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Rademacher-Carlitz polynomials

Matthias Beck, Florian Kohl (2014)

Acta Arithmetica

We introduce and study the Rademacher-Carlitz polynomial $R (u, v, s, t, a, b) : = \sum_{k = ⌈ s ⌉}^{⌈ s ⌉ + b - 1} u^{⌊ (k a + t) ⌋} / b_{v^{k}}$ where $a, b \in ℤ_{> 0}$ , s,t ∈ ℝ, and u and v are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view R(u,v,s,t,a,b) as a polynomial analogue (in the sense of Carlitz) of the Dedekind-Rademacher sum $r_{t} (a, b) : = \sum_{k = 0}^{b - 1} (((k a + t) / b)) ((k / b))$ , which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz...

Radial Minkowski additive operators

Lewen Ji (2021)

Czechoslovak Mathematical Journal

We give some characterizations for radial Minkowski additive operators and prove a new characterization of balls. Finally, we show the property of radial Minkowski homomorphism.

Radial projections of bisectors in Minkowski spaces.

H. Martini, S. Wu (2008)

Extracta Mathematicae

Radii of simplices and some applications to geometric inequalities.

Brandenberg, René, Theobald, Thorsten (2004)

Beiträge zur Algebra und Geometrie

Radiography of perfect lattices. (Radiographie des réseaux parfaits.)

Batut, Christian, Martinet, Jacques (1994)

Experimental Mathematics

Radonpartitionen und konvexe Polyeder.

Jürgen Eckhoff (1975)

Journal für die reine und angewandte Mathematik

Random fixed point theorems for multivalued nonexpansive non-self-random operators.

Plubtieng, S., Kumam, P. (2006)

Journal of Applied Mathematics and Stochastic Analysis

Random polytopes and the volume-product of symmetric convex bodies.

Shlomo Reisner (1985)

Mathematica Scandinavica

Random polytopes in a convex polytope, independence of shape, and concentration of vertices.

Imre Bárány, Christian Buchta (1993)

Mathematische Annalen

Random Polytopes in the d- Dimensional Cube.

Z. Füredi (1986)

Discrete & computational geometry

Random Projections of Regular Simplices.

R. Schneider, F. Affentranger (1992)

Discrete & computational geometry

Random system of lines in the Euclidean plane $E_{2}$ .

Caristi, Giuseppe (2008)

APPS. Applied Sciences

Random walks that avoid their past convex hull.

Angel, Omer, Benjamini, Itai, Virág, Bálint (2003)

Electronic Communications in Probability [electronic only]

Random ε-nets and embeddings in $ℓ_{\infty}^{N}$

Y. Gordon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann (2007)

Studia Mathematica

We show that, given an n-dimensional normed space X, a sequence of $N = {(8 / ε)}^{2 n}$ independent random vectors ${(X_{i})}_{i = 1}^{N}$ , uniformly distributed in the unit ball of X*, with high probability forms an ε-net for this unit ball. Thus the random linear map $Γ : ℝ \to ℝ^{N}$ defined by $Γ x = {(⟨ x, X_{i} ⟩)}_{i = 1}^{N}$ embeds X in $ℓ_{\infty}^{N}$ with at most 1 + ε norm distortion. In the case X = ℓ₂ⁿ we obtain a random 1+ε-embedding into $ℓ_{\infty}^{N}$ with asymptotically best possible relation between N, n, and ε.

Randomness and pattern in convex geometric analysis.

Milman, Vitali (1998)

Documenta Mathematica

Rangements optimaux de carrés unité dans une bande infinie

Saïd El Moumni (1997)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Rank $1$ forms, closed zones and laminae

Michel Deza, Viatcheslav Grishukhin (2002)

Journal de théorie des nombres de Bordeaux

For a given lattice, we establish an equivalence between closed zones for the corresponding Voronoï polytope, suitable hyperplane sections of the corresponding Delaunay partition, and rank $1$ quadratic forms which are extreme rays for the corresponding $L$ -type domain.

Currently displaying 1 – 20 of 79