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Distributing many points on spheres: minimal energy and designs (Q2347956)

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Language	Label	Description	Also known as
English	Distributing many points on spheres: minimal energy and designs	scientific article

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scholarly article

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Distributing many points on spheres: minimal energy and designs (English)

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Johann S. Brauchart

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Peter J. Grabner

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Journal of Complexity

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publication date

10 June 2015

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full work available at URL

https://arxiv.org/abs/1407.8282

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zbMATH Keywords

minimal Riesz and logarithmic energy

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spherical designs

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quasi-Monte Carlo methods

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discrepancy

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quadrature rules

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy

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On the sum of distances betweenn points on a sphere

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On the sum of distances betweenn points on a sphere. II

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Extremal Problems of Distance Geometry Related to Energy Integrals

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Chebyshev constants for the unit circle

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Well Conditioned Spherical Designs for Integration and Interpolation on the Two-Sphere

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Regularized Least Squares Approximations on the Sphere Using Spherical Designs

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Minimizing the discrete logarithmic energy on the sphere: The role of random polynomials

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Designs, groups and lattices

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New upper bounds for kissing numbers from semidefinite programming

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Experimental Study of Energy-Minimizing Point Configurations on Spheres

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A survey on spherical designs and algebraic combinatorics on spheres

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Tight spherical designs. I

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Tight Spherical Disigns, II

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Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry

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Harmonic properties of the logarithmic potential and the computability of elliptic Fekete points

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A facility location formulation for stable polynomials and elliptic Fekete points

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Computational cost of the Fekete problem. I: The forces method on the 2-sphere

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Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten

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Asymptotics of the maximum number of repulsive particles on a spherical surface

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Distributions of positive mass, which maximize a certain generalized energy integral

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Mesh ratios for best-packing and limits of minimal energy configurations

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Optimal asymptotic bounds for spherical designs

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Well-separated spherical designs

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Lower Order Terms of the Discrete Minimal Riesz Energy on Smooth Closed Curves

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Asymptotics of discrete Riesz \(d\)-polarization on subsets of \(d\)-dimensional manifolds

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Asymptotics of best-packing on rectifiable sets

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Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets

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Low complexity methods for discretizing manifolds via Riesz energy minimization

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Renormalized energy concentration in random matrices

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Quadrature rules and distribution of points on manifolds

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About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case

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Optimal logarithmic energy points on the unit sphere

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Optimal Discrete Riesz Energy and Discrepancy

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Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\)

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A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness

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A simple proof of Stolarsky’s invariance principle

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Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling

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Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces

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Riesz extremal measures on the sphere for axis-supported external fields

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A fascinating polynomial sequence arising from an electrostatics problem on the sphere

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The support of the limit distribution of optimal Riesz energy points on sets of revolution in R3

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The Riesz energy of the <i>N</i> th roots of unity: an asymptotic expansion for large <i>N</i>

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Discrete Energy Asymptotics on a Riemannian circle

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The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

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Numerical integration over spheres of arbitrary dimension

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QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere

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Observed asymptotic differences in energies of stable and minimal point configurations on $\mathbb {S}^2$S2 and the role of defects

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Riesz \(s\)-equilibrium measures on \(d\)-rectifiable sets as \(s\) approaches \(d\)

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Computational existence proofs for spherical \(t\)-designs

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Existence of Solutions to Systems of Underdetermined Equations and Spherical Designs

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Computational aspects of Cui-Freeden statistics for equidistribution on the sphere

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Numerical properties of generalized discrepancies on spheres of arbitrary dimension

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Multi-critical unitary random matrix ensembles and the general Painlevé II equation

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New upper bounds on sphere packings. II

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New upper bounds on sphere packings. I

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Universally optimal distribution of points on spheres

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Optimality and uniqueness of the Leech lattice among lattices

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Three-point bounds for energy minimization

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Diffusion on a Sphere with Localized Traps: Mean First Passage Time, Eigenvalue Asymptotics, and Fekete Points

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Spherical designs and zeta functions of lattices

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Energy Minimization, Periodic Sets and Spherical Designs

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Equidistribution on the Sphere

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On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space

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Energies, group-invariant kernels and numerical integration on compact manifolds

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On point energies, separation radius and mesh norm for s-extremal configurations on compact sets in \(\mathbb R^n\)

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Spherical codes and designs

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Discrete logarithmic energy on the sphere.

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Riesz spherical potentials with external fields and minimal energy points separation

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Riesz polarization inequalities in higher dimensions

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Transfinite diameter, Chebyshev constant and energy on locally compact spaces

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Random Riesz energies on compact Kähler manifolds

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Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs

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On the distribution of weighted extremal points on a surface in \(\mathbb R^d\), \(d \geqslant 3\)

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On the Riesz energy of measures.

