-
3
-
-
70350031301
-
Experimental study of energy-minimizing point configurations on spheres
-
Ballinger B., Blekherman G., Cohn H., Giansiracusa N., Kelly E., Schürmann A.: Experimental study of energy-minimizing point configurations on spheres. Exp. Math. 18(3), 257-283 (2009).
-
(2009)
Exp. Math.
, vol.18
, Issue.3
, pp. 257-283
-
-
Ballinger, B.1
Blekherman, G.2
Cohn, H.3
Giansiracusa, N.4
Kelly, E.5
Schürmann, A.6
-
4
-
-
84974189036
-
Sums of distances between points on a sphere-an application of the theory of irregularities of distribution to discrete geometry
-
Beck J.: Sums of distances between points on a sphere-an application of the theory of irregularities of distribution to discrete geometry. Mathematika 31(1), 33-41 (1984).
-
(1984)
Mathematika
, vol.31
, Issue.1
, pp. 33-41
-
-
Beck, J.1
-
5
-
-
62049086310
-
Computational cost of the Fekete problem. I. The forces method on the 2-sphere
-
Bendito E., Carmona A., Encinas A. M., Gesto J. M., Gómez A., Mouriño C., Sánchez M. T.: Computational cost of the Fekete problem. I. The forces method on the 2-sphere. J. Comput. Phys. 228(9), 3288-3306 (2009).
-
(2009)
J. Comput. Phys.
, vol.228
, Issue.9
, pp. 3288-3306
-
-
Bendito, E.1
Carmona, A.2
Encinas, A.M.3
Gesto, J.M.4
Gómez, A.5
Mouriño, C.6
Sánchez, M.T.7
-
6
-
-
26844480956
-
Discrete charges on a two dimensional conductor
-
Berkenbusch M. K., Claus I., Dunn C., Kadanoff L. P., Nicewicz M., Venkataramani S. C.: Discrete charges on a two dimensional conductor. J. Stat. Phys. 116(5-6), 1301-1358 (2004).
-
(2004)
J. Stat. Phys.
, vol.116
, Issue.5-6
, pp. 1301-1358
-
-
Berkenbusch, M.K.1
Claus, I.2
Dunn, C.3
Kadanoff, L.P.4
Nicewicz, M.5
Venkataramani, S.C.6
-
7
-
-
37649012908
-
Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets
-
(electronic)
-
Borodachov S. V., Hardin D. P., Saff E. B.: Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets. Trans. Am. Math. Soc. 360(3), 1559-1580 (2008) (electronic).
-
(2008)
Trans. Am. Math. Soc.
, vol.360
, Issue.3
, pp. 1559-1580
-
-
Borodachov, S.V.1
Hardin, D.P.2
Saff, E.B.3
-
8
-
-
0023979638
-
Algorithm 659: Implementing sobol's quasirandom sequence generator
-
Bratley P., Fox B. L.: Algorithm 659: Implementing sobol's quasirandom sequence generator. ACM Trans. Math. Softw. 14, 88-100 (1988).
-
(1988)
ACM Trans. Math. Softw.
, vol.14
, pp. 88-100
-
-
Bratley, P.1
Fox, B.L.2
-
9
-
-
47249116205
-
Optimal logarithmic energy points on the unit sphere
-
Brauchart J. S.: Optimal logarithmic energy points on the unit sphere. Math. Comp. 77(263), 1599-1613 (2008).
-
(2008)
Math. Comp.
, vol.77
, Issue.263
, pp. 1599-1613
-
-
Brauchart, J.S.1
-
12
-
-
34250831282
-
Universally optimal distribution of points on spheres
-
(electronic)
-
Cohn H., Kumar A.: Universally optimal distribution of points on spheres. J. Am. Math. Soc. 20(1), 99-148 (2007) (electronic).
-
(2007)
J. Am. Math. Soc.
, vol.20
, Issue.1
, pp. 99-148
-
-
Cohn, H.1
Kumar, A.2
-
13
-
-
0031082707
-
Equidistribution on the sphere
-
Cui J., Freeden W.: Equidistribution on the sphere. SIAM J. Sci. Comput. 18(2), 595-609 (1997).
