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1Academic Journal
المؤلفون: Spíchal, Luděk
وصف الملف: application/pdf
Relation: reference:[1] Bellos, A.: Alexova dobrodružství v zemi čísel. Dokořán, Praha, 2015.; reference:[2] Buitrago, A. R.: Polygons, diagonals, and the bronze mean. Nexus Network J. (2007), 321–326.; reference:[3] Douady, S., Couder, Y.: Phyllotaxis as a physical self organised growth process. Phys. Rev. Lett. 68 (1992), 2098–2101. 10.1103/PhysRevLett.68.2098; reference:[4] Fowler, D. R., Hanan, J., Prusinkiewicz, R.: Modelling spiral phyllotaxis. Computer & Graphics 13 (1989), 291–296.; reference:[5] Gielis, J.: Inventing the circle: the geometry of nature. Geniaal Publishers, Antwerp, 2003.; reference:[6] Gielis, J.: A generic geometric transformation that unifies a wide range of natural and abstract shapes. Amer. J. Bot. 90 (2003), 333–338. 10.3732/ajb.90.3.333; reference:[7] Gielis, J.: The geometrical beauty of plants. Atlantis Press, Paris, 2017. MR 3644202; reference:[8] Křížek, M., Somer, L., Šolcová, A.: Kouzlo čísel: od velkých objevů k aplikacím. Academia, Praha, 2018.; reference:[9] Newell, A. C., Shipman, P. D.: Plants and Fibonacci. J. Stat. Phys. 121 (2005), 937–968. MR 2192540; reference:[10] Prusinkiewicz, P., Lindenmayer, A.: Phyllotaxis. In: The Algorithmic Beauty of Plants. The Virtual Laboratory. Springer, New York, 1990. MR 1067146; reference:[11] Ridley, J. N.: Packing efficiency in sunflower heads. Math. Biosci. 58 (1982), 129–139. MR 0674888, 10.1016/0025-5564(82)90056-6; reference:[12] Spíchal, L.: Gielisova transformace logaritmické spirály. Pokroky Mat. Fyz. Astronom. 65 (2020), 76–89.; reference:[13] Spíchal, L.: Superelipsa a superformule. Matematika-fyzika-informatika 29 (2020), 60–75.; reference:[14] Spinadel, V. W. de: From the golden mean to chaos. Editorial Nueva Librería, Buenos Aires, 1998.; reference:[15] Spinadel, V. W. de, Paz, J. M.: A new family of irrational numbers with curious properties. Humanistic Mathematics Network J. 19 (1999), 33–37. 10.5642/hmnj.199901.19.14; reference:[16] Stewart, I.: Neuvěřitelná čísla profesora Stewarta. Dokořán, Praha, 2019.; reference:[17] Vogel, H.: A better way to construct the sunflower head. Math. Biosci. 44 (1979), 119–189. 10.1016/0025-5564(79)90080-4
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2Academic Journal
المؤلفون: Spíchal, Luděk
مصطلحات موضوعية: msc:53A04
وصف الملف: application/pdf
Relation: reference:[1] Anatriello, G., Vincenzi, G.: Logarithmic spirals and continue triangles. J. Comput. Appl. Math. 296 (2016), 127–137. MR 3430129, 10.1016/j.cam.2015.09.004; reference:[2] Gardner, M.: The superellipse: a curve that lies between the ellipse and the rectangle. Sci. Am. 213 (1965), 222–238.; reference:[3] Gielis, J.: Inventing the circle: the geometry of nature. Geniaal Publishers, Antwerp, 2003.; reference:[4] Gielis, J.: A generic geometric transformation that unifies a wide range of natural and abstract shapes. Am. J. Bot. 90 (2003), 333–338. 10.3732/ajb.90.3.333; reference:[5] Gielis, J.: The geometrical beauty of plants. Atlantis Press, Paris, 2017. MR 3644202; reference:[6] Harary, G., Tal, A.: The natural 3D spiral. Comput. Graph. Forum 30 (2011), 237–246. 10.1111/j.1467-8659.2011.01855.x; reference:[7] Holcombe, S. A., Wang, S. C., Grotberg, J. B.: Modeling female and male rib geometry with logarithmic spirals. J. Biomech. 49 (2016), 2995–3003. 10.1016/j.jbiomech.2016.07.021; reference:[8] Jones, R. T., Peterson, B. B.: Almost congruent triangles. Math. Mag. 47 (1974), 180–189. MR 0346650, 10.1080/0025570X.1974.11976393; reference:[9] Jong van Coevorden, C. M. de, Gielis, J., Caratelli, D.: Application of Gielis transformation to the design of metamaterial structures. J. Phys. Conf. Ser. 963 (2018), article no. 012008.; reference:[10] Matsuura, M.: Gielis superformula and regular polygons. J. Geom. 106 (2015), 383–403. MR 3353843, 10.1007/s00022-015-0269-z; reference:[11] Sharma, C., Dinesh, K. V.: Miniaturization of spiral antenna based on Fibonacci sequence using modified Koch curve. IEEE Antennas Wirel. Propag. Lett. 16 (2017), 932–935. 10.1109/LAWP.2016.2614721; reference:[12] Sharma, C., Dinesh, K. V.: Miniaturization of logarithmic spiral antenna using Fibonacci sequence and Koch fractals. 3rd International Conference for Convergence in Technology (I2CT), Pune, 2018, 1–4.; reference:[13] Spíchal, L.: Superelipsa a superformule. Matematika – fyzika – informatika 29 (2020), 60–75.; reference:[14] Verstraelen, L. C. A.: Univerzální přírodní tvary. Pokroky Mat. Fyz. Astronom. 52 (2007), 142–151.
