All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 93

Showing per page

Paths of low weight in planar graphs

Igor Fabrici, Jochen Harant, Stanislav Jendrol' (2008)

Discussiones Mathematicae Graph Theory

The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are: 1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds w G ( P ) : = ∑ u ∈ V ( P ) d e g G ( u ) ≤ ( 3 / 2 ) k ² + ( k ) 2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds w T ( P ) : = ∑ u ∈ V ( P ) d e g T ( u ) ≤ k ² + 13 k 3. Let G be a 3-connected simple planar graph of circumference...

Permanence of moment estimates for p-products of convex bodies

Ulrich Brehm, Hendrik Vogt, Jürgen Voigt (2002)

Studia Mathematica

It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies in ℝⁿ are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the Γ-function.

Perturbing the hexagonal circle packing: a percolation perspective

Itai Benjamini, Alexandre Stauffer (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hexagonal circle packing with radius 1 / 2 and perturb it by letting the circles move as independent Brownian motions for time t . It is shown that, for large enough t , if 𝛱 t is the point process given by the center of the circles at time t , then, as t → ∞ , the critical radius for circles centered at 𝛱 t to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...

Piecewise Convex Curves and their Integral Representation

Nedelcheva, M. D. (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 52A10.A convex arc in the plane is introduced as an oriented arc G satisfying the following condition: For any three of its points c1 < c2 < c3 the triangle c1c2c3 is counter-clockwise oriented. It is proved that each such arc G is a closed and connected subset of the boundary of the set FG being the convex hull of G. It is shown that the convex arcs are rectifyable and admit a representation in the natural parameter by the Riemann-Stieltjes integral...

Planar anisotropy revisited

Viktor Beneš, Arun M. Gokhale (2000)

Kybernetika

The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy....

Currently displaying 21 – 40 of 93