Volume-2 ~ Issue-5
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Paper Type | : | Research Paper |
Title | : | Use of Ordinal Dummy Variables in Regression Models |
Country | : | Nigeria |
Authors | : | I.C.A. Oyeka, C.H. Nwankwo |
: | 10.9790/5728-0250107 | |
Abstract : Many activities and phenomena on earth which are of interest to man and require to be studied are
not quantitative in nature, they are rather qualitative. Sometimes their contributions, as independent variables,
in a multiple regression, to variations in a specified quantitative dependent variable and to characterize them
are of interest. Usually dummy variables with equal spacing are used in generating the design matrix despite its
uninterpretable coefficients. Here a cumulatively coded design matrix is proposed and the coefficients are
interpreted. This method is applied to an illustrative example, alongside two other possible methods, to
demonstrate its applicability, and the proposed method showed a comparatively good performance with an
additional advantage of interpretable coefficients which is very useful for practical purposes.
Keywords:cumulative, dummy, independent, ordinal, qualitative
Keywords:cumulative, dummy, independent, ordinal, qualitative
[1] I.C.A. OYEKA (1993), Estimating effects in ordinal dummy variable regression, "STATISTICA, anno LIII, n. 2" pp. 262-268.
[2] R. P. BOYLE (1970), Path analysis and ordinal data, "American Journal of Sociology", 47, 1970, 461-480.
[3] J. NETER, W. WASSERMAN, M. H. KUTNER (1983), Applied linear regression models (Richard D. Irwin Inc, Illinois).
[4] M. LYONS (1971), Techniques for using ordinal measures in regression and path analysis, in Herbert Costner (ed.)( Sociological Methods , Josey Bass Publishers, San Francisco).
[2] R. P. BOYLE (1970), Path analysis and ordinal data, "American Journal of Sociology", 47, 1970, 461-480.
[3] J. NETER, W. WASSERMAN, M. H. KUTNER (1983), Applied linear regression models (Richard D. Irwin Inc, Illinois).
[4] M. LYONS (1971), Techniques for using ordinal measures in regression and path analysis, in Herbert Costner (ed.)( Sociological Methods , Josey Bass Publishers, San Francisco).
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Paper Type | : | Research Paper |
Title | : | On Generalized Stancu's Polynomials |
Country | : | K S A |
Authors | : | Anwar Habib |
: | 10.9790/5728-0250811 | |
Abstract:We have tested the convergence of the Generalized Stancu's Polynomial 𝑅𝛼𝑛 𝑓,𝑥 and have also tested the degree of approximation of Lebesgue integrable functions by 𝑅𝛼𝑛 𝑓,𝑥
[1] Anwar Habib (1981). On the degree of approximation of functions by certain new Bernstein type Polynomials. Indian J. pure Math. , 12(7):882-888.
[2] Bernstein, S. (1912-13). Démonstration due theorem Weierstrass, fondeé sur le calcul des robabilities. Commun. Soc. Math. Kharkow(2), 13,1-2
[3] Kantorovitch, L.A.(1930). Sur certains développments suivant lés pôlynômes dé la forme S.Bernstein I,II. C.R. Acad. Sci. URSS,20,563-68,595-600.
[4] Lorentz, G.G. (1955). Bernstein Polynomials. University of Toronto Press, Toronto
[5] Popoviciu,T. (1935). Sur l'approximation des fonctions convex-es d' ordre supérierur. Mathematica (cluj) 10,49-54.
[6] Stancu, D.D. : Approximation of function by a new class of linear Polynomial operator. Rev. Roum. Math. Pures at Appl. No. 8, pp.1173-1194. Bucharest 1968
[2] Bernstein, S. (1912-13). Démonstration due theorem Weierstrass, fondeé sur le calcul des robabilities. Commun. Soc. Math. Kharkow(2), 13,1-2
[3] Kantorovitch, L.A.(1930). Sur certains développments suivant lés pôlynômes dé la forme S.Bernstein I,II. C.R. Acad. Sci. URSS,20,563-68,595-600.