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3Book
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4Academic Journal
المؤلفون: Cufí, Julià, Reventós, Agustí
مصطلحات موضوعية: keyword:curvature, keyword:evolutes, keyword:isoperimetric deficit, keyword:Gauss-Bonnet, msc:52A10, msc:52A55, msc:53A04
وصف الملف: application/pdf
Relation: mr:MR3291851; zbl:Zbl 06487008; reference:[1] Bruna, J., Cufí, J.: Complex Analysis.European Mathematical Society, 2013. MR 3076702; reference:[2] Chern, S. S.: Curves and surfaces in Euclidean space.Studies in Global Geometry and Analysis 4 (1967), 16–56. MR 0212744; reference:[3] Escudero, C. A., Reventós, A.: An interesting property of the evolute.Amer. Math. Monthly 114 (7) (2007), 623–628. Zbl 1144.53007, MR 2341325; reference:[4] Escudero, C. A., Reventós, A., Solanes, G.: Focal sets in two-dimensional space forms.Pacific J. Math. 233 (2007), 309–320. Zbl 1152.53063, MR 2366378, 10.2140/pjm.2007.233.309; reference:[5] Fenchel, W.: On the differential geometry of closed space curves.Bull. Amer. Math. Soc. (N.S.) 57 (1951), 44–54. Zbl 0042.40006, MR 0040040, 10.1090/S0002-9904-1951-09440-9; reference:[6] Hurwitz, A.: Sur quelques applications géométriques des séries de Fourier.Annales scientifiques de l' É.N.S. 19 (1902), 357–408. MR 1509016; reference:[7] Martinez-Maure, Y.: Sommets et normales concourantes des courbes convexes de largeur constante et singularités des hérissons.Arch. Math. 79 (2002), 489–498. Zbl 1025.52004, MR 1967267, 10.1007/BF02638386; reference:[9] Santaló, L. A.: Integral Geometry and Geometric Probability.Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976, With a foreword by Mark Kac, Encyclopedia of Mathematics and its Applications, Vol. 1. Zbl 0342.53049, MR 0433364; reference:[10] Spivak, M.: A Comprehensive Introduction to Differential Geometry.Publish or Perish, Inc. Berkeley, 1979, 2a ed., 5 v. Zbl 0439.53005
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5Academic Journal
المؤلفون: Duda, Jakub, Zajíček, Luděk
مصطلحات موضوعية: keyword:curve in Banach spaces, keyword:$C^{1,\rm BV}$ parametrization, keyword:parametrization with bounded convexity, msc:26A51, msc:26E20, msc:53A04
وصف الملف: application/pdf
Relation: mr:MR3165515; zbl:Zbl 06373962; reference:[1] Alexandrov, A. D., Reshetnyak, Yu. G.: General Theory of Irregular Curves. Transl. from the Russian by L. Ya. Yuzina.Mathematics and Its Applications: Soviet Series 29 Kluwer Academic Publishers, Dordrecht (1989). Zbl 0691.53002, MR 1117220; reference:[2] Bourbaki, N.: Éléments de Mathématique. I: Les structures fondamentales de l'analyse. Livre IV: Fonctions d'une variable réelle (théorie élémentaire). Chapitres 1, 2 et 3: Dérievées. Primitives et intégrales. Fonctions élémentaires. Second ed.French Actualés Sci. Indust. 1074 Hermann, Paris (1958).; reference:[3] Chistyakov, V. V.: On mappings of bounded variation.J. Dyn. Control Sys. 3 (1997), 261-289. Zbl 0940.26009, MR 1449984, 10.1007/BF02465896; reference:[4] Duda, J.: Curves with finite turn.Czech. Math. J. 58 (2008), 23-49. Zbl 1167.46321, MR 2402524, 10.1007/s10587-008-0003-1; reference:[5] Duda, J.: Second order differentiability of paths via a generalized $\frac{1}{2}$-variation.J. Math. Anal. Appl. 338 (2008), 628-638. Zbl 1135.46021, MR 2386444, 10.1016/j.jmaa.2007.05.046; reference:[6] Duda, J.: Generalized $\alpha$-variation and Lebesgue equivalence to differentiable functions.Fundam. Math. 205 (2009), 191-217. Zbl 1191.26003, MR 2557935, 10.4064/fm205-3-1; reference:[7] Duda, J., Zajíček, L.: Curves in Banach spaces---differentiability via homeomorphisms.Rocky Mt. J. Math. 37 (2007), 1493-1525. MR 2382898, 10.1216/rmjm/1194275931; reference:[8] Duda, J., Zajíek, L.: Curves in Banach spaces which allow a $C^2$-parametrization or a parametrization with finite convexity.J. London Math. Soc., II. Ser. 83 (2011), 733-754. MR 2802508, 10.1112/jlms/jdq100; reference:[9] Duda, J., Zajíek, L.: On vector-valued curves that allow a $C^{1,\alpha}$-parametrization.Acta Math. Hung. 127 (2010), 85-111. MR 2629670, 10.1007/s10474-010-9094-x; reference:[10] Duda, J., Zajíček, L.: Curves in Banach spaces which allow a $C^2$-parametrization.J. Lond. Math. Soc., II. Ser. 83 (2011), 733-754. MR 2802508, 10.1112/jlms/jdq100; reference:[11] Federer, H.: Geometric Measure Theory.Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 153. Springer, New York (1969). Zbl 0176.00801, MR 0257325; reference:[12] Kirchheim, B.: Rectifiable metric spaces: Local structure and regularity of the Hausdorff measure.Proc. Am. Math. Soc. 121 (1994), 113-123. Zbl 0806.28004, MR 1189747, 10.1090/S0002-9939-1994-1189747-7; reference:[13] Kühnel, W.: Differential Geometry. Curves-Surfaces-Manifolds. Transl. from the German by Bruce Hunt.Student Mathematical Library 16. AMS Providence, RI (2002). Zbl 1009.53002, MR 1882174; reference:[14] Laczkovich, M., Preiss, D.: $\alpha$-variation and transformation into $C\sp n$ functions.Indiana Univ. Math. J. 34 (1985), 405-424. Zbl 0634.26006, MR 0783923, 10.1512/iumj.1985.34.34024; reference:[15] Lebedev, V. V.: Homeomorphisms of an interval and smoothness of a function.Math. Notes 40 (1986), 713-719 translation from Mat. Zametki 40 (1986), 364-373 Russian. Zbl 0637.26006, MR 0869927, 10.1007/BF01142475; reference:[16] Massera, J. L., Schäffer, J. J.: Linear differential equations and functional analysis I.Ann. Math. (2) 67 (1958), 517-573. Zbl 0178.17701, MR 0096985, 10.2307/1969871; reference:[17] Pogorelov, A. V.: Extrinsic Geometry of Convex Surfaces. Translated from the Russian by Israel Program for Scientific Translations.Translations of Mathematical Monographs 35 AMS, Providence, RI (1973). Zbl 0311.53067, MR 0346714, 10.1090/mmono/035; reference:[18] Roberts, A. W., Varberg, D. E.: Convex Functions.Pure and Applied Mathematics 57 Academic Press, a subsidiary of Harcourt Brace Jovanovich, New York (1973). Zbl 0271.26009, MR 0442824; reference:[19] Veselý, L.: On the multiplicity points of monotone operators on separable Banach spaces.Commentat. Math. Univ. Carol. 