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Volumn 207, Issue 2, 2002, Pages 345-358

Discrete logarithmic energy on the sphere

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EID: 0036972509     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2002.207.345     Document Type: Article
Times cited : (44)

References (27)
  • 1
    • 0012952893 scopus 로고    scopus 로고
    • An extremal property of the icosahedron
    • MR 97m:52022, Zbl 0877.51021
    • N.N. Andreev, An extremal property of the icosahedron, East J. Approx., 2(4) (1996), 459-462, MR 97m:52022, Zbl 0877.51021.
    • (1996) East J. Approx. , vol.2 , Issue.4 , pp. 459-462
    • Andreev, N.N.1
  • 2
    • 21344487779 scopus 로고
    • Equilibrium configurations of particles on the sphere: The case of logarithmic interactions
    • Zbl 0839.70009
    • B. Bergersen, D. Boal and P. Palffy-Muhoray, Equilibrium configurations of particles on the sphere: The case of logarithmic interactions, J. Phys. A: Math. Gen., 27 (1994), 2579-2586, Zbl 0839.70009.
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 2579-2586
    • Bergersen, B.1    Boal, D.2    Palffy-Muhoray, P.3
  • 4
    • 0012959082 scopus 로고    scopus 로고
    • Open problems in approximation theory
    • Tampa '96
    • P.D. Dragnev and E.B. Saff, Open problems in approximation theory, Tampa '96, East J. of Approx., 2(4) (1996), 499-517.
    • (1996) East J. of Approx. , vol.2 , Issue.4 , pp. 499-517
    • Dragnev, P.D.1    Saff, E.B.2
  • 5
    • 0001560001 scopus 로고
    • Equilibrium configurations on N equal charges on the sphere
    • MR 98e:78002
    • T. Erber and G.M. Hockney, Equilibrium configurations on N equal charges on the sphere, J. Phys. A: Math. Gen., 24 (1991), L1369-L1377, MR 98e:78002.
    • (1991) J. Phys. A: Math. Gen. , vol.24
    • Erber, T.1    Hockney, G.M.2
  • 6
    • 0001204608 scopus 로고
    • On the sum of distances determined by a point set
    • MR 21 #5937, Zbl 0072.38604
    • L. Fejes Tóth, On the sum of distances determined by a point set, Acta Math. Acad. Sci. Hungar., 7 (1956), 397-401, MR 21 #5937, Zbl 0072.38604.
    • (1956) Acta Math. Acad. Sci. Hungar. , vol.7 , pp. 397-401
    • Fejes Tóth, L.1
  • 7
    • 0004230986 scopus 로고
    • Pergamon-Macmillan, New York, MR 29 #2705, Zbl 0134.15705
    • _, Regular Figures, Pergamon-Macmillan, New York, 1964, MR 29 #2705, Zbl 0134.15705.
    • (1964) Regular Figures
  • 8
    • 0000532022 scopus 로고
    • Stabile anordnungen von elektronen im atom
    • L. Föppl, Stabile anordnungen von elektronen im atom, J. Reine Angew. Math., 141 (1912), 251-301.
    • (1912) J. Reine Angew. Math. , vol.141 , pp. 251-301
    • Föppl, L.1
  • 9
    • 0001579093 scopus 로고
    • Energies and spacings of point charges on a sphere
    • L. Glasser and A.G. Every, Energies and spacings of point charges on a sphere, J. Phys. A: Math. Gen., 25 (1992), 2473-2482.
    • (1992) J. Phys. A: Math. Gen. , vol.25 , pp. 2473-2482
    • Glasser, L.1    Every, A.G.2
  • 10
    • 0001211270 scopus 로고
    • Lagerung von punkten auf der kugel
    • MR 13, 154d, Zbl 0043.35604
    • W. Habicht and B.L. van der Waerden, Lagerung von punkten auf der kugel, Math. Ann., 123 (1951), 223-234, MR 13, 154d, Zbl 0043.35604.
