Volume-1 ~ Issue-6
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Abstract: In the present paper, we formulate the pulmonary blood flow in Lungs. Keeping in view the nature of pulmonary circulatory system in human body, the viscosity increases in the arterioles due to formation of roulex along axis by red blood cells, as we know the Lungs are remote from heart and proximate to the Asthma. P.N. Pandey and V. Upadhyay have considered the blood flow of two phased, one of which is that of red blood cells and other is Plasma. They have also applied the Herschel Bulkley non-Newtonian Model in bio-fluid mechanical set-up. We have collected a clinical data in case of Asthma for Hematocrit v/s Blood Pressure. The graphical presentation for particular parametric value is much closer to the clinical observation. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of pulmonary disease-Asthma.
[1]. Upadhyay V.; some phenomena in two phase blood flow; 2000
[2]. Debnath L. On a micro - continuum model of pulsatile blood flow, Act Mechanica 24 : 165 - 177, (1976),
[3]. Jones D.S. and Sleeman B.D. Differential Equation and Mathematical Biology6 G.A. and V., (1976),
[4]. Upadhyay V. and Pandey P.N. Newtonian Model of two phase blood flow in aorta and arteries proximate to the heart, Proc., of third
Con. of Int Acad. Phy. Sci., (1999)
[5]. Upadhyay V. and Pandey P.N. A Power Law model of two phase blood flow in arteries remote form the heart, Proc. of thilrd con. of
Int. Acad. Phy. Sci. (1999),
[6]. Singh P. and Upadhyay K.S. A new approach for the shock propagation in two - Phase system, Nat. Acad. Sci. Letters No. 2., (1985),
[7]. LKandau L.D. & Liufchitz E.M. Fluid Mechanics, Pergamon Press., (1959),
[8]. Debnath L. On transient flows in Non-Newtonian liquids, Tensor N.S. : Vol. 27, (1973)
[9]. Kanpur J.N. Mathematical models in Biology and Medicine EWP press., (1985),
[10]. Ruch , T. C and H. D ;patton (ends) ; physiology and bio-physics-vols(ii) and (iii) W.B. S; 1973
[11]. A.C .Guyton and john E .hall, Medical physiology, 10th edition ;saunders .
[12]. Mishra R .S .Tensors and Riemannion Geometry ,pothishala pvt, Ltd .Alld 1990 .
[2]. Debnath L. On a micro - continuum model of pulsatile blood flow, Act Mechanica 24 : 165 - 177, (1976),
[3]. Jones D.S. and Sleeman B.D. Differential Equation and Mathematical Biology6 G.A. and V., (1976),
[4]. Upadhyay V. and Pandey P.N. Newtonian Model of two phase blood flow in aorta and arteries proximate to the heart, Proc., of third
Con. of Int Acad. Phy. Sci., (1999)
[5]. Upadhyay V. and Pandey P.N. A Power Law model of two phase blood flow in arteries remote form the heart, Proc. of thilrd con. of
Int. Acad. Phy. Sci. (1999),
[6]. Singh P. and Upadhyay K.S. A new approach for the shock propagation in two - Phase system, Nat. Acad. Sci. Letters No. 2., (1985),
[7]. LKandau L.D. & Liufchitz E.M. Fluid Mechanics, Pergamon Press., (1959),
[8]. Debnath L. On transient flows in Non-Newtonian liquids, Tensor N.S. : Vol. 27, (1973)
[9]. Kanpur J.N. Mathematical models in Biology and Medicine EWP press., (1985),
[10]. Ruch , T. C and H. D ;patton (ends) ; physiology and bio-physics-vols(ii) and (iii) W.B. S; 1973
[11]. A.C .Guyton and john E .hall, Medical physiology, 10th edition ;saunders .
[12]. Mishra R .S .Tensors and Riemannion Geometry ,pothishala pvt, Ltd .Alld 1990 .
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Abstract: The main object of this paper is to obtain n-dimensional generalized Weyl fractional operators
pertaining to multivariable H -function. Here we get the results by using n-dimensional Laplace and Htransforms.
The results of this paper are believed to be new and basic in nature. Some known results have been
obtained by giving suitable values to the coefficients and parameters.
