Other Useful Journals
- IOSR Journal of Mathematics (IOSR-JM)
- IOSR Journal of Computer Engineering (IOSR-JCE)
- IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
- IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
- IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
- IOSR Journal of VLSI and Signal Processing (IOSR-JVSP)
- IOSR Journal of Environmental Science, Toxicology and Food Technology (JESTFT)
- IOSR Journal of Humanities and Social Science (IOSR-JHSS)
- IOSR Journal of Applied Chemistry (IOSR-JAC)
- IOSR Journal of Applied Physics (IOSR-JAP)
- IOSR Journal of Business and Management (IOSR-JBM)
- IOSR Journal of Pharmacy and Biological Sciences (IOSR-JPBS)
- IOSR Journal of Dental and Medical Sciences (IOSR-JDMS)
- IOSR Journal of Agriculture and veterinary Science (IOSR-JAVS)
IOSR Journal of Mathematics (IOSR-JM)
Volume 4 - Issue 6
- Citation
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Abstract: Recently the unified method for finding traveling wave solutions of non-linear evolution equations
was proposed by one of the authors a. It was shown that, this method unifies all the methods being used to find
these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de
Vries (KdV) equation with space dependent coefficients. A new class of multiple-soliton or wave trains is
obtained.
Keywords: Exact solution, Extended unified method, Korteweg-deVries equation, variable coefficients
Keywords: Exact solution, Extended unified method, Korteweg-deVries equation, variable coefficients
[1] P. J. Olivier, Application of Lie Groups to Differential Equations. GTM, Vol. 107 ( Berlin, Springer) (1986).
[2] J. Weiss, M. Tabor, G. Carenville, J. Math. Phys., 24, 522 (1983).
[3] R. Conte, Phys. Lett. A., 134, 100-104 (1988).
[4] B. Y. Gou and Z. X. Chen, J. Phys. A Math. Gen., 24, 645-650(1991).
[5] H.I. Abdel-Gawad , J. Statis. Phys., 97, 395-407 (1999).
[6] C. Rogers and W. F. Shadwick, BΓ€cklund Transformations (Academic, New York) (1982).
[7] K. M. Tamizhmani and M. Lakshamanan, J. Phys. A, Math. Gen. , 16 , 3773 (1983).
[8] Y. Xie, J. Phys. A Math. Gen., 37 5229 (2004).
[9] C. Rogers and Szereszewski, J. Phys. A Math. Theor. 42, 40-4015 (2009).
[10] E. Fan, and H. Zhang, Phys. Lett. A 245, 389-392 (1999)
[2] J. Weiss, M. Tabor, G. Carenville, J. Math. Phys., 24, 522 (1983).
[3] R. Conte, Phys. Lett. A., 134, 100-104 (1988).
[4] B. Y. Gou and Z. X. Chen, J. Phys. A Math. Gen., 24, 645-650(1991).
[5] H.I. Abdel-Gawad , J. Statis. Phys., 97, 395-407 (1999).
[6] C. Rogers and W. F. Shadwick, BΓ€cklund Transformations (Academic, New York) (1982).
[7] K. M. Tamizhmani and M. Lakshamanan, J. Phys. A, Math. Gen. , 16 , 3773 (1983).
[8] Y. Xie, J. Phys. A Math. Gen., 37 5229 (2004).
[9] C. Rogers and Szereszewski, J. Phys. A Math. Theor. 42, 40-4015 (2009).
[10] E. Fan, and H. Zhang, Phys. Lett. A 245, 389-392 (1999)
- Citation
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- Reference
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Abstract:A self- starting hybrid linear multistep method for direct solution of the general second-order initial
value problem is considered. The continuous method is used to obtain Multiple Finite Difference Methods
(MFDMs) (each of order 7) which are combined as simultaneous numerical integrators to provide a direct
solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by
conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and
consistent. The superiority of the MFDMs over published work is established numerically.
Keywords: Multiple Finite Difference Methods, Second Order, Boundary Value Problem, Block Methods, Multistep Methods
Keywords: Multiple Finite Difference Methods, Second Order, Boundary Value Problem, Block Methods, Multistep Methods
[1] Awoyemi, D.O., 2003. A P-stable linear multistep method for solving general third order ordinary differential equations. Int. J.
Comput Math., 8: 985-991. DOI: 10.1080/0020716031000079572
[2] Awoyemi, D. and Idowu,O. 2005. A class hybrid collocation methods for third order of ordinary differential equations, Int. J.
Comput. Math., 82: 1287-1293. DOI: 10.1080/00207160500112902.
[3] Fatunla, S.O., (1994). A class of block methods for second order IVPs. Int. J. Comput. Math., 55: 119-133. DOI:
10.1080/00207169508804368
[4] Lambert, J.D., (1973). Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA., ISBN:
10: 0471511943, p: 294.)
[5] Adee, S.O., Onumanyi, P., Sirisena,U.W., and Yahaya,Y.A (2005). Note on starting numerov method more accurately by a hybrid
formula of order four for an initial value problem,. J.Computat. Applied Math., 175: 369-373. DOI: 10.1016/j.cam.2004.06.016.
[6] Jator, S.N(2007). A sixth order linear multistep method for the direct solution of y00 = f(x, y, y0), International Journal of Pure and
Applied Mathematics, 40, No. 4, 457-472.
