Volume-1 , Issue-1 , Feb 2014, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Optimal Control for Singular Systems via Hybrid Functions

  Lei Zhang and Xing Tao Wang

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.1 , Issue.1 , pp.1-7, Feb-2014

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  By using hybrid functions of general block-pulse functions and Legendre polynomials, the linear-quadratic problem of time-varying singular systems are transformed into the optimization problem of multivariate functions. The approximate solutions of the optimal control and state as well as the optimal value of the objective functional are derived. The numerical examples are worked out.

  Key-Words / Index Term
  General Block-Pulse Functions; Legendre Polynomials; Singular Systems; Optimal Control

  References
  [1] P. Sannuti, “Analysis and Synthesis of Dynamic Systems via Block-pulse Functions”, Proceedings of the Institution of Electrical Engineers, Vol. 124, Issue-6, 1977, pp.569-571.
  [2] G.P. Rao and L. Sivakumar, “Analysis and Synthesis of Dynamic Systems Containing Time Delays via Block-pulse Functions”, Proceedings of the Institution of Electrical Engineers, Vol.125, Issue-9, 1978, pp. 1064-1068.
  [3] A. Deba, G. Sarkara, A. Biswasb and P. Mandal, “Numerical Instability of Deconvolution Operation via Block Pulse Functions”, Journal of the Franklin Institute, Vol.345, Issue-4, 2008, pp. 319--327.
  [4] K.R. Palanisamy and G.P. Rao, “Optimal Control of Linear Systems with Delays in State and Control via Walsh Function”, IEE Proceedings D (Control Theory and Applications), Vol.130, Issue-6, 1983, pp. 300-312.
  [5] C. Hwang and Y.P. Shih, “Laguerre Series Solution of a Functional Differential Equation”, International Journal of Systems Science, Vol.13, Issue-7, 1982, pp. 783-788.
  [6] I.R. Horng and J.H. Chou, “Analysis, Parameter Estimation and Optimal Control of Time-delay Systems via Chebyshev Series”, International Journal of Control, Vol.41, Issue-5, 1985, pp. 1221-1234.
  [7] H. Lee and F.C. Kung, “Shifted Legendre Series Solution and Parameter Estimation of Llinear Delayed Systems”, International Journal of Systems Science, Vol.16, Issue-10, 1985, pp. 1249-1256.
  [8] S. Yalcinbas, M. Aynigula and M. Sezer, “A collocation Method Using Hermite Polynomials for Approximate Solution of Pantograph Equations”, Journal of the Franklin Institute, Vol.348, Issue-6, 2011, pp. 1128-1139.
  [9] P.N. Parskevopoulos, P.D. Sparis and S.G. Mouroutsos, “The Fourier Series Operational Matrix of Integration”, International Journal of Systems Science, Vol.16, Issue-2, 1985, pp. 171-176.
  [10] X.T. Wang and Y.M. Li, “Numerical Solution of Fredholm Iintegral Equation of the Second Kind by General Legendre Wavelets”, International Journal of Innovative Computing, Information and Control, Vol.8, Issue-1(B), 2012, pp. 799-805.
  [11] K. Maleknejad and Y. Mahmoudi, “Numerical Solution of Linear Fredholm Iintegral Equation by Using Hybrid Taylor and Block-pulse Functions”, Applied Mathematics and Computation, Vol.149, Issue-3, 2004, pp. 799-806.
  

  Citation
  Lei Zhang and Xing Tao Wang , "Optimal Control for Singular Systems via Hybrid Functions," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.1, pp.1-7, 2014

• Open Access   Article

  Robustness to Non-Normality and Ar (2) Process of Control Charts

  Singh D.P and Singh J.R

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.1 , Issue.1 , pp.8-17, Feb-2014

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  In this paper we investigate the effect of non-normality and auto-correlation on the OC function of mean chart with known coefficient of variation. We synthesize the second order auto-correlation process by its three different roots. In particular, the shift in the auto-correlation structure from independent data to a random walk, this is a special case of the structural shift occurring in the process. For various values of roots the values of OC functions are tabulated with known coefficient of variation.