Key Words: Multivariable H -function, Weyl fractional operator, H -transform
Mathematics Subject Classification: 33C60, 33C65, 44-99
Key Words: Multivariable H -function, Weyl fractional operator, H -transform
Mathematics Subject Classification: 33C60, 33C65, 44-99
[1] A.K. Arora and R.K. Raina, C.L. Koul, On the two-dimensional Weyl fractional calculus associated with the Laplace transforms, C.R. Acad. Bulg. Sci. 38 (1985), 179-182
[2] R.G. Buschman and H.M. Srivastava, J. Phys. A. : Math. Gen. 23 (1990), 4707-4710
[3] V.B.L. Chaurasia and Amber Srivastava, Tamkang J. Math. Vol. 37 (2006), No.3
[4] V.B.L. Chaurasia and Monika Jain, Scientia, Series A: Mathematical Sciences, Vol.19 (2010), 57-68
[5] A., Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Tables of Integral Transforms, Vol.2, McGraw-Hill, New York – Toronto – London, 1954
[6] C. Fox, The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429
[7] A.A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals : II. A generalization of the Hfunction, J. Phys. A: Math. Gen., 20 (1987), 4119-4128
[8] A.M. Mathai and R.K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes in Mathematics, Vol.348, Springer, State Berlin City Heidelberg-State New-York, 1973
[9] A.M. Mathai and R.K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Halsted Press, New York- London-Sydney-Toronto, 1978
[10] K.S. Miller, The Weyl fractional calculus, Fractional Calculus and its applications, Lecture Notes in Math., Vol.457, Springer, Berlin-Heidelberg-New York, 1875, 80-89
[2] R.G. Buschman and H.M. Srivastava, J. Phys. A. : Math. Gen. 23 (1990), 4707-4710
[3] V.B.L. Chaurasia and Amber Srivastava, Tamkang J. Math. Vol. 37 (2006), No.3
[4] V.B.L. Chaurasia and Monika Jain, Scientia, Series A: Mathematical Sciences, Vol.19 (2010), 57-68
[5] A., Erdelyi, W. Magnus, F. Oberhettinger and F.G. Tricomi, Tables of Integral Transforms, Vol.2, McGraw-Hill, New York – Toronto – London, 1954
[6] C. Fox, The G and H-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429
[7] A.A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals : II. A generalization of the Hfunction, J. Phys. A: Math. Gen., 20 (1987), 4119-4128
[8] A.M. Mathai and R.K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes in Mathematics, Vol.348, Springer, State Berlin City Heidelberg-State New-York, 1973
[9] A.M. Mathai and R.K. Saxena, The H-function with Applications in Statistics and Other Disciplines, Halsted Press, New York- London-Sydney-Toronto, 1978
[10] K.S. Miller, The Weyl fractional calculus, Fractional Calculus and its applications, Lecture Notes in Math., Vol.457, Springer, Berlin-Heidelberg-New York, 1875, 80-89
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Paper Type | : | Research Paper |
Title | : | Asymptotic Behavior of a Generalized Polynomial |
Country | : | K.S.A. |
Authors | : | Anwar Habib |
: | 10.9790/5728-0161215 |
Abstract: We have extended the corresponding result of Voronowskaja for Lebesgue integrable function in 𝐿1-norm by our newly defined Generalized Polynomial.................
[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] Cheney, E.W. , and Sharma, A.(1964). On a generalization of Bernstein polynomials.Rev. Mat. Univ. Parma(2),5,77-84.
[3] Jensen, J. L. W. A. (1902). Sur une identité Abel et sur d'autress formules amalogues. Acta Math. , 26, 307-18
[4] Kantorovitch, L.V.(1930). Sur certains développments suivant lés pôlynômes dé la forme S. Bernstein I,II. C.R. Acad. Sci. URSS,20,563-68,595-600.
[5] Lorentz, G.G. (1955). Bernstein Polynomials. University of Toronto Press, Toronto
[6] Voronowskaja, E. (1932). Determination de la forme asymtotique d' d noitamixorppaé l noitcnof sép sônylô M ed sem Bernstein. C.R. Acad. Sci. URSS,22,79-85
[2] Cheney, E.W. , and Sharma, A.(1964). On a generalization of Bernstein polynomials.Rev. Mat. Univ. Parma(2),5,77-84.