[7] Jator, S.N and Li, J (2007) A self-starting linear multistep method for a direct solution of the general second order initial value
problem, International Journal of Computer Mathematics Vol. 86, No. 5, May 2009, 827β836
[8] Jator, S.N (2008) Multiple finite difference methods for solving third order ordinary differential equations, International Journal of
Pure and Applied Mathematics, 43, No. 2, 253 - 265.
[9] Mohammmed, U.,Jiya, M and Mohammed, A.A(2010). A class of six step block method for solution of general second order
ordinary differential equations, Pacific Journal of Science and Technology. 11(2):pp273-277.
[10] Mohammmed, U (2011). A class of implicit five step block method for general second order ordinary differential equations. Journal
of Nigerian Mathematical Society (JNMS). vol 30 p 25-39
Comput Math., 8: 985-991. DOI: 10.1080/0020716031000079572
[2] Awoyemi, D. and Idowu,O. 2005. A class hybrid collocation methods for third order of ordinary differential equations, Int. J.
Comput. Math., 82: 1287-1293. DOI: 10.1080/00207160500112902.
[3] Fatunla, S.O., (1994). A class of block methods for second order IVPs. Int. J. Comput. Math., 55: 119-133. DOI:
10.1080/00207169508804368
[4] Lambert, J.D., (1973). Computational Methods in Ordinary Differential Equations (John Willey and Sons, New York, USA., ISBN:
10: 0471511943, p: 294.)
[5] Adee, S.O., Onumanyi, P., Sirisena,U.W., and Yahaya,Y.A (2005). Note on starting numerov method more accurately by a hybrid
formula of order four for an initial value problem,. J.Computat. Applied Math., 175: 369-373. DOI: 10.1016/j.cam.2004.06.016.
[6] Jator, S.N(2007). A sixth order linear multistep method for the direct solution of y00 = f(x, y, y0), International Journal of Pure and
Applied Mathematics, 40, No. 4, 457-472.
[7] Jator, S.N and Li, J (2007) A self-starting linear multistep method for a direct solution of the general second order initial value
problem, International Journal of Computer Mathematics Vol. 86, No. 5, May 2009, 827β836
[8] Jator, S.N (2008) Multiple finite difference methods for solving third order ordinary differential equations, International Journal of
Pure and Applied Mathematics, 43, No. 2, 253 - 265.
[9] Mohammmed, U.,Jiya, M and Mohammed, A.A(2010). A class of six step block method for solution of general second order
ordinary differential equations, Pacific Journal of Science and Technology. 11(2):pp273-277.
[10] Mohammmed, U (2011). A class of implicit five step block method for general second order ordinary differential equations. Journal
of Nigerian Mathematical Society (JNMS). vol 30 p 25-39
- Citation
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Abstract:This paper deals with the determination of thermal stresses in a thin clamped hollow disk under
unsteady temperature field due to point heat source situated at centre along radial and axial direction within it.
A thin hollow disk is considered having arbitrary initial temperature and is subjected to arbitrary heat flux at
the outer circular boundary; whereas inner boundary is at zero heat flux. Also, the upper and lower surfaces of
the disk are at zero temperature. The inner and outer edges of the disk are clamped. The governing heat
conduction equation has been solved by the method of integral transform technique. The results are obtained in
a series form in terms of Bessel's functions. The results have been computed numerically and illustrated
graphically.
Keywords: Heat Conduction, Point Heat Source, Thermal Stresses, clamped hollow disk, Unsteady Temperature
[1] Roy Choudhuri S.K., A note on the quasi-static stress in thin circular plate due to transient temperature applied along the
circumference of a circle over the upper face, Bull. Acad. Polon. Sci., Ser. Sci. Techn., 20, 21, (1972).
[2] Gogulwar V.S. and Deshmukh K.C., Thermal stresses in a thin circular plate with heat sources, Journal of Indian Academy of
Mathematics, 27 (1), 129-141, (2005).
[3] Kulkarni V. S., Deshmukh K. C. and Warbhe S. D., Quasi-Static thermal stresses due to heat generation in a thin hollow circular disk,
J. Thermal Stresses, 31(8), 698-705, (2008).
[4] Deshmukh K.C., Warbhe S.D., Kulkarni V.S., Non-homogeneous steady state heat conduction problem in a thin circular plate and
thermal stresses, Int. J. Thermophysics, 30, 1688-1696, (2009.)
[5] Ozisik M.N., Boundary value problems of heat conduction, International Textbook Company, Scranton, Pennsylvania, 148-163,
(1968).
[6] Nowinski J.L., Theory of thermoelasticity with applications, Sijthoff International Publishers B.V. Alphen aan den Rijn, The
Netherlands, 407, (1978).
circumference of a circle over the upper face, Bull. Acad. Polon. Sci., Ser. Sci. Techn., 20, 21, (1972).
[2] Gogulwar V.S. and Deshmukh K.C., Thermal stresses in a thin circular plate with heat sources, Journal of Indian Academy of
Mathematics, 27 (1), 129-141, (2005).
[3] Kulkarni V. S., Deshmukh K. C. and Warbhe S. D., Quasi-Static thermal stresses due to heat generation in a thin hollow circular disk,
J. Thermal Stresses, 31(8), 698-705, (2008).
[4] Deshmukh K.C., Warbhe S.D., Kulkarni V.S., Non-homogeneous steady state heat conduction problem in a thin circular plate and
thermal stresses, Int. J. Thermophysics, 30, 1688-1696, (2009.)
[5] Ozisik M.N., Boundary value problems of heat conduction, International Textbook Company, Scranton, Pennsylvania, 148-163,
(1968).