  Key-Words / Index Term
  Mean chart, non-normality, OC function, auto-correlation, coefficient of variation

  References
  [1]. Albin, S. L., Kang, L., Shea, G. (1997). An X and EWMA chart for individual observations, Journal of quality Technology. 29:41–48.
  [2]. Amin,R.W. and Ethridge,R.A.(1998). A note on Individual and Moving Range Control Vhart, Journal of Quality Technology,30,70-74
  [3]. Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution, J. R. Statist. Soc. B. 61, 579–602.
  [4]. Azzalini, A. (1985). A class of distributions which includes the normal ones, Scand. J. Statist. 171–178.
  [5]. Azzalini, A. (1986). Futher results on a class of distributions which includes the normal ones, Statistica 46, 199–208.
  [6]. Bittanti, S., Lovera, M. and Moiraghi, L. (1998). Application of non-normal process capability indices to semiconductor quality control, IEEE Transactions On Semiconductor Manufacturing 11, 296–303.
  [7]. Borror, C. M., Montgomery, D. C., Runger, G. C. (1999). Robustness of the EWMA control chart to non-normality, Journal of quality Technology. 31:309–316.
  [8]. Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis: Forecasting and Control, 3rd ed. (Prentice-Hall: Englewood Cliffs, NJ).
  [9]. Champ, C.W.,Woodall, W.H. (1987). Exact results for shewhart’s control charts with supplementary runs rules, Journal of quality Technology 19:388–399
  [10]. Chan, L. K. and Cui, H. J. (2003). Skewness correction X and R charts for skewed distributions, Naval Research Logistics 50, 1–19.
  [11]. Chang, Y. S. and Bai, D. S. (1995). X and R control charts for skewed populations, Journal of Quality Technology 27, 120–131.
  [12]. Chang, Y. S. and Bai, D. S. (2001). Control charts for positively-skewed populations with weighted standard deviations, Quality and Reliability Engineering International 17, 397–406.
  [13]. Chang, W. (1994). Practical implementation of the process capability indices, Quality Engineering 7, 239–259.
  [14]. Chou, C.-Y. , Chen, C.-H and Liu, H.-R. (2005). Acceptance control charts for non-normal data, Journal of Applied Statistics 32 25–36.
  [15]. Cowden, D. J. (1957). Statistical Method in Quality Control (Prentice-Hall, Englewood Cliffs, NJ,
  [16]. Dodge, Y. and Rousson, V. (1999). The complications of the fourth central moment, The American Statistician 53 267–269.
  [17]. Domangue, R., Patch, S.C. (1991). Some omnibus exponentially weighted moving average statistical process monitoring schemes,Technometrics 33:299–313
  [18]. Durbin, J. and Watson, G. S. (1950).Testing for serial correlation in least squares regression Biometrika, 37.
  [19]. Gayen, A. K. (1949). Mathematical Investigation in to effect of Non-normality on standard test, Ph.D. Thesis, Combrig University, USA.