    • (1951) Math. Ann. , vol.123 , pp. 223-234
    • Habicht, W.1    Van der Waerden, B.L.2
  • 11
    • 0012952662 scopus 로고    scopus 로고
    • Extremal dispositions of points on the sphere
    • MR 99f:41039, Zbl 0880.51008
    • A.V. Kolushov and V.A. Yudin, Extremal dispositions of points on the sphere, Anal. Math., 23(1) (1997), 25-34, MR 99f:41039, Zbl 0880.51008.
    • (1997) Anal. Math. , vol.23 , Issue.1 , pp. 25-34
    • Kolushov, A.V.1    Yudin, V.A.2
  • 12
    • 0031542184 scopus 로고    scopus 로고
    • Distributing many points on a sphere
    • MR 98h:70011, Zbl 0901.11028
    • A.B.J. Kuijlaars and E.B. Saff, Distributing many points on a sphere, Math. Intelligencer, 19(1) (1997), 5-11, MR 98h:70011, Zbl 0901.11028.
    • (1997) Math. Intelligencer , vol.19 , Issue.1 , pp. 5-11
    • Kuijlaars, A.B.J.1    Saff, E.B.2
  • 13
    • 21944444965 scopus 로고    scopus 로고
    • Asymptotics for minimal discrete energy on the sphere
    • MR 98e:11092, Zbl 0896.52019
    • _, Asymptotics for minimal discrete energy on the sphere, Trans. Amer. Math. Soc., 350(2) (1998), 523-538, MR 98e:11092, Zbl 0896.52019.
    • (1998) Trans. Amer. Math. Soc. , vol.350 , Issue.2 , pp. 523-538
  • 14
    • 0002766272 scopus 로고
    • Equilibrium of sets of particles on the sphere
    • MR 19, 165b, Zbl 0080.14106
    • J. Leech, Equilibrium of sets of particles on the sphere, Math. Gazette, 41 (1957), 81-90, MR 19, 165b, Zbl 0080.14106.
    • (1957) Math. Gazette , vol.41 , pp. 81-90
    • Leech, J.1
  • 15
    • 0001585704 scopus 로고
    • Extremal arrangements of points and unit charges on a sphere: Equilibrium configurations revised
    • MR 56 #2848, Zbl 0367.52012
    • T.W. Melnyk, O. Knop and W.R. Smith, Extremal arrangements of points and unit charges on a sphere: Equilibrium configurations revised, Can. J. Chem., 55 (1977), 1745-1761, MR 56 #2848, Zbl 0367.52012.
    • (1977) Can. J. Chem. , vol.55 , pp. 1745-1761
    • Melnyk, T.W.1    Knop, O.2    Smith, W.R.3
  • 16
    • 0001447029 scopus 로고
    • Minimal discrete energy on the sphere
    • MR 96e:78011, Zbl 0839.31011
    • E.A. Rakhmanov, E.B. Saff and Y.M. Zhou, Minimal discrete energy on the sphere, Math. Res. Lett., 1 (1994), 647-662, MR 96e:78011, Zbl 0839.31011.
    • (1994) Math. Res. Lett. , vol.1 , pp. 647-662
    • Rakhmanov, E.A.1    Saff, E.B.2    Zhou, Y.M.3
  • 17
    • 0006076043 scopus 로고
    • Electrons on the sphere
    • R.M. Ali, St. Ruscheweyh and E.B. Saff, eds., Singapore, World Scientific, MR 97h:78013, Zbl 0870.65049
    • _, Electrons on the sphere, in 'Computational Methods and Functional Theory' (R.M. Ali, St. Ruscheweyh and E.B. Saff, eds.), Singapore, World Scientific, 1995, 111-127, MR 97h:78013, Zbl 0870.65049
    • (1995) Computational Methods and Functional Theory , pp. 111-127
  • 18
    • 0013008043 scopus 로고
    • Arrangement of 24 points on a sphere
    • MR 24 #A3565, Zbl 0107.39802
    • R.M. Robinson, Arrangement of 24 points on a sphere, Math. Ann., 144 (1961), 17-46, MR 24 #A3565, Zbl 0107.39802.