[6] Nowinski J.L., Theory of thermoelasticity with applications, Sijthoff International Publishers B.V. Alphen aan den Rijn, The
Netherlands, 407, (1978).
- Citation
- Abstract
- Reference
- Full PDF
Paper Type | : | Research Paper |
Title | : | On Generalized Half Canonical Cosine Transform |
Country | : | India |
Authors | : | A. S. Gudadhe and A.V. Joshi |
: | 10.9790/5728-0462025 | |
Abstract: As generalization of the fractional Cosine transform (FRCT), the Canonical Cosine Transform
(CCT) has been used in several areas, including optical analysis and signal processing. For practical purpose
half canonical cosine transform is more useful. Hence in this paper we have proved some important results
Differentiation property, Modulation property, Scaling property, Derivative property, Parseval's Identity for
half canonical cosine transform (HCCT).
Keywords: Linear canonical transform, Fractional Fourier Transform.
Keywords: Linear canonical transform, Fractional Fourier Transform.
[1] Akay O. and Bertels, (1998): Fractional Mellin Transformation: An extension of fractional frequency concept for scale, 8th IEEE,
Dig. Sign. Proc. Workshop, Bryce Canyan, Utah.
[2] Almeida, L.B., (1994): The fractional Fourier Transform and time- frequency representations, IEEE. Trans. on Sign. Proc., Vol. 42,
No.11, 3084-3091.
[3] A. S. Gudadhe and A.V. Joshi (August - 2012): Generalized Canonical Cosine Transform, International Journal of Engineering
Research & Technology (IJERT) Vol. 1 Issue 6.
[4] Moshinsky, M.(1971): Linear canonical transform and their unitary representation, Jour. Math, Phy.,Vol.12, No. 8 , P. 1772-1783.
[5] Namias V. (1980): The fractional order Fourier transform and its applications to quantum mechanics, Jour. Inst. Math's. App., Vol.
25, 241-265.
[6] Pei and Ding, (2002) : Eigenfunctions of Linear Canonical Transform Vol. 50, No.1.
[7] Pie and Ding, (2002): Fractional cosine, sine and Hartley Transforms, IEEE. Trans. On Sign. Proc. Vol. 50, No.7, 1661-1680.
[8] Sontakke, Gudadhe (2009): Convolution and Rayleigh's Theorem For Generalized Fractional Hartley Transform, EJPAM Vol. 2, No. 1, (162-170)
Dig. Sign. Proc. Workshop, Bryce Canyan, Utah.
[2] Almeida, L.B., (1994): The fractional Fourier Transform and time- frequency representations, IEEE. Trans. on Sign. Proc., Vol. 42,
No.11, 3084-3091.
[3] A. S. Gudadhe and A.V. Joshi (August - 2012): Generalized Canonical Cosine Transform, International Journal of Engineering
Research & Technology (IJERT) Vol. 1 Issue 6.
[4] Moshinsky, M.(1971): Linear canonical transform and their unitary representation, Jour. Math, Phy.,Vol.12, No. 8 , P. 1772-1783.
[5] Namias V. (1980): The fractional order Fourier transform and its applications to quantum mechanics, Jour. Inst. Math's. App., Vol.
25, 241-265.
[6] Pei and Ding, (2002) : Eigenfunctions of Linear Canonical Transform Vol. 50, No.1.
[7] Pie and Ding, (2002): Fractional cosine, sine and Hartley Transforms, IEEE. Trans. On Sign. Proc. Vol. 50, No.7, 1661-1680.
[8] Sontakke, Gudadhe (2009): Convolution and Rayleigh's Theorem For Generalized Fractional Hartley Transform, EJPAM Vol. 2, No. 1, (162-170)
- Citation
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Abstract: The Airy stress function for a vertical dip-slip line source buried in a homogeneous, isotropic,
perfectly elastic half-space with rigid boundary is obtained. This Airy stress function is used to derive closedform
analytical expressions for the stresses and displacements at an arbitrary point of the half-space caused by
vertical dip-slip line source. The variation of the displacements and stress fields with distance from the fault and
depth from the fault is studied numerically.
Keywords β Dip-slip faulting, Half-space, Rigid boundary, Static deformation
Keywords β Dip-slip faulting, Half-space, Rigid boundary, Static deformation
[1] Bonaccorso, A. and Davis, P., Dislocation Modeling of the 1989 Dike Intrusion into the Flank of Mt. Etna, Sicily, J. Geophys. Res.,
vol. 98(3), 1993, 4261-4268.
[2] Bonafede, M. and Danesi, S., Near-field Modifications of Stress Induced by Dyke Injection at Shallow Depth, Geophys. J. Int., vol.
130, 1997, 435-448.
[3] Bonafede, M. and Rivalta, E., The Tensile Dislocation Problem in a Layered Elastic Medium, Geophys. J. Int., vol. 136, 1999a, 341-
356.
[4] Bonafede, M. and Rivalta, E., On Tensile Cracks Close to and Across the Interface Between Two Welded Elastic Half-spaces,
Geophys. J. Int., vol.138, 1999b, 410-434.
[5] Davis, P. M, Surface Deformation Associated with a Dipping Hydrofracture, Journal of Geophysical Research, vol. 88, 1983, 5826-
5836.
[6] Dundurs, J. and Hetenyi, M., Transmission of Force between Two Semi-infinite Solids, ASME, Journal of Applied Mechanics, vol.
32, 1965, 671-674.
[7] Freund, L.B. and Barnett, D.M, A Two-Dimensional Analysis of Surface Deformation due to Dip-Slip Faulting, Bull. Seismol. Soc.