27 (1986), 551-570. MR 0873628; reference:[20] Veselý, L., Zajíek, L.: Delta-convex mappings between Banach spaces and applications.Dissertationes Math. (Rozprawy Mat.) 289 1-48 (1989). MR 1016045; reference:[21] Veselý, L., Zajíek, L.: On vector functions of bounded convexity.Math. Bohem. 133 (2008), 321-335. MR 2494785
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6Academic Journal
المؤلفون: Koudela, Libor
وصف الملف: application/pdf
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7Conference
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8Academic Journal
المؤلفون: Miyamoto, Yuki, Nagasawa, Takeyuki, Suto, Fumito
مصطلحات موضوعية: keyword:gradient flow, keyword:bending energy, keyword:total-length constraint, keyword:local-length constraint, msc:35K30, msc:35K55, msc:53A04, msc:53C44, msc:58J35
وصف الملف: application/pdf
Relation: mr:MR2588627; zbl:Zbl 1194.53004; reference:[1] G. Dziuk, E. Kuwert, and R. Schätzle: Evolution of elastic curves in $\mathbb R^n$: existence and computation.SIAM J. Math. Anal. 33 (2002), 5, 1228–1245. MR 1897710; reference:[2] T. Kurihara and T. Nagasawa: On the gradient flow for a shape optimization problem of plane curves as a singular limit.Saitama J. Math. 24 (2006/2007), 43–75. MR 2396572; reference:[3] K. Mikula and D. Ševčovič: Evolution of plane curves driven by a nonlinear function of curvature and anisotropy.SIAM J. Appl. Math. 61 (2001), 5, 1473–1501. MR 1824511; reference:[4] K. Mikula and D. Ševčovič: A direct method for solving an anisotropic mean curvature flow of plane curves with an external force.Math. Methods Appl. Sci. 27 (2004), 13, 1545–1565. MR 2077443; reference:[5] K. Mikula and D. Ševčovič: Computational and qualitative aspects of evolution of curves driven by curvature and external force.Comput. Vis. Sci. 6 (2004), 4, 211–225. MR 2071441; reference:[6] K. Mikula and D. Ševčovič: Evolution of curves on a surface driven by the geodesic curvature and external force.Appl. Anal. 85 (2006), 4, 345–362. MR 2196674; reference:[7] Y. Miyamoto: Reformulation of Local-Constraint-Gradient Flow for Bending Energy of Plane Curves Applying the Fredholm Alternative (in Japanese).Master Thesis, Saitama University, 2009.; reference:[8] S. Okabe: The motion of elastic planar closed curve under the area-preserving condition.Indiana Univ. Math. J. 56 (2007), 4, 1871–1912. MR 2354702; reference:[9] F. Suto: On the Global Existence for Local/Total-Constraint-Gradient Flows for the Bending Energy of Plane Curves (in Japanese).Master Thesis, Saitama University, 2009.
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9Conference
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10Academic Journal
المؤلفون: Duda, Jakub
مصطلحات موضوعية: keyword:curve with finite turn, keyword:tangent of a curve, keyword:curve with finite convexity, keyword:delta-convex curve, keyword:d.c. curve, msc:14H50, msc:46T20, msc:46T99, msc:53A04, msc:58B99
وصف الملف: application/pdf
Relation: mr:MR2402524; zbl:Zbl 1167.46321; reference:[1] A. D. Alexandrov, Yu. Reshetnyak: General Theory of Irregular Curves.Mathematics and its Applications (Soviet Series), Vol. 29, Kluwer Academic Publishers, Dordrecht, 1989. MR 1117220; reference:[2] Y. Benyamini, J. Lindenstrauss: Geometric Nonlinear Functional Analysis, Vol. 1. Colloquium Publications 48.American Mathematical Society, Providence, 2000. MR 1727673; reference:[3] J. Duda, L. Veselý, L. Zajíček: On D.C. functions and mappings.Atti Sem. Mat. Fis. Univ. Modena 51 (2003), 111–138. MR 1993883; reference:[4] M. Gronychová: Konvexita a ohyb křivky.Master Thesis, Charles University, Prague, 1987. (Czech); reference:[5] N. Kalton: private communication.; reference:[6] A. V. Pogorelov: Extrinsic geometry of convex surfaces.Translations of Mathematical Monographs, Vol. 35, American Mathematical Society, Providence, 1973. Zbl 0311.53067, MR 0346714; reference:[7] A. W. Roberts, D. E. Varberg: Convex functions.Pure and Applied Mathematics, Vol. 57, Academic Press, New York-London, 1973. MR 0442824; reference:[8] J. J. Schäffer: Geometry of Spheres in Normed Spaces.Lecture Notes in Pure and Applied Mathematics Vol. 20, Marcel Dekker, New York-Basel, 1976. MR 0467256; reference:[9] L. Veselý: On the multiplicity points of monotone operators on separable Banach spaces.Comment. Math. Univ. Carolinae 27 (1986), 551–570. MR 0873628; reference:[10] L. Veselý, L. Zajíček: Delta-convex mappings between Banach spaces and applications.Diss. Math. Vol. 289, 1989. MR 1016045
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11Academic Journal
المؤلفون: Abdel-Baky, Rashad A., Al-Bokhary, Ashwaq J.