[3] Jensen, J. L. W. A. (1902). Sur une identité Abel et sur d'autress formules amalogues. Acta Math. , 26, 307-18
[4] Kantorovitch, L.V.(1930). Sur certains développments suivant lés pôlynômes dé la forme S. Bernstein I,II. C.R. Acad. Sci. URSS,20,563-68,595-600.
[5] Lorentz, G.G. (1955). Bernstein Polynomials. University of Toronto Press, Toronto
[6] Voronowskaja, E. (1932). Determination de la forme asymtotique d' d noitamixorppaé l noitcnof sép sônylô M ed sem Bernstein. C.R. Acad. Sci. URSS,22,79-85
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Abstract : Formation control is an important behavior for multi-agents system (swarm). This paper addresses
the optimal tracking control problem for swarm whose agents are Dubin's car moving together in a specific
geometry formation. We study formation control of the swarm model which consists of three agents and one
agent has a role as a leader. The agents of swarm are moving to follow the leader path. First, we design the
control of the leader with tracking error dynamics. The control of the leader is designed for tracking the desired
path. We show that the tracking error of the path of the leader tracing a desired path is sufficiently small. The
desired path is obtained using calculus variational method. After that, geometry approach is used to design the
control of the other. We show that the positioning and the orientation of each agent can be controlled dependent
on the leader. The simulation results show to illustrate of this method at the last section of this paper.
Keywords - Swarm model, Dubin's car system, Tracking error, Calculus Variational, Numerical simulation.
Keywords - Swarm model, Dubin's car system, Tracking error, Calculus Variational, Numerical simulation.
[1] A. Balluchi, A. Bicchi, A. Balestrino, and G. Casalino, Path Tracking Control for Dubin's Cars, : Proceeding of the IEEE International Conference on Robotics and Automation, Volume: 4, pp. 3123-3128, 1998.
[2] D. Wang and G. Xu, Full State Tracking and Internal Dynamics of Nonholonomic Wheeled Mobile Robots, Proceedings of the American Control Conference, pp. 3274-3278, Chicago, Illinois, June 2000.
[3] E. Bicho and S. Monteiro, Formation Control for Multiple Mobile Robots: a Nonlinear Attractor Dynamics Approach, Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), Vol. 2, pp. 2016- 2022, 2003.
[4] E. Lefeber and H. Nijmeijer, Adaptive Tracking Control of Nonholonomic Systems: an example, Proceedings of the 38th Conference on Decision & Control, Phoenix, Arizona USA, December 1999.
[5] E. Panteley, E. Lefeber, A. Loria and H. Nijmeijer, Exponential Tracking Control of a Mobile Car Using a Cascaded Approach, Proceeding of the IFAC Workshop on Motion Control, pp. 221-226, Grenoble France, September 1998.
[6] G. Orlando, E. Frontoni, A. Mancini, and P. Zingaretti, Sliding Mode Control for Vision Based Leader Following, 3rd European Conference on Mobile Robots, Freiburg, Germany, September 19-21 1999.
[7] G.Y. Tang, Y.D. Zhao and Hui Ma, Optimal Output Tracking Control for Bilinear Systems, Transactions of the Institute of Measurement and Control 28, 4, pp. 387-397, 2006.
[8] H.G. Tanner, G.J. Pappas, and V. Kumar, Leader to Formation Stability, IEEE Trans. on Robotics and Automation, Vol. 20 No. 3, June 2004.
[9] H.S. Shim, J. H. Kim, and K. Koh, Variable Structure Control of Nonholonomic Wheeled Mobile Robot, Proceeding of the IEEE International Conference on Robotics and Automation on Volume 2, Page(s):1694 - 1699, May 21-27 1995.
[10] H. Shi, L. Wang and T. Chu, Swarming Behavior of Multi-Agent Systems, J. Control Theory And Applications Vol. 2 No. 4, pp. 313-318, 2004.
[2] D. Wang and G. Xu, Full State Tracking and Internal Dynamics of Nonholonomic Wheeled Mobile Robots, Proceedings of the American Control Conference, pp. 3274-3278, Chicago, Illinois, June 2000.
[3] E. Bicho and S. Monteiro, Formation Control for Multiple Mobile Robots: a Nonlinear Attractor Dynamics Approach, Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), Vol. 2, pp. 2016- 2022, 2003.