Am.,vol. 66, 1976, 667-675.
[8] Heaton, T. H. and Heaton, R. E., Static Deformation From Point Forces and Point Force Couples Located in Welded Elastic
Poissonian Half-spaces:Implications for Seismic Moment Tensors, Bull. Seism. Soc. Am., vol. 79, 1989, 813-841.
[9] Jungels, P.H. and Frazier, G.A, Finite Element Analyses of the Residual Displacements for an Earthquake Rupture: Source
Parameters for the San Fernando earthquake, J. Geophys. Res., vol. 78, 1973, 5062-5083.
[10] Kumari, G., Singh, S. and Singh, K., Static Deformation of Two Welded Half-spaces Caused by a Point Dislocation Source, Phys.
Earth. Planet, Inter,vol. 73, 1992, 53-76.
vol. 98(3), 1993, 4261-4268.
[2] Bonafede, M. and Danesi, S., Near-field Modifications of Stress Induced by Dyke Injection at Shallow Depth, Geophys. J. Int., vol.
130, 1997, 435-448.
[3] Bonafede, M. and Rivalta, E., The Tensile Dislocation Problem in a Layered Elastic Medium, Geophys. J. Int., vol. 136, 1999a, 341-
356.
[4] Bonafede, M. and Rivalta, E., On Tensile Cracks Close to and Across the Interface Between Two Welded Elastic Half-spaces,
Geophys. J. Int., vol.138, 1999b, 410-434.
[5] Davis, P. M, Surface Deformation Associated with a Dipping Hydrofracture, Journal of Geophysical Research, vol. 88, 1983, 5826-
5836.
[6] Dundurs, J. and Hetenyi, M., Transmission of Force between Two Semi-infinite Solids, ASME, Journal of Applied Mechanics, vol.
32, 1965, 671-674.
[7] Freund, L.B. and Barnett, D.M, A Two-Dimensional Analysis of Surface Deformation due to Dip-Slip Faulting, Bull. Seismol. Soc.
Am.,vol. 66, 1976, 667-675.
[8] Heaton, T. H. and Heaton, R. E., Static Deformation From Point Forces and Point Force Couples Located in Welded Elastic
Poissonian Half-spaces:Implications for Seismic Moment Tensors, Bull. Seism. Soc. Am., vol. 79, 1989, 813-841.
[9] Jungels, P.H. and Frazier, G.A, Finite Element Analyses of the Residual Displacements for an Earthquake Rupture: Source
Parameters for the San Fernando earthquake, J. Geophys. Res., vol. 78, 1973, 5062-5083.
[10] Kumari, G., Singh, S. and Singh, K., Static Deformation of Two Welded Half-spaces Caused by a Point Dislocation Source, Phys.
Earth. Planet, Inter,vol. 73, 1992, 53-76.
- Citation
- Abstract
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Abstract: Deals with the buoyancy effects on laminar mixed convection in vertical channel is considered.
Solutions of the governing parabolic equations are obtained by the use of an implicit finite difference technique
coupled with a marching procedure. The velocity, the temperature and the pressure profiles are presented
graphically for different values of governing parameters like Eckert Number Ek, buoyancy parameter Gr/Re and
Prandtl number Pr and their behaviour discussed.
Keywords: Mixed convection, Vertical channel, Dissipation
Keywords: Mixed convection, Vertical channel, Dissipation
[1] Aung. W. Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, 1987.
[2] Aung. W., and Worku, G., ASME. J. Heat Transfer, Vol. 108, pp.299- 304, 1986.
[3] Aung. W., and Worku, G., ASME. J. Heat Transfer, Vol. 108, pp.485- 488, 1986.
[4] Barletta, A., Int. J. Heat Mass Transfer, Vol.45, pp.641-654, 200
[5] Barletta, A., Int. J. Heat Mass Transfer Vol.48, pp 2042-2049, 2005.
[6] Barletta, A. Zanchini, E., Int. Commun. Heat Mass Transfer Vol. 28, pp.1043-1052, 2001.
[7] Barletta, A., and Zanchini, E., Int. J. Heat Mass Transfer Vol.44, pp 4267-4275, 2001.
[8] Bodoia, J.R., and Osterle, J.F., ASME. J. Heat Transfer, Vol. 84, pp.40-44, 196
[9] Chamkha Ali, J., Int. J. Heat Mass Transfer, Vol.45, pp.2509-2525, 200
[10] Chen, Y.C., and Chung, J.N., ASME J. Heat Transfer, Vol.120, pp.127-131, 1998.
[2] Aung. W., and Worku, G., ASME. J. Heat Transfer, Vol. 108, pp.299- 304, 1986.
[3] Aung. W., and Worku, G., ASME. J. Heat Transfer, Vol. 108, pp.485- 488, 1986.
[4] Barletta, A., Int. J. Heat Mass Transfer, Vol.45, pp.641-654, 200
[5] Barletta, A., Int. J. Heat Mass Transfer Vol.48, pp 2042-2049, 2005.
[6] Barletta, A. Zanchini, E., Int. Commun. Heat Mass Transfer Vol. 28, pp.1043-1052, 2001.
[7] Barletta, A., and Zanchini, E., Int. J. Heat Mass Transfer Vol.44, pp 4267-4275, 2001.
[8] Bodoia, J.R., and Osterle, J.F., ASME. J. Heat Transfer, Vol. 84, pp.40-44, 196
[9] Chamkha Ali, J., Int. J. Heat Mass Transfer, Vol.45, pp.2509-2525, 200
[10] Chen, Y.C., and Chung, J.N., ASME J. Heat Transfer, Vol.120, pp.127-131, 1998.
