Displaying similar documents to “A law of the iterated logarithm for the sample covariance matrix.”

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 ) .

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.

Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

Ralf Bader, Nikolaos Papageorgiou (2000)

Annales Polonici Mathematici

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We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of...