[4] E. Lefeber and H. Nijmeijer, Adaptive Tracking Control of Nonholonomic Systems: an example, Proceedings of the 38th Conference on Decision & Control, Phoenix, Arizona USA, December 1999.
[5] E. Panteley, E. Lefeber, A. Loria and H. Nijmeijer, Exponential Tracking Control of a Mobile Car Using a Cascaded Approach, Proceeding of the IFAC Workshop on Motion Control, pp. 221-226, Grenoble France, September 1998.
[6] G. Orlando, E. Frontoni, A. Mancini, and P. Zingaretti, Sliding Mode Control for Vision Based Leader Following, 3rd European Conference on Mobile Robots, Freiburg, Germany, September 19-21 1999.
[7] G.Y. Tang, Y.D. Zhao and Hui Ma, Optimal Output Tracking Control for Bilinear Systems, Transactions of the Institute of Measurement and Control 28, 4, pp. 387-397, 2006.
[8] H.G. Tanner, G.J. Pappas, and V. Kumar, Leader to Formation Stability, IEEE Trans. on Robotics and Automation, Vol. 20 No. 3, June 2004.
[9] H.S. Shim, J. H. Kim, and K. Koh, Variable Structure Control of Nonholonomic Wheeled Mobile Robot, Proceeding of the IEEE International Conference on Robotics and Automation on Volume 2, Page(s):1694 - 1699, May 21-27 1995.
[10] H. Shi, L. Wang and T. Chu, Swarming Behavior of Multi-Agent Systems, J. Control Theory And Applications Vol. 2 No. 4, pp. 313-318, 2004.
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Abstract: Spatial Scan Statisticusing SaTScan is used to detect randomness in the cluster. This paper aims to
demonstrate some of the properties owned by the spatial scan statistic of Bernoulli model, which exhibit
analytically unbiased, have minimum variance and consistent. Simulations using the SaTScan showed that the
amount of data give different results on the cluster properties of randomness.Analysis with small data provides
a more random cluster, or unfavorable results of the analysis. It is showed that the greater amount of data
provide the LLR enlarge; p-value smaller; RR decreases and Smaller biased.
Key words: SpatialScanStatistic, Bernoullimodel,SaTScan, Unbiased, minimumvariance, consistent.
Key words: SpatialScanStatistic, Bernoullimodel,SaTScan, Unbiased, minimumvariance, consistent.
[1]. Kulldorff, M.A Spatial Scan Statistic.Commun.Statist.-Theory Meth.26(6), 1997, 1481 – 1496.
[2]. Duczmal, L., M. Kulldorff, L. Huang. Evaluation of spatial scan statistics for irregularly shaped disease clusters. To appear in Journal of Computation and Graphical Statistics.2006.
[3]. Tango, T. A Spatial Scan Statistic with a Restricted Likelihood Ratio.Japanese Journal of Biometrics, Vol. 29, No. 2, 2008, 75 – 95.
[4]. Cucala, L., C. Demattei, P. Lopes, & A. Ribeiro. Spatial scan statistics for case event data based on connected components. Biometrics, 2009, 1 – 17.
[5]. Hogg, R.V. & A.T. Craig. Introduction to Mathematical Statistics. 5th ed. (Prentice Hall, London, 2005)
[6]. Ugarte, M.D., T. Goicoa, A.F. Militino. Empirical Bayes and Fully Bayes procedures to detect high-risk areas in disease mapping. Computational Statistics and Data Analysis, 53, 2009, 2938 – 2949.
[7]. BadanPusatStatistik (BPS, Central Bureau of Statistic) Indonesia.Basic Poverty Measurement and Diagnostics Course.(BPS Pubs,Jakarta, Indonesia, 2002).
[8]. BadanPusatStatistik (BPS, Central Bureau of Statistic) Indonesia.Data and information poverty. 2008. (BPS Pubs,Jakarta, Indonesia,2008).
[9]. Badan Pusat Statistik(BPS, Central Bureau of Statistic) Indonesia. Indonesian Statistic2011. (BPS Pubs, Jakarta, Indonesia, 2012).