- Citation
- Abstract
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Paper Type | : | Research Paper |
Title | : | Clique Dominating Sets of Euler Totient Cayley Graphs |
Country | : | India |
Authors | : | M. Manjuri, B. Maheswari |
: | 10.9790/5728-0464649 | |
Abstract: Graph Theory has been realized as one of the most flourishing branches of modern Mathematics
finding widest applications in all most all branches of Sciences, Social Sciences, Engineering, Computer
Science, etc. Number Theory is one of the oldest branches of Mathematics, which inherited rich contributions
from almost all greatest mathematicians, ancient and modern. Using the number theoretic function Euler
totient function we have defined an Euler totient Cayley graph and in this paper we study the Clique domination
parameters of Euler totient Cayley graphs.
Keywords: Cayley Graph, Clique, Complete graph, Dominating clique, Euler totient Cayley Graph
Keywords: Cayley Graph, Clique, Complete graph, Dominating clique, Euler totient Cayley Graph
[1]. Nathanson and B.Melvyn, Connected components of arithmetic graphs, Monat.fur.Math, 29, 1980, 219 β 220.
[2]. L.Madhavi, Studies on domination parameters and enumeration of cycles in some Arithmetic Graphs, Ph. D. Thesis submitted to
S.V.University, Tirupati, India, 2002.
[3]. S.Uma Maheswari, Some Studies on the Product Graphs of Euler Totient Cayley Graphs and Arithmetic ππ Graphs, Ph. D. Thesis submitted to S.P.Women's University, Tirupati, India, 2012.
[4]. S.Uma Maheswari, and B.Maheswari, Domination parameters of Euler Totient Cayley Graphs, Rev.Bull.Cal.Math.Soc. 19 (2),
2011, 207-214.
[5]. O.Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ., 38, Providence, 1962.
[6]. C. Berge, The Theory of Graphs and its Applications, Methuen, London 1962.
[7]. M.B. Cozzens, and L.L. Kelleher, Dominating cliques in graphs, Discrete Math. 86, 1990, 101-116.
[8]. G. Bacso and Z. Tuza, Dominating cliques in P5 β free graphs, Period. Math. Hungar. 21, 1990, 303-308.
[2]. L.Madhavi, Studies on domination parameters and enumeration of cycles in some Arithmetic Graphs, Ph. D. Thesis submitted to
S.V.University, Tirupati, India, 2002.
[3]. S.Uma Maheswari, Some Studies on the Product Graphs of Euler Totient Cayley Graphs and Arithmetic ππ Graphs, Ph. D. Thesis submitted to S.P.Women's University, Tirupati, India, 2012.
[4]. S.Uma Maheswari, and B.Maheswari, Domination parameters of Euler Totient Cayley Graphs, Rev.Bull.Cal.Math.Soc. 19 (2),
2011, 207-214.
[5]. O.Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ., 38, Providence, 1962.
[6]. C. Berge, The Theory of Graphs and its Applications, Methuen, London 1962.
[7]. M.B. Cozzens, and L.L. Kelleher, Dominating cliques in graphs, Discrete Math. 86, 1990, 101-116.
[8]. G. Bacso and Z. Tuza, Dominating cliques in P5 β free graphs, Period. Math. Hungar. 21, 1990, 303-308.
- Citation
- Abstract
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Paper Type | : | Research Paper |
Title | : | A Note on Water Transport Phenomenon by Homotopy Analysis Method |
Country | : | India |
Authors | : | Twinkle Singh, R.K. Singh |
: | 10.9790/5728-0465053 | |
Abstract: In this paper, an analytic technique, named the Homotopy Analysis method (HAM) has
been applied for solving Richard's equation, which is converted into the Basic Burger's equitation,
which shows the well-known equations, to desire the behaviour of the infiltration of unsaturated zones
in soil as a porous medium.
Keywords: Homotopy analysis method, Water transport phenomenon
Keywords: Homotopy analysis method, Water transport phenomenon
[1] Brook, R.H. and A. T. Corey, Hydraulic Properties of Porous Media, Hydrol Paper 3, Colorado State University, Fort Collins, 1964.
[2] Corey, A. T., Mechanics of Immiscible Fluids in Porous Media, Water Resources Publication, Highlands Ranch, CO, 1994, pp: 252.
[3] Davood, D. Ganji, M. Esmaeilpour and E. Moheseni, Application of the Homotopy Perturbation Method to Micropolor Flow in a
Porous Channel, 2009.
[4] Liao, S.J., The proposed homotopy analysis technique for the solution of nonlinear problems. PhD. Thesis, Shanghai Jiao Tong
University, 1992.
[5] Liao, S.J., An explicit, totally analytic approximation of Blasius viscous flow problems. Int. J. Nonlinear Mech., 1999, 34: 759-778.
[6] Liao, S.J., Beyond perturbation; Introduction to the Homotopy Analysis Method. Champan and Hall/CRC Press, Boca Raton,
2003a.
