. 6, pp. 85-106, 2003.
  12. B. M. Benita, "Measuring supply chain performance," International Journal of Operations and Production Management, vol. 19, pp. 275-292, 1999.
  13. T. Davis, "Effective supply chain management," Management Review, vol. 8, pp. 35-46, 1993.
  14. E. T. Tachizawa and G. T. Cristina, "Drivers and sources of supply flexibility: An exploratory study," International Journal of Operations & Production Economics, vol. 27, pp. 1115-1136, 2007.
  15. H. Lee and S. Whang, "Information sharing in a supply chain," International Journal of Technology Management, vol. 20, pp. 373-387, 2000.
  16. N. Pujawan, "Assessing supply chain flexibility: A conceptual framework and a case study," International Journal of Integrated Supply Management, vol. 1, pp. 79-97, 2004.
  17. R. R. Lummus, R. J. V. Okurka, and L. K. Duclos, "Delphi study on supply chain flexibility," International Journal of Production Research, vol. 43, pp. 2687-2708, 2005.
  18. D. K. Sanchoy and A.-M. Layek, "Modeling the flexibility of order quantities and lead-times in supply chains," International Journal of Production Economics, vol. 23, pp. 171-181, 2003.
  19. U. Sezer and S. M. Glen, "Matching product architecture and supply chain design," Production and Operations Management, vol. 20, pp. 16-31, 2011.
  20. V. Shawnce, C. Roger, and D. Cornelia, "Supply chain management: An empirical study," Journal of Supply Chain Management, vol. 35, pp. 16-24, 1999.
  21. M. I. M. Wahab and S. J. Stoyan, "A dynamic approach to measure machine and routing flexibilities of manufacturing systems," International Journal of Production Economics, vol. 13, pp. 895-913, 2008
  22. R. B. Chase, F. R. Jacobes, and N. J. Aquilano, Operations management for competitive advantage. Boston, MA: Irwin/ McGraw-Hill, 2004.
  23. J. Gosling, "Naim, M. (Eds). European operations management association (EuroMA)," presented at the Annual EurOMA Conference, Göteborg, Sweden, 2009.
  24. S. Ian, "Logistics and supply chain integration," Journal of Manufacturing Technology Management, vol. 16, pp. 890-908, 2007.
  25. S. Wadhwa and K. S. Rao, "Flexibility: An emerging meta-competence for managing high technology," International Journal of Technology Management, vol. 19, pp. 820-845, 2000.
  26. V. M. Virolainen, "A survey of procurement strategy development in industrial companies," International Journal of Production Economics, vol. 56, pp. 677-688, 1998.
  27. H. L. Lee, "A triple a supply chain," Harvard Business Review, vol. 82, pp. 102-112, 2004.
  28. R. R. Lummus, R. J. Vokurka, and K. L. Alber, "Strategic supply chain planning," International Production and Inventory Management Journal, vol. 39, pp. 49-58, 1998.
  29. B. Jin, "Achieving an optimal global versus domestic sourcing balance under demand uncertainty," International Journal of Operations and Production Management, vol. 24, pp. 1292-1306, 2004.
  30. H. Tsubone and M. Horikawa, "Impact of various flexibility types in a hybrid fabrication / assembly production system," International Journal of Production Economics, vol. 60-61, pp. 117-123, 1999.
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G. M. G Farok , M. I.M. Wahab (2016). Retracted: Applications of Mathematical Modeling for Sensitivity and Sustainability in Supply Chain Flexibility. International Journal of Mathematical Research, 5(2): 75-102. DOI: 10.18488/journal.24/2016.5.1/24.1.75.102
Supply Chain Management (SCM) demands management of complex dependencies for sensitivity and sustainability on contest of teams, departments, drivers and matrices. It requires risk analysis of global partnerships, win-win contracts and sharing agreements with relevant companies. Supply Chain flexibility, drivers and metrics may include measurements for procurement, production, transportation, inventory, warehousing, material handling, packaging and customer service. There are hundreds of sensitivity that can be used to score Supply Chain Management performance. These results would lead to support and accommodate the sustainability which can be influenced by supply strategies and decisions on supply chain flexibility.

Contribution/ Originality
This study derives new formula to obtain a mathematical relationship among supply chain elements. This calculates the strategy of manufacturers, market and supplier for measures global supply chain flexibility.  These writers would be able to explain that this graduate level research is their own contribution and it can be used as a guideline for future researchers.