[10]. Rao, J.N.K.Small Area Estimation. (Wiley-Interscience, USA, 2003)
[2]. Duczmal, L., M. Kulldorff, L. Huang. Evaluation of spatial scan statistics for irregularly shaped disease clusters. To appear in Journal of Computation and Graphical Statistics.2006.
[3]. Tango, T. A Spatial Scan Statistic with a Restricted Likelihood Ratio.Japanese Journal of Biometrics, Vol. 29, No. 2, 2008, 75 – 95.
[4]. Cucala, L., C. Demattei, P. Lopes, & A. Ribeiro. Spatial scan statistics for case event data based on connected components. Biometrics, 2009, 1 – 17.
[5]. Hogg, R.V. & A.T. Craig. Introduction to Mathematical Statistics. 5th ed. (Prentice Hall, London, 2005)
[6]. Ugarte, M.D., T. Goicoa, A.F. Militino. Empirical Bayes and Fully Bayes procedures to detect high-risk areas in disease mapping. Computational Statistics and Data Analysis, 53, 2009, 2938 – 2949.
[7]. BadanPusatStatistik (BPS, Central Bureau of Statistic) Indonesia.Basic Poverty Measurement and Diagnostics Course.(BPS Pubs,Jakarta, Indonesia, 2002).
[8]. BadanPusatStatistik (BPS, Central Bureau of Statistic) Indonesia.Data and information poverty. 2008. (BPS Pubs,Jakarta, Indonesia,2008).
[9]. Badan Pusat Statistik(BPS, Central Bureau of Statistic) Indonesia. Indonesian Statistic2011. (BPS Pubs, Jakarta, Indonesia, 2012).
[10]. Rao, J.N.K.Small Area Estimation. (Wiley-Interscience, USA, 2003)
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Paper Type | : | Research Paper |
Title | : | Soliton Solutions for Nonlinear Systems (2+1)-Dimensional Equations |
Country | : | Iraq |
Authors | : | Anwar Ja'afar Mohamad Jawad |
: | 10.9790/5728-0162734 |
Abstract : This paper implemented two methods for solving Nonlinear systems of Partial differential equations. These are tanh method, and sine-cosine method. Methods have been successfully tested on Konopelchenko-Dubrovsky, and Dispersive Long Wave systems of equations. The calculations demonstrate the effectiveness and convenience of these two methods for solving nonlinear system of PDEs.
Keywords: Exact Solutions, Konopelchenko-Dubrovsky equations, Nonlinear system PDEs, Sine-cosine method, Tanh method,
Keywords: Exact Solutions, Konopelchenko-Dubrovsky equations, Nonlinear system PDEs, Sine-cosine method, Tanh method,
[1]. Ali A.H.A. , A.A. Soliman , and K.R. Raslan,(2007), Soliton solution for nonlinear partial differential equations by cosine-function method, Physics Letters A 368 (2007) 299–304.
[2]. El-Wakil, S.A. and Abdou, M.A. (2007). New exact travelling wave solutions using modified extended tanh-function method, Chaos Solitons Fractals, Vol. 31, No. 4, pp. 840-852.
[3]. Fan, E. (2000). Extended tanh-function method and its applications to nonlinear equations. PhysLett A, Vol. 277, No.4, pp. 212- 218.
[4]. Hirota, R. (2004). The Direct Method in Soliton Theory, Cambridge University Press. Inc, M. and Ergut, M. (2005). Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method, Appl. Math. E-Notes, Vol. 5, pp. 89-96.
[5]. Khater, A.H., Malfliet, W., Callebaut, D.K. and Kamel, E.S. (2002). The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction–diffusion equations, Chaos Solitons Fractals, Vol. 14, No. 3, PP. 513-522.
[6]. Ma, W. X. and Lee, J. H. (2009). A transformed rational function method and exact solutions to the (3 + 1)-dimensional Jimbo- Miwa equation, Chaos Solitons Fractals, Vol.42; pp. 1356 – 1363.
[7]. Ma, W. X. and Fuchssteiner, B. (1996). Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. Non- Linear Mech. Vol. 31; pp. 329 − 338.
[8]. Malfliet, W. (1992). Solitary wave solutions of nonlinear wave equations, Am. J. Phys, Vol. 60,No. 7, pp. 650-654.
[9]. Mitchell A. R. and D. F. Griffiths(1980), The Finite Difference Method in Partial Differential Equations, John Wiley & Sons.