[4] Lorentz, G.G. (1955). Bernstein Polynomials. University of Toronto Press, Toronto
[5] Popoviciu,T. (1935). Sur l'approximation des fonctions convex-es d' ordre supérierur. Mathematica (cluj) 10,49-54.
[6] Stancu, D.D. : Approximation of function by a new class of linear Polynomial operator. Rev. Roum. Math. Pures at Appl. No. 8, pp.1173-1194. Bucharest 1968
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Abstract: The problem of MHD flow and heat transfer in a Newtonian viscous incompressible fluid over a stretching sheet with temperature gradient dependent heat sink/source and radiation is investigated. The governing partial differential equations are converted into ordinary differential equations by similarity transformation technique . The effects of viscous dissipation, work due to deformation, thermal radiation are considered in the energy equation and the variations of dimensionless surface temperature as well as the heat transfer characteristics with various values of non-dimensional parameters like Prandtl number, suction parameter , radiation parameter, temperature gradient dependent heat sink parameter are graphed and tabulated. The heating process of the type i ) the sheet with prescribed surface temperature (PST case) is studied.
Key words; MHD, viscous fluid, stretching sheet, radiation parameter, temperature gradient dependent heat sink,
Key words; MHD, viscous fluid, stretching sheet, radiation parameter, temperature gradient dependent heat sink,
[1] A. Rapits, C. Perdikis, Viscoelastic Flow by the Presence of Radiation. ZAMM, 78 (1998), 277-279.
[2] A. Raptis, Technical note, Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation. Int. J. Heat Mass Transfer, 41 (1998.), 2865-2866.
[3] A. Raptis, Radiation and Viscoelastic Flow. Int. Comm. Heat Mass. Transfer, 26, (1999), 889-895.
[4] A. Raptis, C. Perdikis, H. S. Takhar, Effect of Thermal Radiation on MHD Flow. Appl. Math. Comput. 153 (2004), 645-649.
[5] Ajay Kumar Singh., Heat transfer and boundary layer flow past a stretching porous wall with temperature gradient dependent heat sink. J.E.H.M.T., 28 (2006), 109-125.
[6] Angirasa, D., Peterson, G.P., and Pop, I., Combined Heat Mass Transfer by Convection in a Saturated Thermally Stratified Porous Medium. Numerical Heat Transfer, A31 (1997), 255-271.
[7] Anjalidevi, S.P., and Thiyagarajan, M., Nonlinear Hydromagnetic Flow and Heat Transfer Over a Surface Stretching with a Power Law Velocity, Heat and Mass Transfer, 38 (2002), 723-726.
[8] B.S.Dandapat, A.S. Gupta, Flow and Heat Transfer in a Visco-elastic Fluid over a Stretching Sheet.Int. J. Non-Linear Mech, 24 (1989), 215-219.
[9] Hong, J. T., and Tien, C.L., Analysis of Thermal Dispersion, Effect on Vertical Plate Natural Convection in Porous Media. International Journal of Heat Mass Transfer, 30 (1987), 143-150.
[10] Khan, S.K., Abel, M.S., and Sonth, R.M., Visco-elastic MHD Flow Heat and Mass Transfer Over a Stretching Sheet with Dissipation of Energy and Stress Work. Heat and Mass Transfer, 40 (2004), 47-57.
[2] A. Raptis, Technical note, Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation. Int. J. Heat Mass Transfer, 41 (1998.), 2865-2866.
[3] A. Raptis, Radiation and Viscoelastic Flow. Int. Comm. Heat Mass. Transfer, 26, (1999), 889-895.
[4] A. Raptis, C. Perdikis, H. S. Takhar, Effect of Thermal Radiation on MHD Flow. Appl. Math. Comput. 153 (2004), 645-649.
[5] Ajay Kumar Singh., Heat transfer and boundary layer flow past a stretching porous wall with temperature gradient dependent heat sink. J.E.H.M.T., 28 (2006), 109-125.
[6] Angirasa, D., Peterson, G.P., and Pop, I., Combined Heat Mass Transfer by Convection in a Saturated Thermally Stratified Porous Medium. Numerical Heat Transfer, A31 (1997), 255-271.