[7] Liao, S.J., On the analytic solution of magneto hydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid
Mech., 2003b, 488:189-212 DOI: 10.1017/S0022112003004865
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=164083
[8] Liao, S.J.,On the homotopy analysis method for nonlinear problems. Applied Mathe. Comput., 147 (2004), pp. 499β
513.10.1016/S0096-3003(02)00790-7
[9] Liao, S.J., A new branch of solutions of boundary-layer flows over a permeable stretching plate. Int. J. Heat Mass Transfer 48
(2005) 2529 2539
[10] M. Ayub, A. Rasheed and T. Hayat.Exact flow of a third grade fluid past a porous plate using homotopy analysis method,
November, Pages 2091-2103 International Journal of Engineering Science Volume 41, Issue 18
[2] Corey, A. T., Mechanics of Immiscible Fluids in Porous Media, Water Resources Publication, Highlands Ranch, CO, 1994, pp: 252.
[3] Davood, D. Ganji, M. Esmaeilpour and E. Moheseni, Application of the Homotopy Perturbation Method to Micropolor Flow in a
Porous Channel, 2009.
[4] Liao, S.J., The proposed homotopy analysis technique for the solution of nonlinear problems. PhD. Thesis, Shanghai Jiao Tong
University, 1992.
[5] Liao, S.J., An explicit, totally analytic approximation of Blasius viscous flow problems. Int. J. Nonlinear Mech., 1999, 34: 759-778.
[6] Liao, S.J., Beyond perturbation; Introduction to the Homotopy Analysis Method. Champan and Hall/CRC Press, Boca Raton,
2003a.
[7] Liao, S.J., On the analytic solution of magneto hydrodynamic flows of non-Newtonian fluids over a stretching sheet. J. Fluid
Mech., 2003b, 488:189-212 DOI: 10.1017/S0022112003004865
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=164083
[8] Liao, S.J.,On the homotopy analysis method for nonlinear problems. Applied Mathe. Comput., 147 (2004), pp. 499β
513.10.1016/S0096-3003(02)00790-7
[9] Liao, S.J., A new branch of solutions of boundary-layer flows over a permeable stretching plate. Int. J. Heat Mass Transfer 48
(2005) 2529 2539
[10] M. Ayub, A. Rasheed and T. Hayat.Exact flow of a third grade fluid past a porous plate using homotopy analysis method,
November, Pages 2091-2103 International Journal of Engineering Science Volume 41, Issue 18
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Paper Type | : | Research Paper |
Title | : | Standard Linear Combination of Incline Vectors |
Country | : | India |
Authors | : | AR. Meenakshi, P. Shakila Banu |
: | 10.9790/5728-0465458 | |
Abstract: We prove that every finite subspace generated by the linearly ordered idempotent elements in an
incline has a unique standard basis. This leads to every finite subspace of a regular incline whose elements are
all linearly ordered has a unique standard basis and thereby we disprove the result of Cao that is "Every
subspace of a finite incline whose idempotent elements are linearly ordered has a unique standard basis". As an
application we exhibit that under certain conditions each vector in a finitely generated subspace of a vector
space has a unique decomposition as a linear combination of the standard basis vectors.
Keywords: incline, regular incline, distributive lattice, basis, standard basis, standard linear combination
Keywords: incline, regular incline, distributive lattice, basis, standard basis, standard linear combination
[1] Z.Q. Cao , K.H, Kim, F.W. Roush, Incline algebra and applications, John Wiley and Sons, New York, 1984.
[2] K.H. Kim, F.W. Roush, Inclines and incline matrices: a survey, Linear algebra appl., 379,457-473(2004).
[3] K.H.Kim, F.W.Roush, Generalized fuzzy matrices, Fuzzy sets and systems, 4 , 293-315 (1980) .
[4] AR.Meenakshi, Fuzzy matrix Theory and its applications, MJP Publishers, Chennai, 2008.
[5] AR.Meenakshi, S. Anbalagan, On regular elements in an incline, Int J. Math. and Math. Sci. (2010) article ID 903063, 12 Pages.
[6] AR.Meenakshi, P.Shakila Banu, Incline relational equations (communicated).
[2] K.H. Kim, F.W. Roush, Inclines and incline matrices: a survey, Linear algebra appl., 379,457-473(2004).
[3] K.H.Kim, F.W.Roush, Generalized fuzzy matrices, Fuzzy sets and systems, 4 , 293-315 (1980) .
[4] AR.Meenakshi, Fuzzy matrix Theory and its applications, MJP Publishers, Chennai, 2008.
[5] AR.Meenakshi, S. Anbalagan, On regular elements in an incline, Int J. Math. and Math. Sci. (2010) article ID 903063, 12 Pages.
[6] AR.Meenakshi, P.Shakila Banu, Incline relational equations (communicated).
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Paper Type | : | Research Paper |
Title | : | Semi-Compatible Maps On Intuitionistic Fuzzy Metric Space |
Country | : | India |
Authors | : | Pradeep Kumar Dwivedi1 & Anil Rajput |
: | 10.9790/5728-0465964 | |
Abstract: In this paper, we prove common flexed point theorems for semi-compatible mappings on
intuitionistic fuzzy metric space with different some conditions of Park and Kim ([10], 2008). This research
extended and generalized the results of Singh and Chauhan ([14], 2000).
The concept of fuzzy set was developed extensively by many authors and used in various fields. Several
authors have defined fuzzy metric space Kramosil and Michalek(([5],1975) etc.) with various methods to use
this concept in analysis. Jungck (([3],1986), ([4],1988)) researched the more generalized concept compatibility
than commutativity and weak commutativity in metric space and proved common fixed point theorems, and
Singh and Chauhan ([14],2000) introduced the concept of compatibility in fuzzy metric space and studied
common fixed point theorems for four compatible mappings.
[1] S. Banach; Theorie des operations linearires, Monografje Mathematyczne., Warsaw 1932.
