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Year 2020, Volume: 38 Issue: 3, 1299 - 1306, 05.10.2021

Abstract

References

  • [1] Ali, A. T. and L´opez, R., (2010) Slant helices in Euclidean 4-space E4 , J. Egypt Math. Soc., 18(2), 223-230.
  • [2] Biton, Y.Y., Coleman, B.D. and Swigon, D., (2007) On bifurcations of equilibria of intrinsically curved, electrically charged, rod-like structures that model DNA molecules in solution, Journal of Elasticity, 87(2), 187-210.
  • [3] Dogan F., (2016) The proof of theorem which characterizes a slant helix, New Trends in Mathematical Sciences 4(2), 56-60.
  • [4] Hananoi, S., Ito, N. and Izumiya, S., (2015) Spherical Darboux images of curves on surfaces, Beitr. Algebra Geom., 56, 575-585.
  • [5] Izumiya, S. and Takeuchi, N., (2004) New special curves and developable surfaces, Turkish Journal of Mathematics, 28, 153-163.
  • [6] Lucas, P. and Ortega-Yag¨ues, J. A., (2016) Slant helices in the Euclidean three-space revisited, Bull. Belg. Math. Soc. Simon Stevin, 23, 133-150.
  • [7] Lucas, P. and Ortega-Yag¨ues, J. A., (2017) Helix surfaces and slant helices in the three-dimensional anti-De Sitter space, RACSAM, 111, 1201-1222.
  • [8] Macit, N. and D¨uld¨ul, M., (2017) Relatively normal-slant helices lying on a surface and their characterizations, Hacettepe Journal of Mathematics and Statistics, 46(3), 397-408.
  • [9] Ma˘gden, A., (1993) On the curves of constant slope, YYU Fen Bilimleri Dergisi ¨ , 4, 103-109.
  • [10] O’Neill, B., (1966) Elementary Differential Geometry, Academic Press, Burlington, MA, USA.
  • [11] Onder, M., Kazaz, M. and Kocayi˘git, H., (2008) ¨ B2-slant helix in Euclidean 4-space E4 , Int. J. Contemp. Math. Sciences, 3(29), 1433-1440.
  • [12] Ozdamar, E. and Hacısaliho˘glu, H.H., (1975) A characterization of inclined curves in Euclidean ¨ n-space, Commun. Fac. Sci. Univ. Ankara, Series A1 24A, 15-23.
  • [13] Toledo-Su´arez, C.D., (2009) On the arithmetic of fractal dimension using hyperhelices, Chaos, Solitons & Fractals, 39(1), 342-349.
  • [14] Weiner, J. L., (2000) How Helical Can a Closed, Twisted Space Curve be? American Mathematical Monthly 107(4), 327-333.
  • [15] Yang, X., (2003) High accuracy approximation of helices by quintic curves, Computer Aided Geometric Design, 20, 303-317.
  • [16] Yavari, M. and Zarrati, M., (2017) The slant helix solutions of the equilibrium shape equations for the biopolymer chains, Chinese Journal of Physics, 55, 444-456.

CHARACTERIZATIONS OF HELICES BY USING THEIR DARBOUX VECTORS

Year 2020, Volume: 38 Issue: 3, 1299 - 1306, 05.10.2021

Abstract

In this study, the behavior of the logistic difference model is investigated under random conditions using discrete probability distributions. The logistic difference model consists of parameters that depend on the population models to be used. For the study of random difference equation population models, the parameters are treated as random variables which constitutes the basis of the study. Random models were created using Uniform, Bernouilli, Binom, Negative Binomial (or Pascal), Geometric, Hypergeometric, Poisson distributions and their numerical characteristics are obtained through their simulations. Then, the results showing random numerical characteristics such as expected value, variance, standard deviation, coefficient of variation and confidence intervals were obtained with MATLAB package program. Analysis of random logistic difference model is given with the help of graphics and tables.

References

  • [1] Ali, A. T. and L´opez, R., (2010) Slant helices in Euclidean 4-space E4 , J. Egypt Math. Soc., 18(2), 223-230.
  • [2] Biton, Y.Y., Coleman, B.D. and Swigon, D., (2007) On bifurcations of equilibria of intrinsically curved, electrically charged, rod-like structures that model DNA molecules in solution, Journal of Elasticity, 87(2), 187-210.
  • [3] Dogan F., (2016) The proof of theorem which characterizes a slant helix, New Trends in Mathematical Sciences 4(2), 56-60.
  • [4] Hananoi, S., Ito, N. and Izumiya, S., (2015) Spherical Darboux images of curves on surfaces, Beitr. Algebra Geom., 56, 575-585.
  • [5] Izumiya, S. and Takeuchi, N., (2004) New special curves and developable surfaces, Turkish Journal of Mathematics, 28, 153-163.
  • [6] Lucas, P. and Ortega-Yag¨ues, J. A., (2016) Slant helices in the Euclidean three-space revisited, Bull. Belg. Math. Soc. Simon Stevin, 23, 133-150.
  • [7] Lucas, P. and Ortega-Yag¨ues, J. A., (2017) Helix surfaces and slant helices in the three-dimensional anti-De Sitter space, RACSAM, 111, 1201-1222.
  • [8] Macit, N. and D¨uld¨ul, M., (2017) Relatively normal-slant helices lying on a surface and their characterizations, Hacettepe Journal of Mathematics and Statistics, 46(3), 397-408.
  • [9] Ma˘gden, A., (1993) On the curves of constant slope, YYU Fen Bilimleri Dergisi ¨ , 4, 103-109.
  • [10] O’Neill, B., (1966) Elementary Differential Geometry, Academic Press, Burlington, MA, USA.
  • [11] Onder, M., Kazaz, M. and Kocayi˘git, H., (2008) ¨ B2-slant helix in Euclidean 4-space E4 , Int. J. Contemp. Math. Sciences, 3(29), 1433-1440.
  • [12] Ozdamar, E. and Hacısaliho˘glu, H.H., (1975) A characterization of inclined curves in Euclidean ¨ n-space, Commun. Fac. Sci. Univ. Ankara, Series A1 24A, 15-23.
  • [13] Toledo-Su´arez, C.D., (2009) On the arithmetic of fractal dimension using hyperhelices, Chaos, Solitons & Fractals, 39(1), 342-349.
  • [14] Weiner, J. L., (2000) How Helical Can a Closed, Twisted Space Curve be? American Mathematical Monthly 107(4), 327-333.
  • [15] Yang, X., (2003) High accuracy approximation of helices by quintic curves, Computer Aided Geometric Design, 20, 303-317.
  • [16] Yavari, M. and Zarrati, M., (2017) The slant helix solutions of the equilibrium shape equations for the biopolymer chains, Chinese Journal of Physics, 55, 444-456.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Mustafa Düldül This is me 0000-0002-7306-6006

Bahar Uyar Düldül This is me 0000-0003-3281-8918

Publication Date October 5, 2021
Submission Date March 16, 2020
Published in Issue Year 2020 Volume: 38 Issue: 3

Cite

Vancouver Düldül M, Uyar Düldül B. CHARACTERIZATIONS OF HELICES BY USING THEIR DARBOUX VECTORS. SIGMA. 2021;38(3):1299-306.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/