-
(1997)
SIAM J. Sci. Comput.
, vol.18
, Issue.2
, pp. 595-609
-
-
Cui, J.1
Freeden, W.2
-
14
-
-
84862264974
-
A best possible upper bound on the star discrepancy of (t, m, 2)-nets
-
Dick J., Kritzer P.: A best possible upper bound on the star discrepancy of (t, m, 2)-nets. Monte Carlo Methods Appl. 12(1), 1-17 (2006).
-
(2006)
Monte Carlo Methods Appl.
, vol.12
, Issue.1
, pp. 1-17
-
-
Dick, J.1
Kritzer, P.2
-
16
-
-
0346894538
-
On a problem in the theory of uniform distribution
-
(Indagationes Math. 10, 370-378, 1948)
-
Erdös, P., Turán, P.: On a problem in the theory of uniform distribution. I. Nederl. Akad. Wetensch., Proc. 51, 1146-1154 (Indagationes Math. 10, 370-378, 1948) (1948).
-
(1948)
I. Nederl. Akad. Wetensch., Proc
, vol.51
, pp. 1146-1154
-
-
Erdös, P.1
Turán, P.2
-
17
-
-
0346894538
-
On a problem in the theory of uniform distribution. II
-
(Indagationes Math. 10, 406-413, 1948)
-
Erdös, P., Turán, P.: On a problem in the theory of uniform distribution. II. Nederl. Akad. Wetensch., Proc. 51, 1262-1269 (Indagationes Math. 10, 406-413, 1948) (1948).
-
(1948)
Nederl. Akad. Wetensch., Proc
, vol.51
, pp. 1262-1269
-
-
Erdös, P.1
Turán, P.2
-
18
-
-
0001013260
-
Discrépance de suites associées àà un système de numération (en dimension s)
-
Faure H.: Discrépance de suites associées àà un système de numération (en dimension s). Acta Arith. 41(4), 337-351 (1982).
-
(1982)
Acta Arith.
, vol.41
, Issue.4
, pp. 337-351
-
-
Faure, H.1
-
19
-
-
0011265052
-
Erdo{double acute}s-Turán type discrepancy bounds
-
Grabner P. J.: Erdo{double acute}s-Turán type discrepancy bounds. Monatsh. Math. 111(2), 127-135 (1991).
-
(1991)
Monatsh. Math.
, vol.111
, Issue.2
, pp. 127-135
-
-
Grabner, P.J.1
-
20
-
-
27844497928
-
Discretizing manifolds via minimum energy points
-
Hardin D. P., Saff E. B.: Discretizing manifolds via minimum energy points. Not. Am. Math. Soc. 51(10), 1186-1194 (2004).
-
(2004)
Not. Am. Math. Soc.
, vol.51
, Issue.10
, pp. 1186-1194
-
-
Hardin, D.P.1
Saff, E.B.2
-
21
-
-
13844275746
-
Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds
-
Hardin D. P., Saff E. B.: Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds. Adv. Math. 193(1), 174-204 (2005).
-
(2005)
Adv. Math.
, vol.193
, Issue.1
, pp. 174-204
-
-
Hardin, D.P.1
Saff, E.B.2
-
23
-
-
10844292762
-
Remark on algorithm 659: Implementing sobol′s quasirandom sequence generator
-
Joe S., Kuo F. Y.: Remark on algorithm 659: Implementing sobol′s quasirandom sequence generator. ACM Trans. Math. Softw. 29, 49-57 (2003).
-
(2003)
ACM Trans. Math. Softw.
, vol.29
, pp. 49-57
-
-
Joe, S.1
Kuo, F.Y.2
-
24
-
-
33646877546
-
An inequality connected with Weyl's criterion for uniform distribution
-
Amer. Math. Soc., Providence, R. I
-
LeVeque, W. J.: An inequality connected with Weyl's criterion for uniform distribution. In: Proc. Sympos. Pure Math., vol. VIII, pp. 22-30. Amer. Math. Soc., Providence, R. I. (1965).