[2] M. Grabiec; Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), 385-389.
[3] G. Jungck; Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 779-791.
[4] G.Jungck, K.B. Moon and S. Park; Compatible mappings and common fixed point (2), Internat, J. Math. Math. Sci. 11 (1988), No. 2, 285-288.
[5] J. Kramosil and J. Michalek; Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326-334.
[6] J. H. Park; Intuitionistic fuzzy metric spaces, Chaos Solitons & Fractals 22 (2004), no. 5, 1039-1046.
[7] J.H. Park, J.S. Park, and Y.C. Kwun; A common fixed point theorem in the intuitionistic fuzzy metric space, Advances in Natural
Comput. Data Mining (Proc. 2nd ICNC and 3rd FSKD) (2006), 293-300.
[8] J.S. Park; On some results intuitionistic fuzzy metric space, J. Fixed Point Theory & Appl. 3 (2008), No. 1, 39-48.
[9] J.S. Park and S. Y. Kim; A fixed point Theorem in a fuzzy m3etric space, F. J.M.S. 1 (1999), No. 6, 927-934.
[10] J.S. Park and S. Y. Kim; Common fixed point theorem and example in intuitionistic fuzzy metric space, J.K.I.I.S. 18 (2008), no. 4,
524-529.
[2] M. Grabiec; Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), 385-389.
[3] G. Jungck; Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 779-791.
[4] G.Jungck, K.B. Moon and S. Park; Compatible mappings and common fixed point (2), Internat, J. Math. Math. Sci. 11 (1988), No. 2, 285-288.
[5] J. Kramosil and J. Michalek; Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326-334.
[6] J. H. Park; Intuitionistic fuzzy metric spaces, Chaos Solitons & Fractals 22 (2004), no. 5, 1039-1046.
[7] J.H. Park, J.S. Park, and Y.C. Kwun; A common fixed point theorem in the intuitionistic fuzzy metric space, Advances in Natural
Comput. Data Mining (Proc. 2nd ICNC and 3rd FSKD) (2006), 293-300.
[8] J.S. Park; On some results intuitionistic fuzzy metric space, J. Fixed Point Theory & Appl. 3 (2008), No. 1, 39-48.
[9] J.S. Park and S. Y. Kim; A fixed point Theorem in a fuzzy m3etric space, F. J.M.S. 1 (1999), No. 6, 927-934.
[10] J.S. Park and S. Y. Kim; Common fixed point theorem and example in intuitionistic fuzzy metric space, J.K.I.I.S. 18 (2008), no. 4,
524-529.
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- Abstract
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Paper Type | : | Research Paper |
Title | : | On Certain Class of Analytic Functions Involving Linear Operators |
Country | : | India |
Authors | : | Chena Ram, Garima Agarwal |
: | 10.9790/5728-0466572 | |
Abstract: Invoking the Hadamard product (or convolution) , a class of univalent functions has been
introduced. In the present paper we obtain necessary and sufficient conditions and some important properties
for the analytic functions for its belongingness to certain class of functions. The distortion inequalities, closer
theorems, radii of close-to-convexity, radii of starlikeness and radii of convexity are obtained for the same class
of functions. Some properties involving Hadamard product are also obtained
Keywords: Univalent function; Hadamard product; Starlike function; convex function; Generalized hypergeometric function; Linear operator; Fractional differential and integral operators.
Keywords: Univalent function; Hadamard product; Starlike function; convex function; Generalized hypergeometric function; Linear operator; Fractional differential and integral operators.
[1] A.A. Attiya and M.K.Aouf, A study on certain class of analytic function define by Ruscheweyh derivative, J. Soochow Journal of
mathematics, 33(2)(2007), 273-289.
[2] M. K. Aouf, H. E. Darwish and A. A. Attiya, Generalization of certain subclasses of analyticfunctions with negative coefficients,
Studia Univ. Babe-Bolyai Math., 45(1) (2000), 11-22.
[3] M. K. Aouf, H. E. Darwish and A. A. Attiya, On certain subclasses of analytic functions with negative coefficients, Southeast Asian
Bull. Math., 29(1)(2005), 1-16.
[4] M. K. Aouf, H. M. Hossen and A. Y. Lashin, On certain families of analytic functions with negative coefficients, Indian J. Pure
Appl. Math., 31(8) (2000), 999-1015.
[5] S. B. Joshi, An application of fractional calculus operator to a subclass of analytic functions with negative coefficients, J. Indian
Acad. Math., 25(2) (2003), 277-286.
[6] Chena Ram and Garima, On a class of meromorphically multivalent functions involving generalized hypergeometric functions, J.
Raj. Acad. of Phy. Sci., 11(3), 2012
[7] G. S. Salagean, Integral properties of certain classes of analytic functions with negativecoefficients, Int. J. Math. Math. Sci., 2005(1)
(2005), 125-131.
[8] A. Schild and H. Silverman, Convolutions of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska
Sect. A., 29(1975), 99-106.
[9] Virchenko, N., Kalla, S.L. and Al-Zamel, A. (2001). Some results on a generalized hypergeometric function, Integral Transforms
and special Functions 12(1), 89-100.
mathematics, 33(2)(2007), 273-289.
[2] M. K. Aouf, H. E. Darwish and A. A. Attiya, Generalization of certain subclasses of analyticfunctions with negative coefficients,
Studia Univ. Babe-Bolyai Math., 45(1) (2000), 11-22.