    • (1961) Math. Ann. , vol.144 , pp. 17-46
    • Robinson, R.M.1
  • 19
    • 0002102930 scopus 로고
    • Complexity of Bezout's theorem III
    • MR 94g:65152, Zbl 0846.65018
    • M. Shub and S. Smale, Complexity of Bezout's theorem III, J. of Complexity, 9 (1993), 4-14, MR 94g:65152, Zbl 0846.65018.
    • (1993) J. of Complexity , vol.9 , pp. 4-14
    • Shub, M.1    Smale, S.2
  • 20
    • 84968466899 scopus 로고
    • Sums of distances between points on a sphere
    • MR 46 #2555, Zbl 0255.52004
    • K.B. Stolarsky, Sums of distances between points on a sphere, Proc. Amer. Math. Soc., 35 (1972), 547-549, MR 46 #2555, Zbl 0255.52004.
    • (1972) Proc. Amer. Math. Soc. , vol.35 , pp. 547-549
    • Stolarsky, K.B.1
  • 21
    • 84968518878 scopus 로고
    • Sums of distances between points on a sphere II
    • MR 48 #12314, Zbl 0274.52012
    • _, Sums of distances between points on a sphere II, Proc. Amer. Math. Soc., 41 (1973), 575-582, MR 48 #12314, Zbl 0274.52012.
    • (1973) Proc. Amer. Math. Soc. , vol.41 , pp. 575-582
  • 22
    • 84974288974 scopus 로고
    • On the product of distances to a point set on a sphere
    • MR 90j:11080, Zbl 0706.11046
    • G. Wagner, On the product of distances to a point set on a sphere, J. Austral. Math. Soc. (Series A), 47 (1989), 466-489, MR 90j:11080, Zbl 0706.11046.
    • (1989) J. Austral. Math. Soc. (Series A) , vol.47 , pp. 466-489
    • Wagner, G.1
  • 23
    • 84973998293 scopus 로고
    • On the mean of distances on the surface of a sphere
    • MR 91e:52014, Zbl 0648.10033
    • _, On the mean of distances on the surface of a sphere, Pacific J. Math., 144 (1990), 389-398, MR 91e:52014, Zbl 0648.10033.
    • (1990) Pacific J. Math. , vol.144 , pp. 389-398
  • 24
    • 84973999972 scopus 로고
    • On the mean of distances on the surface of a sphere, II
    • MR 93b:52007, Zbl 0767.11033
    • _, On the mean of distances on the surface of a sphere, II, Pacific J. Math., 153 (1992), 381-396, MR 93b:52007, Zbl 0767.11033.
    • (1992) Pacific J. Math. , vol.153 , pp. 381-396
  • 25
    • 0001646399 scopus 로고
    • Unique arrangements of points on a sphere
    • MR 14, 310c, Zbl 0048.13602
    • L.L. Whyte, Unique arrangements of points on a sphere, Amer. Math. Monthly, 59 (1952), 606-611, MR 14, 310c, Zbl 0048.13602.
    • (1952) Amer. Math. Monthly , vol.59 , pp. 606-611
    • Whyte, L.L.1
  • 26
    • 0012909755 scopus 로고
    • The minimum of potential energy of a system of point charges
    • (in Russian)
    • V.A. Yudin, The minimum of potential energy of a system of point charges Discretnaya Matematika 4(2) (1992), 115-121 (in Russian); Discrete Math. Appl., 3(1) (1993), 75-81, MR 93f:31008, Zbl 0797.31006.
    • (1992) Discretnaya Matematika , vol.4 , Issue.2 , pp. 115-121
    • Yudin, V.A.1
  • 27
    • 85036699227 scopus 로고
    • 75-81, MR 93f:31008, Zbl 0797.31006
    • V.A. Yudin, The minimum of potential energy of a system of point charges Discretnaya Matematika 4(2) (1992), 115-121 (in Russian); Discrete Math. Appl., 3(1) (1993), 75-81, MR 93f:31008, Zbl 0797.31006.
    • (1993) Discrete Math. Appl. , vol.3 , Issue.1


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