  [20]. Genton, M. G., He, L. and Liu, X. (2001). Moments of skew-normal random vectors and their quadratic forms, Statistics and Probability Letters 51 319–325.
  [21]. Gunter, W. H. (1989). The use and abuse of Cpk, Quality Progress 22 108 109.
  [22]. Gupta, R. C. and Brown, N. (2001). Reliability studies of the skew-normal distribution and its application to a strength-stress model, Commun. Statist.-Theory Math. 30 2427–2445.
  [23]. Lowry, C.A., Champ, C.W., Woodall, W.H. (1995). The Performance of Control Charts for Monitoring Process Variation, Communications in Statistics Simulation and Computation, 24(2), 409–437.
  [24]. Lu, C.W. and Reynolds, M.R. Jr. (1999).Control charts for monitoring the mean and variance of autocorrelated processes, Journal of Quality Technology, 31, 259–274.
  [25]. Lucas, J.M., Saccucci, M.S. (1990). Exponential weighted moving average control schemes: properties and enhancements,Technometrics 32:1–12
  [26]. MacGregor, J. F. and Harris, T. J. (1993). The Exponentially Weighted Moving Variance, Journal of Quality Technology 25: 106–118.
  [27]. Maragah, H.O. and Woodall, W.H. (1992).The effects of autocorrelation on the retrospective X-chart, J. Statist. Compu. Simul. 40, 29–42.
  [28]. Montgomery, D. C. (1997). Statistical Quality Control, 3rd ed. New York: John Wiley.
  [29]. Pyzdek, T. (1995). Why normal distribution aren’t – all that normal, Quality Engineering 7 769–777.
  [30]. Rao, K. A. and Bhatta, A. R. S. (1989). A note on test for coefficient of variation, University of Agricultural Science, Dharwad.
  [31]. Reynolds, M. R. Jr. (1996b). Variable Sampling Interval Control Charts with Sampling at Fixed Times, IIE Transactions 28: 497–510.
  [32]. Reynolds, M.R. Jr. and Stoumbos, Z.G. (2001). Monitoring the process mean and variance using individual observations and variable sampling intervals, Journal of Quality Technology, 33, pp. 181–205.
  [33]. Rigdon, S. E., Cruthis, E. N., Champ, C. W. (1994). Design strategies for individuals and moving range control charts, Journal of quality Technology. 26:274–287.
  [34]. Ryan, T.P. (2000). Statistical Methods for Quality Improvements. John Wiley & Sons: New York,.
  [35]. Srivastava, S. R. and Banarasi (1980). A note on the estimation of mean of asymmetrical population, Jar. Ind. Soc. Agri. Stat. 26(2), 33-36.
  [36]. Stoumbos, Z. G. and Reynolds, M. R. Jr. (1997). Control Charts Applying a Sequential Test at Fixed Sampling Intervals, Journal of Quality Technology 29: 21–40.
  [37]. Sullivan, J.H., Woodall, W.H. (1996). A control chart for preliminary analysis of individual observations, Journal of quality Technology, 28:265–278
  [38]. Zhang, N.F. (1998). A statistical control chart for stationary process data, Technometrics, 40: 24 – 38.
  

