Displaying similar documents to “On Rowland's sequence.”

The Hausdorff dimension of some special plane sets

Jan Mařík (1994)

Mathematica Bohemica

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A compact set T ⊂ 𝐑 2 is constructed such that each horizontal or vertical line intersects T in at most one point while the α -dimensional measure of T is infinite for every α ∈ ( 0 , 2 ) .

General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations

N. Dilna, A. Rontó (2008)

Mathematica Bohemica

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New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.

Endpoint bounds for convolution operators with singular measures

E. Ferreyra, T. Godoy, M. Urciuolo (1998)

Colloquium Mathematicae

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Let S ⊂ ℝ n + 1 be the graph of the function ϕ : [ - 1 , 1 ] n → ℝ defined by ϕ ( x 1 , ⋯ , x n ) = ∑ j = 1 n | x j | β j , with 1< β 1 ≤ ⋯ ≤ β n , and let μ the measure on ℝ n + 1 induced by the Euclidean area measure on S. In this paper we characterize the set of pairs (p,q) such that the convolution operator with μ is L p - L q bounded.

A cohomological index of Fuller type for parameterized set-valued maps in normed spaces

Robert Skiba (2014)

Open Mathematics

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We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.