-
(1965)
Proc. Sympos. Pure Math.
, vol.VIII
, pp. 22-30
-
-
LeVeque, W.J.1
-
25
-
-
0347174830
-
Some trigonometric extremal functions and the Erdo{double acute}s-Turán type inequalities
-
Li X.-J., Vaaler J. D.: Some trigonometric extremal functions and the Erdo{double acute}s-Turán type inequalities. Indiana Univ. Math. J. 48(1), 183-236 (1999).
-
(1999)
Indiana Univ. Math. J.
, vol.48
, Issue.1
, pp. 183-236
-
-
Li, X.-J.1
Vaaler, J.D.2
-
26
-
-
84990604340
-
Hecke operators and distributing points on the sphere
-
[Frontiers of the mathematical sciences: 1985 (New York, 1985)]
-
Lubotzky, A., Phillips, R., Sarnak, P.: Hecke operators and distributing points on the sphere. I. Commun. Pure Appl. Math., 39(suppl.): S149-S186, 1986 [Frontiers of the mathematical sciences: 1985 (New York, 1985)].
-
(1986)
I. Commun. Pure Appl. Math.
, vol.39
, Issue.SUPPL.
-
-
Lubotzky, A.1
Phillips, R.2
Sarnak, P.3
-
27
-
-
0000382131
-
2-discrepancy for anchored boxes
-
2-discrepancy for anchored boxes. J. Complex. 14(4), 527-556 (1998).
-
(1998)
J. Complex.
, vol.14
, Issue.4
, pp. 527-556
-
-
Matoušek, J.1
-
29
-
-
77952671977
-
Leveque type inequalities and discrepancy estimates for minimal energy configurations on spheres
-
Narcowich F. J., Sun X., Ward J. D., Wu Z.: Leveque type inequalities and discrepancy estimates for minimal energy configurations on spheres. J. Approx. Theory 162(6), 1256-1278 (2010).
-
(2010)
J. Approx. Theory
, vol.162
, Issue.6
, pp. 1256-1278
-
-
Narcowich, F.J.1
Sun, X.2
Ward, J.D.3
Wu, Z.4
-
30
-
-
0002071152
-
Low-discrepancy and low-dispersion sequences
-
Niederreiter H.: Low-discrepancy and low-dispersion sequences. J. Number Theory 30(1), 51-70 (1988).
-
(1988)
J. Number Theory
, vol.30
, Issue.1
, pp. 51-70
-
-
Niederreiter, H.1
-
31
-
-
0003244922
-
Random number generation and quasi-Monte Carlo methods
-
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
-
Niederreiter, H.: Random number generation and quasi-Monte Carlo methods. In: CBMS-NSF Regional Conference Series in Applied Mathematics, vol 63. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1992).
-
(1992)
CBMS-NSF Regional Conference Series in Applied Mathematicsz
, vol.63
-
-
Niederreiter, H.1
-
32
-
-
0030194541
-
Low-discrepancy sequences and global function fields with many rational places
-
Niederreiter H., Xing C.: Low-discrepancy sequences and global function fields with many rational places. Finite Fields Appl. 2(3), 241-273 (1996).
-
(1996)
Finite Fields Appl.
, vol.2
, Issue.3
, pp. 241-273
-
-
Niederreiter, H.1
Xing, C.2
-
33
-
-
21844523415
-
Low-discrepancy sequences obtained from algebraic function fields over finite fields
-
Niederreiter H., Xing C. P.: Low-discrepancy sequences obtained from algebraic function fields over finite fields. Acta Arith. 72(3), 281-298 (1995).
-
(1995)
Acta Arith.
, vol.72
, Issue.3
, pp. 281-298
-
-
Niederreiter, H.1
Xing, C.P.2
-
34
-
-
4243059534
-
Variance with alternative scramblings of digital nets
-
Owen A. B.: Variance with alternative scramblings of digital nets. ACM Trans. Model. Comput. Simul. 12, 363-378 (2003).
-
(2003)
ACM Trans. Model. Comput. Simul.