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Erdős-Turán type discrepancy bounds

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Spherical Designs, Discrepancy and Numerical Integration

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On the computation of spherical designs by a new optimization approach based on fast spherical Fourier transforms

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Quadrature Errors, Discrepancies, and Their Relations to Halftoning on the Torus and the Sphere

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Lagerung von Punkten auf der Kugel

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A proof of the Kepler conjecture

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On Riesz minimal energy problems

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Riesz minimal energy problems on Ck−1,1-manifolds

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Polarization optimality of equally spaced points on the circle for discrete potentials

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Minimal Riesz energy point configurations for rectifiable \(d\)-dimensional manifolds

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Periodic discrete energy for long-range potentials

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Support of the logarithmic equilibrium measure on sets of revolution in R3

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Quasi-uniformity of minimal weighted energy points on compact metric spaces

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A new approach to the construction of optimal designs

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McLaren's improved snub cube and other new spherical designs in three dimensions

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New spherical 4-designs

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Sums of distances between points of a sphere

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A lower bound for the worst-case cubature error on spheres of arbitrary dimension

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Optimal lower bounds for cubature error on the sphere \(S^2\)

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Worst-case errors in a Sobolev space setting for cubature over the sphere <i>S</i><sup>2</sup>

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Cubature over the sphere \(S^{2}\) in Sobolev spaces of arbitrary order

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An octahedral equal area partition of the sphere and near optimal configurations of points

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Spherical distribution of 5 points with maximal distance sum

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Spherical faraday cage for the case of equal point charges and chebyshev-type quadrature on the sphere

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Chebyshev-type quadrature on multidimensional domains

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Asymptotics for minimal discrete energy on the sphere

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Multiscale Analysis in Sobolev Spaces on the Sphere

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A partition of the unit sphere into regions of equal area and small diameter

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Discrepancy, separation and Riesz energy of finite point sets on the unit sphere

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Some trigonometric extremal functions and the Erdos-Turan type inequalities

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Asymptotics of greedy energy points

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Hecke operators and distributing points on the sphere I

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Hecke operators and distributing points on <i>S</i><sup>2</sup>. II

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Isometric embeddings between classical Banach spaces, cubature formulas, and spherical designs

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Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝ<i><sup>d</sup></i>

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Equidistribution of Fekete points on the sphere

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A real quaternion spherical ensemble of random matrices

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Where does the sup norm of a weighted polynomial live? (A generalization of incomplete polynomials)

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Minimal theta functions

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Spherical harmonics

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The kissing number in four dimensions

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Boris Venkov's Theory of Lattices and Spherical Designs

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On lattices whose minimal vectors form a 6-design

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Optimal \(N\)-point configurations on the sphere: ``magic'' numbers and Smale's 7th problem

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Tractability of multivariate problems. Volume I: Linear information

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On the numerical solution of minimal energy problems

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Distribution of point charges with small discrete energy

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Reverse triangle inequalities for Riesz potentials and connections with polarization

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Minimal discrete energy on the sphere

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Hyperinterpolation on the sphere at the minimal projection order

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Multivariate polynomial approximation

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Distributing many points on a sphere

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From the Ginzburg-Landau model to vortex lattice problems

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Minima of Epstein's zeta function and heights of flat tori

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Error estimates and condition numbers for radial basis function interpolation

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Metric Spaces and Positive Definite Functions

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The Five-Electron Case of Thomson’s Problem

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Ginzburg-Landau vortices, Coulomb gases, and renormalized energies

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Averaging sets: A generalization of mean values and spherical designs

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Complexity of Bezout's Theorem I: Geometric Aspects

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Complexity of Bezout's theorem. III: Condition number and packing

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Extremal systems of points and numerical integration on the sphere

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A variational characterisation of spherical designs

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Mathematical problems for the next century

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Sums of Distances Between Points on a Sphere

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Sums of Distances Between Points on a Sphere. II

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Dithering by Differences of Convex Functions

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New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

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Minimal biquadratic energy of 5 particles on 2-sphere

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On means of distances on the surface of a sphere (lower bounds)

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On means of distances on the surface of a sphere. II: Upper bounds

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Lower bounds for spherical designs

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Equilibrium Potentials with External Fields

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Theory of Potential with Respect to Consistent Kernels; Theorem on Completeness and Sequences of Potentials

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Identifiers

zbMATH Open document ID

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10.1016/j.jco.2015.02.003

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2347956

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