[10]. Parkes E. J. and B. R. Duffy(1998), An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Commun. 98 , 288-300.
[2]. El-Wakil, S.A. and Abdou, M.A. (2007). New exact travelling wave solutions using modified extended tanh-function method, Chaos Solitons Fractals, Vol. 31, No. 4, pp. 840-852.
[3]. Fan, E. (2000). Extended tanh-function method and its applications to nonlinear equations. PhysLett A, Vol. 277, No.4, pp. 212- 218.
[4]. Hirota, R. (2004). The Direct Method in Soliton Theory, Cambridge University Press. Inc, M. and Ergut, M. (2005). Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method, Appl. Math. E-Notes, Vol. 5, pp. 89-96.
[5]. Khater, A.H., Malfliet, W., Callebaut, D.K. and Kamel, E.S. (2002). The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction–diffusion equations, Chaos Solitons Fractals, Vol. 14, No. 3, PP. 513-522.
[6]. Ma, W. X. and Lee, J. H. (2009). A transformed rational function method and exact solutions to the (3 + 1)-dimensional Jimbo- Miwa equation, Chaos Solitons Fractals, Vol.42; pp. 1356 – 1363.
[7]. Ma, W. X. and Fuchssteiner, B. (1996). Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. Non- Linear Mech. Vol. 31; pp. 329 − 338.
[8]. Malfliet, W. (1992). Solitary wave solutions of nonlinear wave equations, Am. J. Phys, Vol. 60,No. 7, pp. 650-654.
[9]. Mitchell A. R. and D. F. Griffiths(1980), The Finite Difference Method in Partial Differential Equations, John Wiley & Sons.
[10]. Parkes E. J. and B. R. Duffy(1998), An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Commun. 98 , 288-300.
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Abstract: The paper considers a marketing decision problem in a periodic review model. The demand
distribution is assumed to be exponential, with the meanv demand being a concave increasing function of the
level of marketing effort. The optimum ordering policy and the optimum level of marketing are determined so as
to minimize the total expected cost over a re-order interval. Optimum decision rules are given for some
particular functional forms of the mean demand.
[1]. Bhunia, A.K. and Maiti, M. (1997): An inventory model for decaying items with selling price, frequency of advertisement and linearly dependent demand with shortages, IAPQR Transactions, 22, 1-49.
[2]. Eliashberg, J. and Steinberg, M.S. (1993): Marketing production joint decision making, Handbook in OR and MS, Vol. 5 (Eds. J. Eliashberg and G.L. Lilien). Elsevier, Amsterdam.
[3]. Jucker, J.K. and Rosenblatt, M.J. (1985): A single period inventory model with demand uncertainty and quantity discounts: behavioural implications and a new solution procedure, Naval Research Logistic Quarterly, 32, 537-550.
[4]. Ladany, S. and Sternlieb, A (1974): The interaction of economic ordering quantities and marketing policies, AIIE Transactions, 6, 35-40.
[5]. Lal, R. and Staelin, R. (1984): An approach for developing an optimal discount pricing policy, Management Science, 30, 1524-1539.
[6]. Pal and Manna (2003): A marketing decision problem in a single period stochastic inventory model, Opsearch, 40(3), 230-240.
[7]. Shah, Y.K. and Jha, P.J. (1991): A single-period stochastic inventory model under the influence of marketing policies, Journal of the Operational Research Society, 42, 173-176.
[2]. Eliashberg, J. and Steinberg, M.S. (1993): Marketing production joint decision making, Handbook in OR and MS, Vol. 5 (Eds. J. Eliashberg and G.L. Lilien). Elsevier, Amsterdam.
[3]. Jucker, J.K. and Rosenblatt, M.J. (1985): A single period inventory model with demand uncertainty and quantity discounts: behavioural implications and a new solution procedure, Naval Research Logistic Quarterly, 32, 537-550.
[4]. Ladany, S. and Sternlieb, A (1974): The interaction of economic ordering quantities and marketing policies, AIIE Transactions, 6, 35-40.
[5]. Lal, R. and Staelin, R. (1984): An approach for developing an optimal discount pricing policy, Management Science, 30, 1524-1539.