مصطلحات موضوعية: keyword:lines of curvature, keyword:line congruence, keyword:E. Study’s map, keyword:instantaneous revolution axis, msc:53A04, msc:53A05, msc:53A17
وصف الملف: application/pdf
Relation: mr:MR2462978; zbl:Zbl 1212.53001; reference:[1] Abdel-Baky, R. A.: On the congruences of the tangents to a surface.Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 136 (1999), 9–18. Zbl 1017.53003, MR 1908813; reference:[2] Abdel-Baky, R. A.: On instantaneous rectilinear congruences.J. Geom. Graph. 7 (2) (2003), 129–135. Zbl 1066.53036, MR 2071274; reference:[3] Abdel Baky, R. A.: Inflection and torsion line congruences.J. Geom. Graph. 11 (1) (2004), 1–14. MR 2364050; reference:[4] Abdel-Baky, R. A.: On a line congruence which has the parameter ruled surfaces as principal ruled surfaces.Appl. Math. Comput. 151 (2004), 849–862. Zbl 1058.53010, MR 2052463, 10.1016/S0096-3003(03)00541-1; reference:[5] Blaschke, W.: Vorlesungen über Differential Geometrie.Dover Publications, New York, 1945. MR 0015247; reference:[6] Bottema, O., Roth, B.: Theoretical Kinematics.North-Holland Press, New York, 1979. Zbl 0405.70001, MR 0533960; reference:[7] Clifford, W. K.: Preliminary Sketch of bi-quaternions.Proc. London Math. Soc. 4 (64, 65) (1873), 361–395.; reference:[8] Eisenhart, L. P.: A Treatise in Differential Geometry of Curves and Surfaces.New York, Ginn Camp., 1969.; reference:[9] Gugenheimer, H. W.: Differential Geometry.Graw-Hill, New York, 1956.; reference:[10] Gursy, O.: The dual angle of pitch of a closed ruled surface.Mech. Mach. Theory 25 (47) (1990), 131–140. 10.1016/0094-114X(90)90114-Y; reference:[11] Hlavaty, V.: Differential Line Geometry.Groningen, P. Noordhoff Ltd. X, 1953. Zbl 0051.39101, MR 0057592; reference:[12] Hoschek, J.: Liniengeometrie.B.I. Hochschultaschenbuch, Mannheim, 1971. Zbl 0227.53007, MR 0353164; reference:[13] Karger, A., Novak, J.: Space Kinematics and Lie Groups.Gordon and Breach Science Publishers, New York, 1985. MR 0801394; reference:[14] Koch, R.: Zur Geometrie der zweiten Grundform der Geradenkongruenzen des $E^3$.Verh. K. Acad. Wet. Lett. Schone Kunsten Belg., Kl. Wet. 43 (162) (1981). MR 0629825; reference:[15] Kose, Ö.: Contributions to the theory of integral invariants of a closed ruled surface.Mech. Mach. Theory 32 (2) (1997), 261–277. 10.1016/S0094-114X(96)00034-1; reference:[16] Mc-Carthy, J. M.: On the scalar and dual formulations of curvature theory of line trajectories.ASME, J. Mech. Transmiss. Automation in Design 109 (1987), 101–106. 10.1115/1.3258772; reference:[17] Muller, H. R.: Kinematik Dersleri.Ankara University Press, 1963. MR 0157519; reference:[18] Schaaf, J. A.: Curvature theory of line trajectories in spatial kinematics.Doctoral dissertation, University of California, Davis (1988). MR 2636385; reference:[19] Schaaf, J. A.: Geometric continuity of ruled surfaces.Comput. Aided Geom. Design 15 (1998), 289–310. Zbl 0903.68192, MR 1614079, 10.1016/S0167-8396(97)00032-0; reference:[20] Stachel, H.: Instantaneous spatial kinematics and the invariants of the axodes.Tech. report, Institute für Geometrie, TU Wien 34, 1996.; reference:[21] Veldkamp, G. R.: On the use of dual numbers, vectors, and matrices in instantaneous spatial kinematics.Mech. Mach. Theory 11 (1976), 141–156. 10.1016/0094-114X(76)90006-9; reference:[22] Weatherburn, M. A.: Differential Geometry of Three Dimensions.Cambridge University Press, 1, 1969.; reference:[23] Yang, A. T.: Application of Quaternion Algebra and Dual Numbers to the Analysis of Spatial Mechanisms.Doctoral dissertation, Columbia (1967).
