References
- [1] J. Arsuaga, M. Vazquez, P. McGuirk, S. Trigueros, De W. Sumners, J. Roca, DNA knots reveal a chiral organization of DNA in phage capsids, PNAS USA, 102, 9165-9169, (2005).10.1073/pnas.0409323102116658815958528
- [2] O. Belova, J. Mikeš, M. Sherkuziyev, N. Sherkuziyeva, An analytical inflexibility of surfaces attached along a curve to surface regarding a point and plane, Rusults in Math., 76, 56, (2021).10.1007/s00025-021-01362-0
- [3] R. Capovilla, C. Chryssomalakos, J. Guven, Hamiltonians for curves, J. Phys.A:Math. Gen., 35(31), 65-71, (2002).
- [4] B.D. Coleman, D. Swigon, Theory of self-contact in Kirchhoff rods with applications to supercoiling of knotted and unknotted DNA plasmids, Phil.Trans.R.Soc.Lond. A, 362, 1281-1299, (2004).10.1098/rsta.2004.139315306451
- [5] N. Efimov, Kachestvennye voprosy teorii deformacii poverhnostei, UMN 3.2, 47-158, (1948).
- [6] U. Gözütok, HA. Coban, Y. Sağiroğlu, Ruled surfaces obtained by bending of curves, Turk.J.Math., 44(1), 300-306, (2020).10.3906/mat-1908-21
- [7] I. Hinterleitner, J. Mikeš, J. Stranska, Infinitesimal F-planar transformations, Russ. Math., 52(4), 13-18, (2008).10.3103/S1066369X08040026
- [8] V. Katritch, J. Bednar, D. Michoud, R.G. Scharein, J. Dubochet, A. Stasiak, Geometry and physics of knots, Nature, 384, 142-145, (1996).10.1038/384142a0
- [9] L. Kauffman, Lj. Velimirović, M. Najdanović, S. Rančić, Infinitesimal bending of knots and energy change, J. Knot Theo. Ramifications, 28(11), 1940009, (2019).10.1142/S0218216519400091
- [10] F. Maggioni, S.Z. Alamri, C.F. Barenghi, R.L. Ricca, Velocity, energy and helicity of vortex knots and unknots, Phys. Rev. E, 82, 26309-26317, (2010).10.1103/PhysRevE.82.02630920866907
- [11] M. Maksimović, Flexibility of curves on a single-sheet hyperboloid, J. Eng. Math., 123, 19-27, (2020).10.1007/s10665-020-10048-5
- [12] M. Maksimović, Lj. Velimirović, M. Najdanović, Infinitesimal bending of DNA helices, Turk.J.Math., 45(1), 520-528, (2021).10.3906/mat-2003-106
- [13] H.K. Moffat, The energy spectrum of knots and links, Nature, 347, (1990).10.1038/347367a0
- [14] M. Najdanović, Infinitesimal bending influence on the Willmore energy of curves, Filomat, 29(10), 2411-2419, (2015).10.2298/FIL1510411N
- [15] M. Najdanović, Lj. Velimirović, On the Willmore energy of curves under second order infinitesimal bending, Miskolc Math. Notes, 17(2), 979-987, (2017).10.18514/MMN.2017.2133
- [16] M. Najdanović, Lj. Velimirović, Infinitesimal bending of curves on the ruled surfaces, The University Thought - Publication in Natural Sciences, 8(1), 46-51, (2018).10.5937/univtho8-17403
- [17] M. Najdanović, S. Rančić, L. Kauffman, Lj. Velimirović, The total curvature of knots under second-order infinitesimal bending, J. Knot Theo. Ramifications, 28(1), 1950005, (2019).10.1142/S0218216519500056
- [18] C. Oberti, R.L. Ricca, On torus knots and unknots, J. Knot Theo. Ramifications, 25(6), 1650036, (2016).10.1142/S021821651650036X
- [19] C. Oberti, R.L. Ricca, Induction effects of torus knots and unknots, J. Phys. A: Math. Theor., 50, 365501, (2017).
- [20] D. Proment, M. Onorato, C.F. Barenghi, Vortex knots in a Bose- Einstein condensate, Phys. Rev. E, 85, 036306, (2012).10.1103/PhysRevE.85.03630622587179
- [21] D. Reith, P. Cifra, A. Stasiak,P. Virnau, Effective stiffening of DNA due to nematic ordering causes DNA molecules packed in phage capsids to preferentially form torus knots, Nucleic Acids Res., 22, 1-9, (2012).10.1093/nar/gks157336719322362732
- [22] L. RýparováL,J.Mikeš, Infinitesimal rotary transformation, Filomat -The 20th Geometrical Seminar 2018, 33(4), 1153-1157, (2019).10.2298/FIL1904153R
- [23] I. Vekua, Obobschennye Analiticheskie Funkcii, Moskva, (1959).
- [24] Lj. Velimirović, Change of geometric magnitudes under infinitesimal bending, Facta Univ., 3(11), 135-148, (2001).
- [25] Lj. Velimirović, Infinitesimal bending, Faculty Sci. Math.,Niš, 2009. ISBN 86-83481-42-5.
- [26] Lj. Velimirović, M.Ćirić, M. Cvetković, Change of the Willmore energy under infinitesimal bending of membranes, Comput. Math. with Appl., 59(12), 3679-3686, (2010).10.1016/j.camwa.2010.03.069
- [27] Lj. Velimirović, M.Ćirić, N. Velimirović, On the Willmore energy of shells under infinitesimal deformations, Comput. Math. with Appl., 61(11), 3181-3190, (2011).10.1016/j.camwa.2011.03.035
- [28] Lj. Velimirović, M. Cvetković, M.Ćirić, N. Velimirović, Analysis of Gaudi surfaces at small deformations, Appl. Math. Comput., 218, 6999-7004, (2012).10.1016/j.amc.2011.12.005