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Dariusz Janecki, Leszek Cedro and Jarosław Zwierzchowski

(3), 647–50. [9] Zhang, H., Yuan, Y., Piao, W. (2010). A universal spline filter for surface metrology. Measurement , 43(10), 1575–1582. [10] Hanada, H., Saito, T., Hasegawa, M., Yanagi, K. (2008). Sophisticated filtration technique for 3D surface topography data of rectangular area. Wear , 264(5–6), 422–427. [11] Schoenberg, I.J. (1969). Cardinal interpolation and spline functions. J. Approx. Theory , 2(2), 167–206. [12] Unser, M., Aldroubi, A., Eden, M. (1993). B-spline signal processing. Part I – Theory. IEEE Trans. Signal Processing , 41

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Waldemar Rakowski

signal and image processing,” IEEE Signal Processing Magazine, pp. 22-38, 1999. [5] A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems. Prentice-Hall International, Inc., 2/E, 1997. [6] J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Pearson Prentice Hall, 2007. [7] M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: Part i - theory,” IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 821-833, 1993. [8] ——, “B-spline signal processing: Part ii - efficient design and applications,” IEEE Transactions on Signal

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Ján Mihalík

References The Special Issue of the IEEE Trans. on Circuits and Systems for Video Technology on MPEG-4 SNHC, July 2004. MIHALÍK, J.: Standard Videocodec MPEG-4, Electronic Horizon 60 No. 2 (2003), 7-11. (In Slovak) MIHALÍK, J.: Modeling of Human Head Surface by using Triangular B-Splines., Radioengineering, 19 , No. 1, 2010, p.39-45. MIHALÍK, J.—MICHALČIN, V.: Animation of 3D Model of Human Head, Radioengineering 16 No. 1 (2007), 58

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Alaattin Esen and Orkun Tasbozan

References [1] Dehghan M., Jalil M., Abbas S., Solving nonlinear fractional partial differential equations using the homotopy analysis method, Numer. Meth. Part. D. E. 26 (2010), 448-479. [2] Ertürk V.S., Momani S., Solving systems of fractional differential equations using differential transform method, J. Comput. Appl. Math. 215 (2008), 142-151. [3] Esen A., Tasbozan O., An approach to time fractional gas dynamics equation: Quadratic B-spline Galerkin method, Appl. Math. Comput. 261 (2015), 330

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A. Esen, O. Tasbozan, Y. Ucar and N.M. Yagmurlu

References [1] K. B. Oldham and J. Spanier, The Fractional Calculus, Academic, New York, 1974. [2] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [3] F. Mainardi, Fractional Diffusive Waves in Viscoeslactic Solids., Non-linear Waves in Solids, J.L. Wegner and F.R. Norwood, eds., ASME/AMR, Fairfield, NJ, pp. 93-97, 1995. [4] F. Mainardi and P.Paradisi, A Model of Diffusive Waves in Viscoelasticity Based on Fractional Calculus, Proceedings of the 36th Conference on

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A. Esen and O. Tasbozan

and S.Momani, Solving fractional diffusion and waves equations by modifiy- ing homotopy perturbation method, Phys. Lett. A 370 (2007) 388-396. [10] A. Esen, Y. Ucar, N. Yagmurlu and O. Tasbozan, A Galerkin finite element method to solve fractional diffusion and fractional diffusion-wave equations, Math. Model. and Anal. 18 (2013) 260-273. [11] A. Esen, O. Tasbozan, Y. Ucar and N.M. Yagmurlu, A B-spline collocation method for solving fractional diffusion and fractional diffusion-wave equations, Tbilisi Math- ematical Journal 8 (2015) 181-193. [12] A. Mohebbi, A

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A. Moghaddam, A. Nayeri and S.M. Mirhosseini

. Bhattacharya, S., Bolton, M.D. and Madabhushi, S.P.G., 2005. A reconsideration of the safety of piled bridge foundations in liquefiable soils. Soils and Foundations , 45 (4), pp.13-25. Chi Wai, L., 2013. Parametric studies on buckling of piles in cohesionless soils by numerical methods. Hkie Transactions , 20 (1), pp.12-33. Caglar, H. and Caglar, N., 2008. Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations. Applied Mathematics and Computation , 201 (1-2), pp.597-603. Caglar, H., Caglar, N. and Ozer, M., 2008

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Dušan Páleš, Veronika Váliková, Ján Antl and František Tóth

In this contribution, we present the description of a B-spline curve. We deal with creation of its basis function as well as with creation of the curve itself from entered control points. Following the literature, we formed an algorithm for B-spline modelling and we used it for the planar and spatial curve. The planar curve is made of chosen points. The spatial curve approximates the trajectory of a real vehicle, which trajectory was obtained by the set of measured points. The modelled curve very exactly describes the polygon created from the linked control points. With the lowering degree of the curve, this one is more clamping to the given polygon and for the extreme case it is transformed to the polygon itself. The advantage of the B-spline curve use is, for example in comparison with a Bézier curve, high adaptability, which is expressed in its parameters - besides entered control points, these are knots generated on the curve and degree of the curve.

Open access

Stanisław Rosłoniec

. B. C. Wadell, Transmission Line Design Handbook. Boston (MA): Artech House Inc., 1991. C. Boor, A practical Guide to Splines-Second Edition. New York: Springer-Verlag, 2001. J. H. Mathews, Numerical Methods for Mathematics, Science and Engineering. Englewood Cliffs, N. J.: Prentice-Hall International Inc., 1992. E. V. Shikin and A. I. Plis, Handbook on Splines for the User. New York: CRC Press, 1995. P. Kiciak, Private information of March 17. Warsaw

Open access

Magnolia Tilca and Meda Bojor

References 1. Blundell, R., Chen, X. K. (2007). Semi-Nonparametric IV Estimation of Shape- Invariant Engel Curves. Econometrica, Vol. 75, No. 6 , pp. 1613-1669. 2. Breiman, L., Friedman, J. H., Olshen, R. A., Stone, C. J. (1984). Classification and regression trees. Wadsworth and Books/Cole, Belmont, CA. 3. de Boor, C. (1972). On calculating with B-splines. J. Approx. Theory, 6 , pp 50-62. 4. Friedman, J. H. (1991). Multivariate Adaptive Regression Splines. The Annals of Statistics, Vol. 19, No