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12Academic Journal
المؤلفون: Yazaki, Shigetoshi
مصطلحات موضوعية: keyword:tangential velocity, keyword:intrinsic heat equation, keyword:crystalline algorithm, keyword:admissible polygonal curve, msc:34A26, msc:34A34, msc:35K65, msc:53A04, msc:53C44, msc:53C80, msc:65L20, msc:65M12, msc:65N12
وصف الملف: application/pdf
Relation: mr:MR2388404; zbl:Zbl 1139.53033; reference:[1] Angenent S., Gurtin M. E.: Multiphase thermomechanics with interfacial structure, 2.Evolution of an isothermal interface. Arch. Rational Mech. Anal. 108 (1989), 323–391 MR 1013461, 10.1007/BF01041068; reference:[2] Deckelnick K.: Weak solutions of the curve shortening flow.Calc. Var. Partial Differential Equations 5 (1997), 489–510 Zbl 0990.35076, MR 1473305, 10.1007/s005260050076; reference:[3] .Dziuk, G: Convergence of a semi discrete scheme for the curve shortening flow.Math. Models Methods Appl. Sci. 4 (1994), 589–606 Zbl 0811.65112, MR 1291140, 10.1142/S0218202594000339; reference:[4] Giga Y.: Anisotropic curvature effects in interface dynamics.Sūgaku 52 (2000), 113–127; English transl., Sugaku Expositions 16 (2003), 135–152 MR 2019167; reference:[5] Giga M.-H., Giga Y.: Crystalline and level set flow – convergence of a crystalline algorithm for a general anisotropic curvature flow in the plane.GAKUTO Internat. Ser. Math. Sci. Appl. 13 (2000), 64–79 Zbl 0957.35122, MR 1793023; reference:[6] Gurtin M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane.Clarendon Press, Oxford 1993 Zbl 0787.73004, MR 1402243; reference:[7] Hirota C., Ishiwata, T., Yazaki S.: Numerical study and examples on singularities of solutions to anisotropic crystalline curvature flows of nonconvex polygonal curves.In: Advanced Studies in Pure Mathematics (ASPM); Proc. MSJ-IRI 2005 “Asymptotic Analysis and Singularity”, Sendai 2005 (to appear) Zbl 1143.35308, MR 2387254; reference:[8] Hontani H., Giga M.-H., Giga, Y., Deguchi K.: Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis.Discrete Appl. Math. 147 (2005), 265–285 Zbl 1117.65036, MR 2127078, 10.1016/j.dam.2004.09.015; reference:[9] Ishiwata T., Ushijima T. K., Yagisita, H., Yazaki S.: Two examples of nonconvex self-similar solution curves for a crystalline curvature flow.Proc. Japan Academy, Ser. A 80 (2004), 8, 151–154 Zbl 1077.53054, MR 2099341; reference:[10] Kimura M.: Accurate numerical scheme for the flow by curvature.Appl. Math. Letters 7 (1994), 69–73 Zbl 0792.65100, MR 1349897, 10.1016/0893-9659(94)90056-6; reference:[11] Mikula K., Ševčovič D.: Solution of nonlinearly curvature driven evolution of plane curves.Appl. Numer. Math. 31 (1999), 191–207 Zbl 0938.65145, MR 1708959, 10.1016/S0168-9274(98)00130-5; reference:[12] Mikula K., Ševčovič D.: Evolution of plane curves driven by a nonlinear function of curvature and anisotropy.SIAM J. Appl. Math. 61 (2001), 1473–1501 Zbl 0980.35078, MR 1824511, 10.1137/S0036139999359288; reference:[13] Taylor J. E.: Constructions and conjectures in crystalline nondifferential geometry.In: Proc. Conference on Differential Geometry, Rio de Janeiro, Pitman Monographs Surveys Pure Appl. Math. 52 (1991), pp. 321–336, Pitman, London 1991 Zbl 0725.53011, MR 1173051; reference:[14] Taylor J. E.: Motion of curves by crystalline curvature, including triple junctions and boundary points.Diff. Geom.: Partial Diff. Eqs. on Manifolds (Los Angeles 1990), Proc. Sympos. Pure Math., 54 (1993), Part I, pp, 417–438, AMS, Providence MR 1216599; reference:[15] Taylor J. E., Cahn, J., Handwerker C.: Geometric models of crystal growth.Acta Metall. 40 (1992), 1443–1474 10.1016/0956-7151(92)90090-2; reference:[16] Ushijima T. K., Yagisita H.: Approximation of the Gauss curvature flow by a three-dimensional crystalline motion.In: Proc. Czech–Japanese Seminar in Applied Mathematics 2005; Kuju Training Center, Oita, Japan, September 15–18, 2005, COE Lecture Note 3, Faculty of Mathematics, Kyushu University (M. Beneš, M. Kimura, and T. Nakaki, eds.), 2006, pp. 139–145 Zbl 1145.53051, MR 2279054; reference:[17] Ushijima T. K., Yagisita H.: Convergence of a three-dimensional crystalline motion to Gauss curvature flow.Japan J. Indust. Appl. Math. 22 (2005), 443–459 Zbl 1089.53046, MR 2179771, 10.1007/BF03167494; reference:[18] Ushijima T. K., Yazaki S.: Convergence of a crystalline approximation for an area-preserving motion.Journal of Comput. and Appl. Math. 166 (2004), 427–452 Zbl 1052.65082, MR 2041191, 10.1016/j.cam.2003.08.041; reference:[19] Yazaki S.: Motion of nonadmissible convex polygons by crystalline curvature.Publ. Res. Inst. Math. Sci. 43 (2007), 155–170 Zbl 1132.53036, MR 2317117, 10.2977/prims/1199403812
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13Academic Journal
المؤلفون: Yazaki, Shigetoshi
مصطلحات موضوعية: keyword:essentially admissible polygon, keyword:crystalline curvature, keyword:the Wulff shape, keyword:isoperimetric inequality, msc:34A26, msc:34A34, msc:34K25, msc:39A12, msc:53A04, msc:74N05, msc:82D25
وصف الملف: application/pdf
