On the four vertex theorem in planes with radial density $e^{φ(r)}$

Doan The Hieu; Tran Le Nam

Displaying similar documents to “On the four vertex theorem in planes with radial density $e^{φ (r)}$ ”

Mean value densities for temperatures

N. Suzuki, N. A. Watson (2003)

Colloquium Mathematicae

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A positive measurable function K on a domain D in $ℝ^{n + 1}$ is called a mean value density for temperatures if $u (0, 0) = \int \int_{D} K (x, t) u (x, t) d x d t$ for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.

A density estimate for the $3 x + 1$ problem

Ivan Korec (1994)

Mathematica Slovaca

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On the structural result on normal plane maps

Tomás Madaras, Andrea Marcinová (2002)

Discussiones Mathematicae Graph Theory

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We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree Δ(G) ≤ D, D ≥ 12 is proved to be upper bounded by $6 + [(2 D + 12) / (D - 2)] ({(D - 1)}^{(t - 1)} - 1)$ . This improves a recent bound $6 + [(3 D + 3) / (D - 2)] ({(D - 1)}^{t - 1} - 1)$ , D ≥ 8 by Jendrol’ and Skupień, and the upper bound for distance-2 chromatic number.

Construction of an Uncountable Difference between Φ(B) and $Φ_{f} (B)$

Josh Campbell, David Swanson (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We construct a set B and homeomorphism f where f and $f^{- 1}$ have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.

On the measurability of sets of pairs of straight lines in the simply isotropic space

Margarita G. Spirova, Adrijan V. Borisov (2005)

Banach Center Publications

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We study the measurability of sets of pairs of straight lines with respect to the group of motions in the simply isotropic space $I ₃^{(1)}$ by solving PDEs. Also some Crofton type formulas are obtained for the corresponding densities.

Analytic functions are $ℐ$ -density continuous

Krzysztof Ciesielski, Lee Larson (1994)

Commentationes Mathematicae Universitatis Carolinae

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A real function is $ℐ$ -density continuous if it is continuous with the $ℐ$ -density topology on both the domain and the range. If $f$ is analytic, then $f$ is $ℐ$ -density continuous. There exists a function which is both $C^{\infty}$ and convex which is not $ℐ$ -density continuous.

Bounds On The Disjunctive Total Domination Number Of A Tree

Michael A. Henning, Viroshan Naicker (2016)

Discussiones Mathematicae Graph Theory

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Let G be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, γt(G). A set S of vertices in G is a disjunctive total dominating set of G if every vertex is adjacent to a vertex of S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number, [...] γtd(G) $γ_{t}^{d} (G)$ , is the minimum cardinality of such a set. We observe that [...] γtd(G)≤γt(G)...

Coalescing Fiedler and core vertices

Didar A. Ali, John Baptist Gauci, Irene Sciriha, Khidir R. Sharaf (2016)

Czechoslovak Mathematical Journal

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The nullity of a graph $G$ is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex...

Characterization of $n$ -vertex graphs with metric dimension $n - 3$

Mohsen Jannesari, Behnaz Omoomi (2014)

Mathematica Bohemica

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For an ordered set $W = {w_{1}, w_{2}, ..., w_{k}}$ of vertices and a vertex $v$ in a connected graph $G$ , the ordered $k$ -vector $r (v | W) : = (d (v, w_{1}), d (v, w_{2}), ..., d (v, w_{k}))$ is called the metric representation of $v$ with respect to $W$ , where $d (x, y)$ is the distance between vertices $x$ and $y$ . A set $W$ is called a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$ . The minimum cardinality of a resolving set for $G$ is its metric dimension. In this paper, we characterize all graphs of order $n$ with metric dimension $n - 3$ .

Existence problem of the osculating planes of a curve in $R_{n}$

S. Topa (1964)

Annales Polonici Mathematici

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How many clouds cover the plane?

James H. Schmerl (2003)

Fundamenta Mathematicae

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The plane can be covered by n + 2 clouds iff $2^{ℵ ₀} \leq ℵ ₙ$ .

The density of states of a local almost periodic operator in $ℝ^{ν}$

Andrzej Krupa (2003)

Studia Mathematica

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We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on $H^{m} (ℝ^{ν})$ . The support of the density coincides with the spectrum of the operator in $L ² (ℝ^{ν})$ .

Displaying similar documents to “On the four vertex theorem in planes with radial density e φ ( r ) ”

Displaying similar documents to “On the four vertex theorem in planes with radial density $e^{φ (r)}$ ”