  Citation
  Singh D.P and Singh J.R, "Robustness to Non-Normality and Ar (2) Process of Control Charts," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.1, pp.8-17, 2014

• Open Access   Article

  Factors Influencing the use of Fertilizers in Agriculture of Madhya Pradesh in India

  Hemant Singh and Ramkrishna Singh Solanki

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.1 , Issue.1 , pp.18-40, Feb-2014

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  Fertilizer is a significant input for the gross production in Indian agriculture. The present paper throws light on the use of fertilizer in context of Madhya Pradesh. This research paper expatiate the factors, affecting the use of fertilizers, which will indisputably contribute to the government’s fertilizer policy. The analysis starts with the use and the percentage contribution of NPK in Madhya Pradesh. The percentage growth of the use of fertilizer is analyzed under two circumstances that are before and after liberalization.

  Key-Words / Index Term
  Fertilizer, NPK, Liberalization, The Regression Model, Madhya Pradesh

  References
  [1]. Desai, G.M and Singh G. (1973): Growth of fertilizer use in district of India. Performance and Policy Implications, IIM, Ahmedabad, pp. 26-29.
  [2]. FIA (2007-08): Fertilizer Association of India “A few facts about fertilizer in the western region”, Mumbai, pp. 8.
  [3]. Maharaja, M.H. (1975): Demand for fertilizers: An analysis of factors affecting demand and estimation of future demand. India Good Companions, pp. 113-136.
  [4]. Namboodiri, N.V. and Desai, G.M. (1994): Demand verses supply factor in growth of fertilizer use: Strategic Issue in Issue in Future Growth of Fertilizer Use in India. Indian Council of Agricultural Research, New Delhi, pp. 67-71.
  [5]. Parikh, A. (1966): Consumption of Nitrogen fertilizer: A continuous cross–section study and covariance-analysis. Indian Economic Journal, 14(2), pp. 258- 274.
  [6]. Sagar, V (1991): Fertilizer pricing: are subsidies essential. Economics and Political Weekly, 14, pp. 59.
  [7]. Sah, D.C. and Shah Am. (1966): Farmer’s response to rise in fertilizers prices. Indian Journal of Agricultural Economics, 50 (4), pp. 609-611.
  [8]. Swaminathan, M.S. (1969): Scientific implications of HYV program. Economic and Political Weekly, 4, pp. 71-73.
  

  Citation
  Hemant Singh and Ramkrishna Singh Solanki, "Factors Influencing the use of Fertilizers in Agriculture of Madhya Pradesh in India," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.1, pp.18-40, 2014

• Open Access   Article

  A Review and Study of Coupled and Tripled Fixed Point Theory in Partially Ordered Metric Spaces

  C. S. Chauhan

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.1 , Issue.1 , pp.41-46, Feb-2014

  Abstract

  Full-Text HTML

  References

  Citation

  Abstract
  The aim of this paper is to present a review study of coupled and tripled fixed point in partially ordered complete metrics spaces. A.A.Harandi introduced a new simple and unified approach to coupled and tripled fixed point theory . Our results are review results of A.A.Harandi.

  Key-Words / Index Term
  Fixed Point, Tripled Fixed Point Metric Spaces

  References
  [1]. A.C.M. Ran , M.C.B. Reuring, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443 .
  [2]. R.P. Agrawal, M.A. EI-GEbeily, D. O’Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87(2008) 1-8.
  [3]. Gnana Bhaskar, V. Lakshmikanthan, Fixed point theorem in partially ordered metric spaces, Appl. Anal.87(2008) 1-8.
  [4]. V. Lakshmikanthan, L. Ciric, Coupled fixed point theorem for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70(2009) 4341-4349.
  [5]. J.J. Nietro, R.R.Lopeez, contractive mapping theorem in partially ordered set and applications to ordinary differential equations, order 22 (2005) 223-239.
  [6]. J.J. Nietro, R.R.Lopeez, Existence and uniqueness and fixed point in partially ordered set and applications to ordinary differential equations, Acta Math. Sinica, Engl. Ser. 23(12) (2007) 2205-2212.
  [7]. N. Van Luang, N. Xuan Thuan, coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74(2011) 983-992
  [8]. B. Samet, C. Vetro, Coupled fixed points, F- invariant set and fixed point of N-order, Ann. Func. Anal.1(2010) 46-56.
  [9]. M. Borcut, V. Berrinde, Tripled fixed point theorem for contractive type mapping in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889-4897.
  [10]. L.B.Ciric, A generalization of Babach’s contraction principle Amer. Math. Soc. 45 (1974) .
  [11]. V. Berinde, Generalized coupled fixed point theorem for mixed monotone mapping in partially ordered metric spaces, Nonlinear Anal. 74 ( 2011) 7347-7355.
  [12]. E. Hille, R.S. Phillips, Functional Analysis and Semigroups, In :Amer. Math. Society Colloquium Publications, Vol.13, Amer. Math. Society, Providence, RI, 1957.
  [13]. A.A. Harandi : Coupled and tripled fixed point theory in partially ordered metric spaces with application to initial value problem, Math. And Comp. Modelling 57(2013) 2343-2348.
  [14]. Babach, S. Surles, Operations dabseles ensembles abstracts at leur applications and equations integrals, Fund. Math Sci. 3(1992).
  

  Citation
  C. S. Chauhan, "A Review and Study of Coupled and Tripled Fixed Point Theory in Partially Ordered Metric Spaces," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.1, Issue.1, pp.41-46, 2014