Relation: mr:MR2388403; zbl:Zbl 1139.53032; reference:[1] Almgren F., Taylor J. E.: Flat flow is motion by crystalline curvature for curves with crystalline energies.J. Differential Geom. 42 (1995), 1–22 Zbl 0867.58020, MR 1350693; reference:[2] Angenent S., Gurtin M. E.: Multiphase thermomechanics with interfacial structure, 2.Evolution of an isothermal interface. Arch. Rational Mech. Anal. 108 (1989), 323–391 MR 1013461, 10.1007/BF01041068; reference:[3] Gage M.: On an area-preserving evolution equations for plane curves.Contemp. Math. 51 (1986), 51–62 MR 0848933, 10.1090/conm/051/848933; reference:[4] Giga Y.: Anisotropic curvature effects in interface dynamics.Sūgaku 52 (2000), 113–127; English transl., Sūgaku Expositions 16 (2003), 135–152; reference:[5] Gurtin M. E.: Thermomechanics of Evolving Phase Boundaries in the Plane.Clarendon Press, Oxford 1993 Zbl 0787.73004, MR 1402243; reference:[6] Hontani H., Giga M.-H., Giga, Y., Deguchi K.: Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis.Discrete Appl. Math. 147 (2005), 265–285 Zbl 1117.65036, MR 2127078, 10.1016/j.dam.2004.09.015; reference:[7] Roberts S.: A line element algorithm for curve flow problems in the plane.CMA Research Report 58 (1989); J. Austral. Math. Soc. Ser. B 35 (1993), 244–261 MR 1244207; reference:[8] Taylor J. E.: Constructions and conjectures in crystalline nondifferential geometry.In: Proc. Conference on Differential Geometry, Rio de Janeiro, Pitman Monographs Surveys Pure Appl. Math. 52 (1991), 321–336, Pitman London Zbl 0725.53011, MR 1173051; reference:[9] Taylor J. E.: Motion of curves by crystalline curvature, including triple junctions and boundary points.Diff. Geom.: partial diff. eqs. on manifolds (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., 54 (1993), Part I, 417–438, AMS, Providence MR 1216599; reference:[10] Taylor J. E., Cahn, J., Handwerker C.: Geometric models of crystal growth.Acta Metall. 40 (1992), 1443–1474 10.1016/0956-7151(92)90090-2; reference:[11] Yazaki S.: On an area-preserving crystalline motion.Calc. Var. 14 (2002), 85–105 Zbl 1143.37320, MR 1883601, 10.1007/s005260100094; reference:[12] Yazaki S.: On an anisotropic area-preserving crystalline motion and motion of nonadmissible polygons by crystalline curvature.Sūrikaisekikenkyūsho Kōkyūroku 1356 (2004), 44–58; reference:[13] Yazaki S.: Motion of nonadmissible convex polygons by crystalline curvature.Publ. Res. Inst. Math. Sci. 43 (2007), 155–170 Zbl 1132.53036, MR 2317117, 10.2977/prims/1199403812
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14Academic Journal
المؤلفون: Verstraelen, Leopold
مصطلحات موضوعية: keyword:geometry, keyword:curve, keyword:surface, msc:00A99, msc:51-01, msc:53A04, msc:53A05, msc:53A07, msc:92-01
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Relation: zbl:Zbl 1265.53006; reference:[1] Verstraelen, L.: The geometry of eye and brain.Soochow Journal of Mathematics 30 (2004) (volume in honour of Professor Bang-Yen Chen), 367–376. Zbl 1131.92303, MR 2093862; reference:[2] Coolidge, J. L.: A history of geometrical methods.Dover Publ., London (1963). Zbl 0113.00103, MR 0160143; reference:[3] Bronowski, J.: The ascent of man.Litte, Brown & Co, Boston 1973.; reference:[4] Lejeune, A.: Euclide et Ptolémée, deux stades de l’optique géométrique grecque.Université de Louvain, Bureau du “Recueil” (1948). Zbl 0039.24102, MR 0028212; reference:[5] Montel, P.: Encyclopédie française, Tome 1.Larousse, Paris 1937.; reference:[6] Dillen, F., Verstraelen, L.: Handbook of differential geometry.North-Holland, Amsterdam, Vol. 1 (2000) and Vol. 2 (2005). Zbl 1069.00010, MR 1736851; reference:[7] Chern, S. S., Chen, W. H., Laser, K. S.: Lectures on differential geometry.World Scientific, Singapore 1999. MR 1735502; reference:[8] Kühnel, W.: Differential geometry: curves-surfaces-manifolds.AMS-Student Math. Library, vol. 16 (2002). Zbl 1009.53002, MR 1882174; reference:[9] Penrose, R.: The geometry of the universe.In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980. MR 0599181; reference:[10] Penrose, R.: The emperor’s new mind, concerning computers, minds and the laws of physics.Oxford University Press, Oxford 1989. MR 1048125; reference:[11] Browder, F. E., Mac Lane, S.: The relevance of mathematics.In Mathematics Today (ed. Steen, L. A.), Vintage Books, New York 1980.; reference:[12] Hilbert, D.: Mathematical problems (1900 – Paris – Lecture).AMS-Proceedings of Symposia in Pure Mathematics, Vol. 28 (1976).; reference:[13] d’Arcy Thompson, W.: On growth and form.Cambridge University Press, Cambridge 1917. MR 0128562; reference:[14] Lamé, G.: Examen des différentes méthodes employées pour résoudre les problèmes de géométrie.Hermann, Paris 1818.; reference:[15] Thompson, A. C.: Minkowski geometry.Encyclopedia of mathematics and its applications, Vol. 63, Cambridge University Press, Cambridge 1996. Zbl 0868.52001, MR 1406315; reference:[16] Chen, B.-Y.: What can we do with Nash’s embedding theorem?.Soochow Journal of Mathematics 30 (2004), 303–338. Zbl 1077.53044, MR 2093858; reference:[17] Chen, B.-Y.: Riemannian submanifolds.In [6, Vol. 1]. Zbl 1079.53077; reference:[18] Hildebrandt, S., Tromba, A.: Panoptimum.Spektrum, Heidelberg 1986. MR 1040828; reference:[19] Willmore, T. J.: A survey on Willmore immersions.In Geometry and Topology of submanifolds, Vol. IV, (eds. Dillen, F., Verstraelen, L.), World Scientific, Singapore 1992. Zbl 0841.53051, MR 1185712; reference:[20] Chen, B.