[7] Anjalidevi, S.P., and Thiyagarajan, M., Nonlinear Hydromagnetic Flow and Heat Transfer Over a Surface Stretching with a Power Law Velocity, Heat and Mass Transfer, 38 (2002), 723-726.
[8] B.S.Dandapat, A.S. Gupta, Flow and Heat Transfer in a Visco-elastic Fluid over a Stretching Sheet.Int. J. Non-Linear Mech, 24 (1989), 215-219.
[9] Hong, J. T., and Tien, C.L., Analysis of Thermal Dispersion, Effect on Vertical Plate Natural Convection in Porous Media. International Journal of Heat Mass Transfer, 30 (1987), 143-150.
[10] Khan, S.K., Abel, M.S., and Sonth, R.M., Visco-elastic MHD Flow Heat and Mass Transfer Over a Stretching Sheet with Dissipation of Energy and Stress Work. Heat and Mass Transfer, 40 (2004), 47-57.
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../papers/vol2-issue5/D0252024.pdf
Abstract:In this paper, we study two most general integral operators whose kernels are the product of the
generalized Riemann Zeta function, a general class of polynomials and two multivariable H-function. First, we
established the Mellin-transform of these operators. Then, due to general nature of the kernel, we can obtain a
large number of Mellin-transforms involving product of several useful special functions.
Key Words: Fractional Integral Operators, Generalized Riemann Zeta function, General class of polynomials, Multivariable H-function, Mellin transform.
AMS Subject Classification: primary 26A33, 44A10, secondary 33C60
Key Words: Fractional Integral Operators, Generalized Riemann Zeta function, General class of polynomials, Multivariable H-function, Mellin transform.
AMS Subject Classification: primary 26A33, 44A10, secondary 33C60
[1] R. Patni: A study of generalized hypergeometric polynomials and special functions of several complex variables with their
applications, Ph.D. Thesis, Univ. of Rajasthan, Jaipur, India, 2001.
[2] A. Erdélyi et al.: Higher Transcendental Functions, Vol.1, McGraw-Hill, New York, 1953.
[3] I.S. Gradshteyn and I.M. Ryzhik: Table of integrals, Series and products, Academic Press, New York and London, 1965.
[4] H.M. Srivastava: A contour integral involving Fox's H-function. Indian J. Math. 14, 1-6 (1972).
[5] H.M. Srivastava and N.P. Singh: The integration of certain products of the multivariable H-function with a general class of polynomials, Rendiconti del Circolo Mathematics di Palermo, 32, 157-187 (1983).
[6] G.S. Olkha and V.B.L. Chaurasia: Series representation for the H-function of general complex variables, Math. Edu., 19: 1, 38-40 (1985).
[7] H.M. Srivastva and R. Panda: Some bilateral generating function for a class of generalized hypergeometeric polynomials, J. Reine.
Angew. Math., 283/284, 265-274 (1976).
[8] B.P. Parashar: Domain and range of fractional integration operators, Math. Japan. 12, 141-145 (1968).
[9] S.L. Kalla and R.K. Saxena: Integral operators involving hypergeometric functions, Math. Zeitschr 108, 231-234 (1969).
[10] A. Erdélyi: On fractional integration and its Application to the theory of Hankel transforms, Quart. J. Math. Oxford Ser. 2, 293-303 (1940).
applications, Ph.D. Thesis, Univ. of Rajasthan, Jaipur, India, 2001.
[2] A. Erdélyi et al.: Higher Transcendental Functions, Vol.1, McGraw-Hill, New York, 1953.
[3] I.S. Gradshteyn and I.M. Ryzhik: Table of integrals, Series and products, Academic Press, New York and London, 1965.
[4] H.M. Srivastava: A contour integral involving Fox's H-function. Indian J. Math. 14, 1-6 (1972).
[5] H.M. Srivastava and N.P. Singh: The integration of certain products of the multivariable H-function with a general class of polynomials, Rendiconti del Circolo Mathematics di Palermo, 32, 157-187 (1983).
[6] G.S. Olkha and V.B.L. Chaurasia: Series representation for the H-function of general complex variables, Math. Edu., 19: 1, 38-40 (1985).
