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On capacitated covering with unit balls
International Journal of Computer Mathematics, 2014In this paper, we consider the problem of capacitated covering with unit balls. In this problem, a set of weighted points in a metric space is given, and we want to cover them with a minimum number of the unit balls of that metric space provided that the total weight assigned to each unit ball is at most one.
Taha Ghasemi, Mohammadreza Razzazi
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Hamel‐isomorphic images of the unit ball
Mathematical Logic Quarterly, 2010AbstractIn this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals.
Jacek Cichon, Przemyslaw Szczepaniak
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Polynomial Interpolation on the Unit Sphere and on the Unit Ball
Advances in Computational Mathematics, 2004Let \(S^d\) be the unit shere of \(R^{d+1}\) and \(B^d\) the unit ball of \(R^d\). Let \(\Pi_n^d\) denote the space of polynomials of degree at most \(n\) in \(R^d\), whose dimension is \(M_n^d={{n+d}\choose d}\). Finally let \(\Pi_n(S^d)\) denote the space of spherical polynomials of \(d+1\) variables, which are the restriction of polynomials in ...
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Subharmonic Functions in the Unit Ball
Positivity, 2005Let $u$ be a subharmonic function on the unit ball $B_{N}$ in $\Bbb{R}^N$ $(N\geq2)$, and let $µ$ be its associated Riesz measure. This paper establishes growth properties of $µ(s)\coloneq µ(\{\vert x\vert\leq s\})$ when growth restrictions are imposed on $u$. For example, let $g$ denote the Green function for $B_{N}$ with pole at $0$, and suppose that
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On connected domination in unit ball graphs
Optimization Letters, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sergiy Butenko +2 more
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On Packings of Congruent Balls in the Unit Ball
1987Let (X, ) be an infinite-dimensional real or complex inner product space. If I ≠O, r ∈ IR+: = (0,∞), uj ∈ X (for all j ∈ I), uj ≠ uk for j ≠ k, then the family (Br(uj): j ∈I) of open r-balls with centers uj is said to be packable ...
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The Octonionic Bergman Kernel for the Unit Ball
Advances in Applied Clifford Algebras, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Jinxun, Li, Xingmin
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