[6]. Pal and Manna (2003): A marketing decision problem in a single period stochastic inventory model, Opsearch, 40(3), 230-240.
[7]. Shah, Y.K. and Jha, P.J. (1991): A single-period stochastic inventory model under the influence of marketing policies, Journal of the Operational Research Society, 42, 173-176.
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Paper Type | : | Research Paper |
Title | : | Po-𝚪-Ideals in Po-𝚪-Semigroups |
Country | : | India |
Authors | : | V. B. Subrahmanyeswara Rao Seetamraju, A. Anjaneyulu, D. Madhusudana Rao |
: | 10.9790/5728-0163951 | |
ABSTRACT : In this paper the terms; a completely prime po-Γ-ideal, c-system,a prime po-Γ-ideal, m-system of a po-𝚪-semigroup are introduced. It is proved that every po- 𝚪-subsemigroup of a po-𝚪-semigroup is a csystem.
It is also proved that a po-𝚪-ideal P of a po-𝚪-semigroup S is completely prime if and only if S\P is either a c-system or empty. It is proved that if P is a po-Γ-ideal of a po-Γ-semigroup S, then the conditions (1) if A, B are po-Γ-ideals of S and AΓB⊆P then either A⊆P or B⊆P, (2) if a, b ∈ S such that aΓS1Γb ⊆ P, then either a ∈ P or b ∈ P, are equivalent. It is proved that every completely prime po-𝚪-ideal of a po-𝚪-semigroup S is a prime po-𝚪-ideal of S. It is also proved that in a commutative po-𝚪-semigroup S, a po-𝚪-ideal P is a prime
po-𝚪-ideal if and only if P is a completely prime po-𝚪-ideal. Further it is proved that a po-𝚪-ideal P of a po-𝚪- semigroup S is a prime po-𝚪-ideal of S if and only if S\P is an m-system or empty. In a globally idempotent po- Γ-semigroup, it is proved that every maximal po- Γ-ideal is a prime po- Γ-ideal. It is also proved that a globally idempotent po-Γ-semigroup having a maximal po-Γ-ideal, contains semisimple elements. The terms completely semiprime po- Γ-ideal,a semiprime po-Γ-ideal, n-system, d-system are introduced. It is proved that (1) every completely semiprime po-Γ-ideal of a po-Γ-semigroup is a semiprime po-Γ-ideal, (2) every completely prime po- Γ-ideal of a po- Γ-semigroup is a completely semiprime po-Γ-ideal. It is also proved that the nonempty intersection of any family of (1) completely prime po-Γ-ideals of a po-Γ-semigroup is a completely semiprime po-Γ-ideal, (2) prime po- Γ-ideals of a po-Γ-semigroup is a semiprime po-Γ-ideal. It is also proved that a po- Γ-ideal Q of a po-Γ-semigroup S is a semiprime iff S\Q is either an n-system or empty. Further it is proved that if N is an n-system in a po-Γ- semigroup S and a ∈ N, then there exists an m-system M of S such that a ∈ M and M ⊆ N. Mathematics Subject Clasification (2010) : 06F05, 06F99, 20M10, 20M99
Keywords : Apo-Γ-semigroup,po-Γ-ideal,primepo-Γ-ideal,acompletelyprimepo-Γ-ideal,a completely semiprime po-Γ-ideal,asemiprimepo-Γ-ideal,po-c-system, po-d-system, po-m-system, po-n-system
It is also proved that a po-𝚪-ideal P of a po-𝚪-semigroup S is completely prime if and only if S\P is either a c-system or empty. It is proved that if P is a po-Γ-ideal of a po-Γ-semigroup S, then the conditions (1) if A, B are po-Γ-ideals of S and AΓB⊆P then either A⊆P or B⊆P, (2) if a, b ∈ S such that aΓS1Γb ⊆ P, then either a ∈ P or b ∈ P, are equivalent. It is proved that every completely prime po-𝚪-ideal of a po-𝚪-semigroup S is a prime po-𝚪-ideal of S. It is also proved that in a commutative po-𝚪-semigroup S, a po-𝚪-ideal P is a prime