[7] H.M. Srivastva and R. Panda: Some bilateral generating function for a class of generalized hypergeometeric polynomials, J. Reine.
Angew. Math., 283/284, 265-274 (1976).
[8] B.P. Parashar: Domain and range of fractional integration operators, Math. Japan. 12, 141-145 (1968).
[9] S.L. Kalla and R.K. Saxena: Integral operators involving hypergeometric functions, Math. Zeitschr 108, 231-234 (1969).
[10] A. Erdélyi: On fractional integration and its Application to the theory of Hankel transforms, Quart. J. Math. Oxford Ser. 2, 293-303 (1940).
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Paper Type | : | Research Paper |
Title | : | Chaotic Behavior and Strange Attractors in Dynamical Systems |
Country | : | Bangladesh |
Authors | : | Md. Shariful Islam Khan and Md. Shahidul Islam |
: | 10.9790/5728-0252531 | |
Abstract: In this paper, we study the invariant set of dynamical systems in which attractor and non-attractor sets exist. We aim to carve out a small section of the theory of chaotic dynamical systems – that of attractors – and outline its fundamental concepts from a computational mathematics perspective. The motivation for this paper is primarily to define what an attractor is and to clarify what distinguishes its various types (non-strange, strange non-chaotic, and strange chaotic). We discuss the Hénon and Lorenz attractors as important examples of this type of chaotic system.
Keywords: Attractor, Basin of attractor, Chaos, Strange
Keywords: Attractor, Basin of attractor, Chaos, Strange
[1] Ruelle D. and Takens F., On the nature of turbulence, Commun. Math. Phy., 20 (1971), 167-192, and 23 (1971), 343-344.
[2] Temam R., Infinite dimensional dynamical systems in Mechanics and Physics, Springer Verlag, 1988.
[3] Milnor J., On the concept of attractor, Commun. Math. Phy., 99 (1985), 177-195.
[4] Guckenheimer J., Sensitive dependence to initial conditions for one dimensional maps, Commun. Math. Phy., 70 (1979), 133-160.
[5] Hénon M., A two dimensional mapping with a strange attractor, Commun. Math. Phy., 50 (1976), 69-77.
[6] Khan M. S. I. and Islam M. S., Hyperbolic Dynamics in Two Dimensional Maps, Int. J. Pure Appl. Sci. Technol., 11(1) (2012), 57-66.
[7] Benedicks M. and Carleson L., The dynamics of Hénon map, Annals of Mathematics, 133 (1991), 73-169.
[8] Benedicks M. and Young L.-S., Sinai-Bowen-Ruelle measures for certain Hénon maps, Inventions Math., 112 (1993), 541-576.
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[10] Lorenz, E. N., Deterministic nonperiodic flows, Journal of the atmospheric sciences, 20 (1963), 130–141.
[2] Temam R., Infinite dimensional dynamical systems in Mechanics and Physics, Springer Verlag, 1988.
[3] Milnor J., On the concept of attractor, Commun. Math. Phy., 99 (1985), 177-195.
[4] Guckenheimer J., Sensitive dependence to initial conditions for one dimensional maps, Commun. Math. Phy., 70 (1979), 133-160.
[5] Hénon M., A two dimensional mapping with a strange attractor, Commun. Math. Phy., 50 (1976), 69-77.
[6] Khan M. S. I. and Islam M. S., Hyperbolic Dynamics in Two Dimensional Maps, Int. J. Pure Appl. Sci. Technol., 11(1) (2012), 57-66.
[7] Benedicks M. and Carleson L., The dynamics of Hénon map, Annals of Mathematics, 133 (1991), 73-169.
[8] Benedicks M. and Young L.-S., Sinai-Bowen-Ruelle measures for certain Hénon maps, Inventions Math., 112 (1993), 541-576.
[9] Gidea, Marian and Niculescu, Constantin P., Chaotic dynamical systems: An introduction, Craiova University Press, 2002.
[10] Lorenz, E. N., Deterministic nonperiodic flows, Journal of the atmospheric sciences, 20 (1963), 130–141.