-Y.: Total mean curvature and submanifolds of finite type.World Scientific, Singapore 1984. Zbl 0537.53049, MR 0749575; reference:[21] Barros, M.: The conformal total tension variational problem in Kaluza-Klein supergravity.Nuclear Physics B 535 (1998), 531–551. Zbl 1041.83512, MR 1666496, 10.1016/S0550-3213(98)00601-4; reference:[22] Barros, M.: Willmore-Chen branes and Hopf T-duality.Class. Quantum Grav. 17 (2000), 1979–1988. Zbl 0967.83031, MR 1764006, 10.1088/0264-9381/17/9/308; reference:[23] Gielis, J., Haesen, S., Verstraelen, L.: Universal natural shapes; from the supereggs of Piet Hein to the cosmic egg of Georges Lemaître.Kragujevac Journal of Mathematics 28 (2005), 57–68. MR 2211243; reference:[24] Gielis, J.: A generic transformation that unifies a large number of natural and abstract shapes.American Journal of Botamy 90 (2003), 333–338. 10.3732/ajb.90.3.333; reference:[25] Gielis, J.: Inventing the circle.Geniaal Press, Antwerpen (2003).; reference:[26] Gielis, J., Gerats, T.: A botanical perspective on plant shape modeling.Proc. International Conference on Computing, Communications and Control Technologies, Vol. VI (2004), 265–272.; reference:[27] Gielis, J.: Wiskundige supervormen bij bamboes.Newsletter Belgian Bamboo Society 13 (1996), 20–26.; reference:[28] Gielis, J., Beirinckx, B., Bastiaens, E.: Superquadrics with rational and irrational symmetries.Proc. 8th ACM symposium on Solid Modeling and Applications (2003), 262–265.; reference:[29] Gielis, J.: Variational superformula curves for 2D- and 3D graphic arts.Proc. World Multi-Conference on Systemics, Cybernetics and Informatics, Vol. V: Computer Science and Engineering (2004), 119–124.; reference:[30] Haesen, S., Sebeković, A., Verstraelen, L.: Relations between intrinsic and extrinsic curvatures.Kragujevac J. Math. 25 (2003), 139–145. Zbl 1274.53024, MR 2120586; reference:[31] Dillen, F., Haesen, S., Petrović-Torgasev, M., Verstraelen, L.: An inequality between intrinsic and extrinsic scalar curvature invariants for codimension 2 embeddings.J. Geom. Phys. 52 (2004), 101–112. Zbl 1083.53062, MR 2088970, 10.1016/j.geomphys.2004.02.003; reference:[32] Haesen, S., Verstraelen, L.: Ideally embedded space-times.J. Math. Phys. 45 (2004), 1497–1510. Zbl 1068.53053, MR 2043839, 10.1063/1.1668333; reference:[33] Lemaître, G.: Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactique.Annales Soc. Sc. Bruxelles 47 (1927), 49–59.; reference:[34] O’Neill, B.: Semi-Riemannian geometry, with applications to relativity.Acad. Press, New York 1983. MR 0719023; reference:[35] Helmholtz, H. von: Ueber die Tatsachen welche der Geometrie zu Grunde liegen.In Abhandlungen zur Philosophie und Geometrie, Junghaus, Cuxhausen 1987.; reference:[36] Riemann, B.: Ueber die Hypothesen welche der Geometrie zu Grunde liegen.In Gaussche Flächentheorie, Riemannsche Räume und Minkowski-Welt, Teubner, Leipzig 1984.
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15Academic Journal
المؤلفون: Pech, Pavel
وصف الملف: application/pdf
Relation: mr:MR1179309; zbl:Zbl 0786.52007; reference:[1] J. R. Alexander: Metric embedding techniques applied to geometric inequalities.Lecture Notes in Math., vol. 490, Springer, Berlin, 1975. Zbl 0314.52004, MR 0405245; reference:[2] H. Herda: A characterization of circles and other closed curves.Amer. Math. Monthly 81 (1974), 146–149. Zbl 0279.50007, MR 0333971, 10.2307/2976957; reference:[3] P. Pech: Inequality between sides and diagonals of a space $n$-gon and its integral analog.Čas. pro pěst. mat. 115 (1990), 343–350. Zbl 0722.52006, MR 1090858
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16Academic Journal
المؤلفون: Pázman, Andrej
وصف الملف: application/pdf
Relation: mr:MR763647; zbl:Zbl 0548.62043; reference:[1] B. Hostinský: Diferenciální geometrie křivek a ploch.(Differential geometry of curves and surfaces). Přírodovědecké nakladatelství JČSMF, Praha 1950.; reference:[2] V. Jarník: Diferenciální počet II.(Differential calculus). NČSAV, Praha 1956.; reference:[3] J. Milnor: Morse Theory.Princeton Univ. Press, Princeton, N. J. 1963. Zbl 0108.10401, MR 0163331; reference:[4] A. Pázman: Geometry of gaussian nonlinear regression - parallel curves and confidence intervals.Kybernetika 18 (1982), 376-396. MR 0686519; reference:[5] A. Pázman: Nonlinear least squares - uniqueness versus ambiguity.Math. Operationsforsch. Statist. Ser. Statistics 14 (1984) (to appear.) MR 0756337; reference:[6] A. Rényi: Teorie pravděpodobnosti.(Probability theory). Academia, Praha 1972. MR 0350789; reference:[7] S. Sternberg: Lectures on Differential Geometry.Second printing. Prentice-Hall, Englewood Cliffs 1965. MR 0193578
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17Academic Journal
المؤلفون: Nádeník, Zbyněk
مصطلحات موضوعية: msc:53A04
وصف الملف: application/pdf
Relation: mr:MR597913; zbl:Zbl 0461.53001; reference:[1] W. Blaschke, K. Leichtweiss: /: Elementare Differentialgeometrie.5. Aufl. Berlin-Heidelberg-New York 1973. Zbl 0264.53001, MR 0350630; reference:[2] L. Boček: Isoperimetrische Ungleichungen für räumliche Kurven und Polygone.Čas. pěst. mat. 104(1979), 86-92. MR 0523575; reference:[3] H. Hadwiger: Vorlesungen über Inhalt, Oberfläche und Isoperimetrie.Berlin-Göttingen - Heidelberg 1957. Zbl 0078.35703, MR 0102775; reference:[4] Z. Nádeník: Eine isoperimetrische Ungleichung für geschlossene Kurven im vierdimensionalen Raum.Čas. pěst. mat. 105 (1980), 302-310. MR 0588681; reference:[5] L. Tonelli: Fondamenti di calcolo delle variazioni.I. Bologna 1921.