po-𝚪-ideal if and only if P is a completely prime po-𝚪-ideal. Further it is proved that a po-𝚪-ideal P of a po-𝚪- semigroup S is a prime po-𝚪-ideal of S if and only if S\P is an m-system or empty. In a globally idempotent po- Γ-semigroup, it is proved that every maximal po- Γ-ideal is a prime po- Γ-ideal. It is also proved that a globally idempotent po-Γ-semigroup having a maximal po-Γ-ideal, contains semisimple elements. The terms completely semiprime po- Γ-ideal,a semiprime po-Γ-ideal, n-system, d-system are introduced. It is proved that (1) every completely semiprime po-Γ-ideal of a po-Γ-semigroup is a semiprime po-Γ-ideal, (2) every completely prime po- Γ-ideal of a po- Γ-semigroup is a completely semiprime po-Γ-ideal. It is also proved that the nonempty intersection of any family of (1) completely prime po-Γ-ideals of a po-Γ-semigroup is a completely semiprime po-Γ-ideal, (2) prime po- Γ-ideals of a po-Γ-semigroup is a semiprime po-Γ-ideal. It is also proved that a po- Γ-ideal Q of a po-Γ-semigroup S is a semiprime iff S\Q is either an n-system or empty. Further it is proved that if N is an n-system in a po-Γ- semigroup S and a ∈ N, then there exists an m-system M of S such that a ∈ M and M ⊆ N. Mathematics Subject Clasification (2010) : 06F05, 06F99, 20M10, 20M99
Keywords : Apo-Γ-semigroup,po-Γ-ideal,primepo-Γ-ideal,acompletelyprimepo-Γ-ideal,a completely semiprime po-Γ-ideal,asemiprimepo-Γ-ideal,po-c-system, po-d-system, po-m-system, po-n-system
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[3] Anjaneyulu. A., Semigroup in which Prime Ideals are maximal, Semigroup Forum, Vol.22(1981), 151-158.
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[10] Kwon. Y. I. and Lee. S. K., Some special elements ina po- Γ-semigroups, Kyungpook Mathematical Journal., 35 (1996), 679-685.
[11] Madhusudhana Rao. D, Anjaneyulu. A and Gangadhara Rao. A, Pseudo symmetric Γ-ideals in Γ-semigroups, International eJournal of Mathematics and Engineering 116(2011) 1074-1081.
[12] Madhusudhana rao. D, Anjaneyulu. A & Gangadhara rao. A, Prime Γ-radicals in Γ-semigroups, International eJournal of Mathematics and Engineering 138(2011) 1250 - 1259.
[2] Anjaneyulu. A., Structure and ideal theory of Duo semigroups, Semigroup Forum, Vol.22(1981), 257-276.
[3] Anjaneyulu. A., Semigroup in which Prime Ideals are maximal, Semigroup Forum, Vol.22(1981), 151-158.
[4] Clifford. A.H. and Preston. G.B., The algebraic theory of semigroups, Vol-I, American Math.Society, Providence(1961).
[5] Clifford. A.H. and Preston. G.B., The algebraic theory of semigroups, Vol-II, American Math.Society, Providence(1967).
[6] Chinram. R and Jirojkul. C., On bi- Γ -ideal in Γ - Semigroups, Songklanakarin J. Sci. Tech no.29(2007), 231-234.
[7] Giri. R. D. and Wazalwar. A. K., Prime ideals and prime radicals in non- commutative semigroup, Kyungpook Mathematical Journal Vol.33(1993), no.1, 37-48.
[8] Dheena. P. and Elavarasan. B., Right chain a po-Γ-semigroups, Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 3 (2008), No. 3, pp. 407-415.
[9] Kostaq Hila., Filters in a po- Γ-semigroups, Rocky Mountain Journal of Mathematics Volume 41, Number 1, 2011.
[10] Kwon. Y. I. and Lee. S. K., Some special elements ina po- Γ-semigroups, Kyungpook Mathematical Journal., 35 (1996), 679-685.
[11] Madhusudhana Rao. D, Anjaneyulu. A and Gangadhara Rao. A, Pseudo symmetric Γ-ideals in Γ-semigroups, International eJournal of Mathematics and Engineering 116(2011) 1074-1081.
[12] Madhusudhana rao. D, Anjaneyulu. A & Gangadhara rao. A, Prime Γ-radicals in Γ-semigroups, International eJournal of Mathematics and Engineering 138(2011) 1250 - 1259.