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Abstract: Modeling of the stress accumulation process during quasi-static aseismic period in the presence of non planar strike-slip fault in seismically active regions has been considered. A viscoelastic half space was taken to represent the lithosphere-asthenosphere system and forces arising out some tectonic processes e.g. mantle convection and the resulting driving forces, were considered to be the main reason for the accumulation of stress in the lithosphere near the earthquake faults. When the accumulated stresses exceed the frictional and cohesive forces across the fault, a sudden and/or creeping movement across the fault occurs. In this paper the pattern of stress accumulation near the faults and the surface shear strain during the aseismic period have been considered using suitable mathematical techniques including integral transforms and Green's functions. A detail study may lead to an estimation of the time-span between two consecutive seismic events. It is expected that such studies may be useful in earthquake prediction.
Key Words- Aseismic, Earthquake prediction, Stress Accumulation, Strike-slip faults, Viscoelastic.
Key Words- Aseismic, Earthquake prediction, Stress Accumulation, Strike-slip faults, Viscoelastic.
[1] Steketee, J.A. (1958b)."Some geophysical applications of the theory of dislocations". Can. J. Phys., 36, pp. 1168-1198.
[2] Maruyama, T. (1964). "Static elastic dislocations in an infinite and semiinfinite medium". Bull. Earthquake Res. Inst., Tokyo Univ., 42, pp. 289-368.
[3] Maruyama, T. (1966)."On two dimensional dislocation in an infinite and semi-infinite medium". Bull. Earthquake Res. Inst., Tokyo Univ., 44, part 3, pp. 811-871.
[4] Rybicki, K. (1971) : "The elastic residual field of a very long strike-slip fault in the presence of a discontinuity." Bull. Seis. Soc. Am., 61, 79-92.
[5] Lisowski, M. and Savage , J.C. (1979). "Strain accumulation from 1964 to 1977 near the epicentral zone of the 1976-1977 earthquake Swarm Southeast of Palmdale, California". Bull. Seis. Soc. Am., vol-69, pp. 751-756.
[6] Sato, R. (1971). "Crustal due to dislocation in a multilayered medium". Jour. Of Phys. Of Earth, 19, No. 1, pp. 31-46.
[7] Sato, R. (1972). "Stress drop for a finite fault". J. Phys. Earth, 20, pp. 397-407.
[8] Sato, R. and Matsuura, M. (1973). "Static deformation due to the fault spreading over several layers in a multilayered medium, part-I: Displacement". J. Phys. Earth, 21, pp. 227-269.
[9] Chinnery, M.A. (1961). "The deformation of the ground around surface faults". Bull. Seis. Soc. Am., vol-51, pp. 355-372.
[10] Chinnery, M.A. (1963). "The stress changes that accompany strike-slip faulting". Bull. Seis. Soc. Am. vol-53, pp. 921-932.
[2] Maruyama, T. (1964). "Static elastic dislocations in an infinite and semiinfinite medium". Bull. Earthquake Res. Inst., Tokyo Univ., 42, pp. 289-368.
[3] Maruyama, T. (1966)."On two dimensional dislocation in an infinite and semi-infinite medium". Bull. Earthquake Res. Inst., Tokyo Univ., 44, part 3, pp. 811-871.
[4] Rybicki, K. (1971) : "The elastic residual field of a very long strike-slip fault in the presence of a discontinuity." Bull. Seis. Soc. Am., 61, 79-92.
[5] Lisowski, M. and Savage , J.C. (1979). "Strain accumulation from 1964 to 1977 near the epicentral zone of the 1976-1977 earthquake Swarm Southeast of Palmdale, California". Bull. Seis. Soc. Am., vol-69, pp. 751-756.
[6] Sato, R. (1971). "Crustal due to dislocation in a multilayered medium". Jour. Of Phys. Of Earth, 19, No. 1, pp. 31-46.
[7] Sato, R. (1972). "Stress drop for a finite fault". J. Phys. Earth, 20, pp. 397-407.
[8] Sato, R. and Matsuura, M. (1973). "Static deformation due to the fault spreading over several layers in a multilayered medium, part-I: Displacement". J. Phys. Earth, 21, pp. 227-269.