[3] M. K. Aouf, H. E. Darwish and A. A. Attiya, On certain subclasses of analytic functions with negative coefficients, Southeast Asian
Bull. Math., 29(1)(2005), 1-16.
[4] M. K. Aouf, H. M. Hossen and A. Y. Lashin, On certain families of analytic functions with negative coefficients, Indian J. Pure
Appl. Math., 31(8) (2000), 999-1015.
[5] S. B. Joshi, An application of fractional calculus operator to a subclass of analytic functions with negative coefficients, J. Indian
Acad. Math., 25(2) (2003), 277-286.
[6] Chena Ram and Garima, On a class of meromorphically multivalent functions involving generalized hypergeometric functions, J.
Raj. Acad. of Phy. Sci., 11(3), 2012
[7] G. S. Salagean, Integral properties of certain classes of analytic functions with negativecoefficients, Int. J. Math. Math. Sci., 2005(1)
(2005), 125-131.
[8] A. Schild and H. Silverman, Convolutions of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska
Sect. A., 29(1975), 99-106.
[9] Virchenko, N., Kalla, S.L. and Al-Zamel, A. (2001). Some results on a generalized hypergeometric function, Integral Transforms
and special Functions 12(1), 89-100.
- Citation
- Abstract
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Paper Type | : | Research Paper |
Title | : | Fourier series And Fourier Transform |
Country | : | India |
Authors | : | Mr. Karan Asher |
: | 10.9790/5728-0467376 | |
Abstract: An introduction to Fourier Series and Fourier Transform is the topic of this paper. It deals with what
a Fourier Series means and what it represents. The general form of a Fourier Series with a provision for
specific substitution has also been mentioned.
The paper also includes a brief overview of Fourier Transform. The use of Fourier Transform to convert a time
domain function into a frequency domain equivalent has also been shown. A method of converting the
continuous Fourier Transform into a discrete form and thus obtaining the Discrete Fourier Transform has also
been discussed. A few practical life application of Fourier analysis have been stated.
[1] www.tutorial.math.lamar.edu
[2] www.sunlightd.com/fourier/3
[2] www.sunlightd.com/fourier/3
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Paper Type | : | Research Paper |
Title | : | Planar Near-Rings And Coding Theory |
Country | : | India |
Authors | : | Anil Kumar Kashyap, Madan Mohan Singh |
: | 10.9790/5728-0467780 | |
Abstract: The purpose of this paper is to discuss the importance of algebraic coding theory and to investigate
the special case in which BIB designs and codes are constructed from planar near-rings. Application of planar
near-rings to binary codes were first explored by Modisett [12] and by Fuchs, Hofer and Pilz [14].
Keywords: planar near-ring, incidence structure, tactical configuration, BIBD, binary codes, block code.
Keywords: planar near-ring, incidence structure, tactical configuration, BIBD, binary codes, block code.
[1] Aichinger, E.: "Planar rings", Results in Mathematics 30 (1996), 10β15.
[2] Abbasi, S.J. and Iqbal, K. : "On Units in Near Rings", TECHNOLOGY FORCES (Technol. forces): PAF -KIET Journal of
Engineering and Sciences Volume 02, Number 01, January- June 2008.
[3] Beidar, K. I., Fong, Yuen, and KE, Wen Fong "On finite circular planar near-rings", J. Algebra 85 (1996), 688β709.
[4] Blake, I. F. and Mullin, R. C.: "The Mathematical Theory of Coding", New York: Academic, 1975 .
[5] Clay, J. R.: "Generating balanced incomplete block designs from planar near-rings", J. Algebra 22 (1972), 319β331.
[6] Clay, J. R.: "Generating balanced incomplete block designs from planar nearrings", Oberwolfach, 1972.
[7] Claude Shannon: "The Mathematical Theory of Communications", Bell system,Technical journal,1948.
[8] Clay, J. R.: "Near-ring: Geneses and application", Oxford Univ. Press Inc. Oxford, 1992.
[9] Eggetsberger, Roland: "Codes from some residue class ring generated finite planar near-rings",Institutsber. No. 467,1993, Univ. Linz,
Austria.
[10] Ferrero, G.:"Stems planari e BIB - disegni", Riv. Mat, Univ, Panna., Vol.11, pp 79-96, 1970.
[2] Abbasi, S.J. and Iqbal, K. : "On Units in Near Rings", TECHNOLOGY FORCES (Technol. forces): PAF -KIET Journal of
Engineering and Sciences Volume 02, Number 01, January- June 2008.
[3] Beidar, K. I., Fong, Yuen, and KE, Wen Fong "On finite circular planar near-rings", J. Algebra 85 (1996), 688β709.
[4] Blake, I. F. and Mullin, R. C.: "The Mathematical Theory of Coding", New York: Academic, 1975 .
[5] Clay, J. R.: "Generating balanced incomplete block designs from planar near-rings", J. Algebra 22 (1972), 319β331.
[6] Clay, J. R.: "Generating balanced incomplete block designs from planar nearrings", Oberwolfach, 1972.
[7] Claude Shannon: "The Mathematical Theory of Communications", Bell system,Technical journal,1948.
[8] Clay, J. R.: "Near-ring: Geneses and application", Oxford Univ. Press Inc. Oxford, 1992.
[9] Eggetsberger, Roland: "Codes from some residue class ring generated finite planar near-rings",Institutsber. No. 467,1993, Univ. Linz,
Austria.
[10] Ferrero, G.:"Stems planari e BIB - disegni", Riv. Mat, Univ, Panna., Vol.11, pp 79-96, 1970.