, vol.12
, pp. 363-378
-
-
Owen, A.B.1
-
35
-
-
0002851522
-
On irregularities of distribution
-
Roth K. F.: On irregularities of distribution. Mathematika 1, 73-79 (1954).
-
(1954)
Mathematika
, vol.1
, pp. 73-79
-
-
Roth, K.F.1
-
36
-
-
0002462777
-
Irregularities of distribution. IV
-
Schmidt W. M.: Irregularities of distribution. IV. Invent. Math. 7, 55-82 (1969).
-
(1969)
Invent. Math.
, vol.7
, pp. 55-82
-
-
Schmidt, W.M.1
-
37
-
-
0002278399
-
Estimates of mass distributions from their potentials and energies
-
Sjögren P.: Estimates of mass distributions from their potentials and energies. Ark. Mat. 10, 59-77 (1972).
-
(1972)
Ark. Mat.
, vol.10
, pp. 59-77
-
-
Sjögren, P.1
-
38
-
-
4043098361
-
Extremal systems of points and numerical integration on the sphere
-
Sloan I. H., Womersley R. S.: Extremal systems of points and numerical integration on the sphere. Adv. Comput. Math. 21(1-2), 107-125 (2004).
-
(2004)
Adv. Comput. Math.
, vol.21
, Issue.1-2
, pp. 107-125
-
-
Sloan, I.H.1
Womersley, R.S.2
-
39
-
-
0001352321
-
Distribution of points in a cube and approximate evaluation of integrals
-
Soboĺ I. M.: Distribution of points in a cube and approximate evaluation of integrals. Ž Vyčisl. Mat. i Mat. Fiz. 7, 784-802 (1967).
-
(1967)
ŽVyčisl. Mat. I Mat. Fiz.
, vol.7
, pp. 784-802
-
-
Soboĺ, I.M.1
-
40
-
-
84968518878
-
Sums of distances between points on a sphere. II
-
Stolarsky K. B.: Sums of distances between points on a sphere. II. Proc. Am. Math. Soc. 41, 575-582 (1973).
-
(1973)
Proc. Am. Math. Soc.
, vol.41
, pp. 575-582
-
-
Stolarsky, K.B.1
-
41
-
-
41549086984
-
Spherical basis functions and uniform distribution of points on spheres
-
Sun X., Chen Z.: Spherical basis functions and uniform distribution of points on spheres. J. Approx. Theory 151(2), 186-207 (2008).
-
(2008)
J. Approx. Theory
, vol.151
, Issue.2
, pp. 186-207
-
-
Sun, X.1
Chen, Z.2
-
42
-
-
84973998293
-
On means of distances on the surface of a sphere (lower bounds)
-
Wagner G.: On means of distances on the surface of a sphere (lower bounds). Pac. J. Math. 144(2), 389-398 (1990).
-
(1990)
Pac. J. Math.
, vol.144
, Issue.2
, pp. 389-398
-
-
Wagner, G.1
-
43
-
-
1542638369
-
Erdo{double acute}s-Turán inequalities for distance functions on spheres
-
Wagner G.: Erdo{double acute}s-Turán inequalities for distance functions on spheres. Michigan Math. J. 39(1), 17-34 (1992).
-
(1992)
Michigan Math. J.
, vol.39
, Issue.1
, pp. 17-34
-
-
Wagner, G.1
-
44
-
-
84973999972
-
On means of distances on the surface of a sphere. II. Upper bounds
-
Wagner G.: On means of distances on the surface of a sphere. II. Upper bounds. Pac. J. Math. 154(2), 381-396 (1992).
-
(1992)
Pac. J. Math.
, vol.154
, Issue.2
, pp. 381-396
-
-
Wagner, G.1
-
45
-
-
21844527203
-
A construction of low-discrepancy sequences using global function fields
-
Xing C. P., Niederreiter H.: A construction of low-discrepancy sequences using global function fields. Acta Arith. 73(1), 87-102 (1995).
-
(1995)
Acta Arith.
, vol.73
, Issue.1
, pp. 87-102
-
-
Xing, C.P.1
Niederreiter, H.2
|