[9] Chinnery, M.A. (1961). "The deformation of the ground around surface faults". Bull. Seis. Soc. Am., vol-51, pp. 355-372.
[10] Chinnery, M.A. (1963). "The stress changes that accompany strike-slip faulting". Bull. Seis. Soc. Am. vol-53, pp. 921-932.
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Paper Type | : | Research Paper |
Title | : | On Fuzzy Complex Derivatives |
Country | : | Iraq |
Authors | : | Pishtiwan O. Sabir, Adil K. Jabbar, Munir A. Al-Khafagi |
: | 10.9790/5728-0254752 | |
Abstract: In this paper, we define and study the concepts of bounded closed complex complement normalized fuzzy numbers, and generalized rectangular valued bounded closed complex complement normalized fuzzy numbers, so that some basic properties and some characterizations are presented. Some important theorems of a fuzzy derivative for fuzzy complex functions which map a regular complex numbers into bounded closed complex complement normalized fuzzy numbers are proved. All this may be a foundation for researching fuzzy complex analysis.
Keywords− Fuzzy numbers, Fuzzy complex numbers, Fuzzy derivatives.
Keywords− Fuzzy numbers, Fuzzy complex numbers, Fuzzy derivatives.
[1] J. J. Buckley, and Y. Qu, Fuzzy complex analysis I: Differentiation, Fuzzy Sets and Systems 41 (1991) 269–284.
[2] J. J. Buckley, Fuzzy complex analysis II: integration, Fuzzy Sets and systems 49 (1992) 171–179.
[3] J. J. Buckley, Fuzzy complex numbers, Fuzzy Sets and systems 33 (1989) 333–345.
[4] Q. P. Cai, The continuity of complex fuzzy function, AISC 62 (2009) 695-704.
[5] Dubois, D. and Prade, H., Towards fuzzy differential calculus, Part 3: Differentiation, Fuzzy Sets and systems 8 (1982) 225-233.
[6] X. Fu, Q. Shen, fuzzy complex numbers and their application for classifiers performance evaluation, Pattern Recognition 44 (2011) 1403-1417.
[7] Z. Guangquan, Fuzzy limit theory of Fuzzy complex numbers, Fuzzy Sets and systems 46 (1992) 227–235.
[8] W. Guijun, Y. Shumin, The convergence of fuzzy complex valued series, BUSEFAL, 69 (1997) 156–162.
[9] M. Ha, W. Pedrycz, L. Zheng, The theoretical fundamentals of learning theory based on fuzzy complex random samples, Fuzzy Sets and systems 160 (2009) 2429-2441.
[10] S. Ma, D. Peng, The fixed point of fuzzy complex number valued mapping AMS 1 (2007) 739-747
[2] J. J. Buckley, Fuzzy complex analysis II: integration, Fuzzy Sets and systems 49 (1992) 171–179.
[3] J. J. Buckley, Fuzzy complex numbers, Fuzzy Sets and systems 33 (1989) 333–345.
[4] Q. P. Cai, The continuity of complex fuzzy function, AISC 62 (2009) 695-704.
[5] Dubois, D. and Prade, H., Towards fuzzy differential calculus, Part 3: Differentiation, Fuzzy Sets and systems 8 (1982) 225-233.
[6] X. Fu, Q. Shen, fuzzy complex numbers and their application for classifiers performance evaluation, Pattern Recognition 44 (2011) 1403-1417.
[7] Z. Guangquan, Fuzzy limit theory of Fuzzy complex numbers, Fuzzy Sets and systems 46 (1992) 227–235.
[8] W. Guijun, Y. Shumin, The convergence of fuzzy complex valued series, BUSEFAL, 69 (1997) 156–162.
[9] M. Ha, W. Pedrycz, L. Zheng, The theoretical fundamentals of learning theory based on fuzzy complex random samples, Fuzzy Sets and systems 160 (2009) 2429-2441.
[10] S. Ma, D. Peng, The fixed point of fuzzy complex number valued mapping AMS 1 (2007) 739-747