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18Academic Journal
المؤلفون: Nádeník, Zbyněk
مصطلحات موضوعية: msc:53A04
وصف الملف: application/pdf
Relation: mr:MR588681; zbl:Zbl 0461.53001; reference:[1] E. F. Beckenbach, R. Bellman: Inequalities.Berlin-Göttingen-Heidelberg 1961; 1965. Zbl 0186.09606; reference:[2] W. Blaschke, K. Leichtweiss: Elementare Differentialgeometrie.5. Aufl. Berlin-Heidelberg-New York 1973. Zbl 0264.53001, MR 0350630; reference:[3] L. Boček: Isoperimetrische Ungleichungen für räumliche Kurven und Polygone.Čas. pěst. mat. 104(1979), 86-92. MR 0523575; reference:[4] G. H. Hardy, J. E. Littlewood- G. Polya: Inequalities.Cambridge 1934; 2. Aufl. 1952. MR 0046395; reference:[5] V. Hlavatý: Diferenciální přímková geometrie.Praha 1941 (Differentielle Liniengeometrie, Groningen-Batavia 1945). MR 0018936; reference:[6] E. Kamke: Differentialgleichungen. Teil I: Gewöhnliche Differentialgleichungen.5. Aufl. Leipzig 1964.; reference:[7] Z. Nádeník: Eine isoperimetrische Ungleichung für die Paareder Raumkurven.Im Druck in Čas. pěst. mat. 105 (1980).; reference:[8] I. J. Schoenberg: An isoperimetric inequality for closed curves convex in even-dimensional euclidean spaces.Acta Math. 91 (1954), 143-164. Zbl 0056.15705, MR 0065944
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19Academic Journal
المؤلفون: Jankovský, Zdeněk, Šejdl, Miroslav
مصطلحات موضوعية: keyword:equiform geometry, keyword:equiform invariants, keyword:theory of curves, msc:53A04, msc:53A15, msc:53A40, msc:53A55
وصف الملف: application/pdf
Relation: mr:MR0879330; zbl:Zbl 0616.53013; reference:[1] L. Burmester: Kinematisch-geometrische Theorie der Bewegungen der affinveränderlichen, der ähnlich veränderlichen und starren räumlichen oder ebenen Systeme.Zeitschrift für Math. und Physik, 23 (1878), 103-131.; reference:[2] M. Krause: Zur Theorie der ebenen ähnlich veränderlichen Systeme.Jahresbericht der deutschen Mathematik-Vereinigung, 19 (1910), 327-329.; reference:[3] R. Müller: Über die Momentanbewegung eines ebenen ähnlich-veränderlichen Systems in seiner Ebene.Jahresbericht der deutschen Mathematik-Vereinigung, 19 (1910), 29-89.; reference:[4] G. Kowalewski: Vorlesungen über allgemeine natürliche Geometrie und Liesche Transformationsgruppen.Berlin 1931. Zbl 0002.35003; reference:[5] Z. Pírko: Einführung in die kinematische Geometrie in der Ebene.(Tschechisch). Praha SNTL 1968.; reference:[6] K. Drábek J. Chudý: Beitrag zur $\mathcal E$-Kinematik in der Ebene: Gruppentheoretische Grundlagen der $\mathcal E$-Bewegung.Acta polytechnica - Práce ČVUT Praha, 3 (IV-2), 1978, 77-92.; reference:[7] Z. Jankovský: Zu einigen Fragen der kinematischen Geometrie auf der $\mathcal M$-Gruppe.(Tschechisch). Acta polytechnica - Práce ČVUT Praha, 7 (IV-3), 1978, 43-51.; reference:[8] M. Šejdl: Grundeigenschaften der 1- und 2-parametrigen äquiformen Bewegungen.(Tschechisch). Referat zur kandidatischen Fachprüfung, Praha 1985.
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20Academic Journal
المؤلفون: Jankovský, Zdeněk
مصطلحات موضوعية: keyword:Möbius group, keyword:curve, keyword:approximation of curves, keyword:kinematics, msc:53A04, msc:53A17, msc:53A30
وصف الملف: application/pdf
Relation: mr:MR0547042; zbl:Zbl 0436.53003; reference:[1] G. V. Buschmanova A. P. Norden: Elementy konformnoj geometrii.Iz. Kazaňskogo univ., Kazaň, 1972 (russisch).; reference:[2] Z. Jankovský: $\mathcal M$-Bewegungen mit den (U)-Automorphismen.Čas. pro pěst. mat., 101 (1976), 2, 140-152. MR 0474028; reference:[3] Z. Jankovský: Die Grundlage der $\mathcal M$-Kinematik und der $\mathcal M$-kinematischen Geometrie in der Ebene.Praha, 1974, kandidátská disertace (tschechisch).; reference:[4] Z. Jankovský: Zu den einigen Fragen der Ebene kinematische Geometrie auf der $\mathcal M$-Gruppe.Acta polytechnica-Práce ČVUT v Praze, (1978), 7 (IV., 3), 43 - 51 (tschechisch).; reference:[5] J. Maeda: Diferential Möbius geometry of plane curves.Japan. J. Math., 18 (1941/43), 67-260 (englisch). MR 0014288, 10.4099/jjm1924.18.0_67
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