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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 354237, 6 pages
http://dx.doi.org/10.1155/2014/354237
Research Article

Time Scale in Least Square Method

1Department of Statistics, Faculty of Sciences, Hacettepe University, Beytepe, 06800 Ankara, Turkey
2Department of Statistics, Faculty of Sciences, Muğla Sıtkı Koçman University, 48000 Muğla, Turkey
3Department of Statistics, Faculty of Sciences, Ankara University, Beşevler, 06100 Ankara, Turkey

Received 8 January 2014; Accepted 6 March 2014; Published 3 April 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Özgür Yeniay et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  2. W. B. Powell, Approximate Dynamic Programming: Solving the Curses of Dimensionality, John Wiley & Sons, New York, NY, USA, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  3. E. Girejko, A. B. Malinowska, and D. F. M. Torres, “The contingent epiderivative and the calculus of variations on time scales,” Optimization: A Journal of Mathematical Programming and Operations Research, vol. 61, no. 3, pp. 251–264, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. H. Du and N. T. Dieu, “The first attempt on the stochastic calculus on time scale,” Stochastic Analysis and Applications, vol. 29, no. 6, pp. 1057–1080, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Almeida and D. F. M. Torres, “Isoperimetric problems on time scales with nabla derivatives,” Journal of Vibration and Control, vol. 15, no. 6, pp. 951–958, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. Bohner and A. Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003.
  7. M. Bohner, “Calculus of variations on time scales,” Dynamic Systems and Applications, vol. 13, no. 3-4, pp. 339–349, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Seiffertt, S. Sanyal, and D. C. Wunsch, “Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 38, no. 4, pp. 918–923, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. Z. Han, S. Sun, and B. Shi, “Oscillation criteria for a class of second-order Emden-Fowler delay dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 334, no. 2, pp. 847–858, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. C. Tisdell and A. Zaidi, “Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 11, pp. 3504–3524, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. C. Lizama and J. G. Mesquita, “Almost automorphic solutions of dynamic equations on time scales,” Journal of Functional Analysis, vol. 265, no. 10, pp. 2267–2311, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Sanyal, Stochastic Dynamic Equations [PhD dissertation], Missouri University of Science and Technology, Rolla, Mo, USA, 2008.
  13. Q. Sheng, M. Fadag, J. Henderson, and J. M. Davis, “An exploration of combined dynamic derivatives on time scales and their applications,” Nonlinear Analysis: Real World Applications, vol. 7, no. 3, pp. 395–413, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. X. Chen and Q. Song, “Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales,” Neurocomputing, vol. 121, no. 9, pp. 254–264, 2013. View at Publisher · View at Google Scholar
  15. A. Chen and F. Chen, “Periodic solution to BAM neural network with delays on time scales,” Neurocomputing, vol. 73, no. 1–3, pp. 274–282, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. F. M. Atici, D. C. Biles, and A. Lebedinsky, “An application of time scales to economics,” Mathematical and Computer Modelling, vol. 43, no. 7-8, pp. 718–726, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Bohner, M. Fan, and J. Zhang, “Periodicity of scalar dynamic equations and applications to population models,” Journal of Mathematical Analysis and Applications, vol. 330, no. 1, pp. 1–9, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. Bohner and T. Hudson, “Euler-type boundary value problems in quantum calculus,” International Journal of Applied Mathematics & Statistics, vol. 9, no. J07, pp. 19–23, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. G. Sh. Guseinov and E. Özyılmaz, “Tangent lines of generalized regular curves parametrized by time scales,” Turkish Journal of Mathematics, vol. 25, no. 4, pp. 553–562, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. I. Gravagne, R. J. Marks II, J. Davis, and J. DaCunha, “Application of time scales to real world time communications networks,” in Proceedings of the American Mathematical Society Western Section Meeting, 2004.
  21. I. A. Gravagne, J. M. Davis, and R. J. Marks, “How deterministic must a real-time controller be?” in Proceedings of the IEEE IRS/RSJ International Conference on Intelligent Robots and Systems (IROS '05), pp. 3856–3861, Edmonton, Canada, August 2005. View at Publisher · View at Google Scholar · View at Scopus
  22. I. Gravagne, J. Davis, J. DaCunha, and R. J. Marks II, “Bandwidth reduction for controller area networks using adaptive sampling,” in Proceedings of the International Conference on Robotics and Automation, pp. 2–6, New Orleans, La, USA, April 2004.
  23. R. J. Marks II, I. A. Gravagne, J. M. Davis, and J. J. DaCunha, “Nonregressivity in switched linear circuits and mechanical systems,” Mathematical and Computer Modelling, vol. 43, no. 11-12, pp. 1383–1392, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J. S. Armstrong, Principles of Forecasting: A Handbook for Researchers and Practitioners, Kluwer Academic, Dordrecht, The Netherlands, 2001. View at Publisher · View at Google Scholar
  25. D. R. Anderson and J. Hoffacker, “Green's function for an even order mixed derivative problem on time scales,” Dynamic Systems and Applications, vol. 12, no. 1-2, pp. 9–22, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. R. Agarwal, M. Bohner, D. O'Regan, and A. Peterson, “Dynamic equations on time scales: a survey,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 1–26, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. Q. Sheng and A. Wang, “A study of the dynamic difference approximations on time scales,” International Journal of Difference Equations, vol. 4, no. 1, pp. 137–153, 2009. View at Google Scholar · View at MathSciNet
  28. J. Neter, M. H. Kutner, C. J. Nachtsheim, and W. Wasserman, Applied Linear Statistical Models, McGraw-Hill, New York, NY, USA, 4th edition, 1996.
  29. D. C. Montgomery and G. C. Runger, Applied Statistics and Probability for Engineers, John Wiley & Sons, New York, NY, USA, 3rd edition, 2002.
  30. J. R. Hass, F. R. Giordano, and M. D. Weir, Thomas’ Calculus, Pearson Addison Wesley, 10th edition, 2004.
  31. R. P. Agarwal and M. Bohner, “Basic calculus on time scales and some of its applications,” Results in Mathematics, vol. 35, no. 1-2, pp. 3–22, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet