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The subject of Diophantine approximation studies how a real vector is approximated by rational vectors. Diophantine sets are subsets of real vectors defined by certain approximate functions. Among the...
We show that a germ of a real analytic Lorentz metric on R 3 which is locally homogeneous on an open set containing the origin in its closure is necessarily locally homogeneous. We classifiy L...
We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a map of the boundaries.
The dead-end depth of an element g of a group with finite generating set A is the distance from g to the complement of the radius d(1,g) closed ball, in the word metric d. We exhibit a finitely presen...
The Convergenceof an Euler Approximation of an Initial ValueProblemIs Not Always Obvious.
The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming...
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply s...
Recently there has been much study of nonlinear dynamical systems (differential equations) which have chaotic solutions. While there is not precise definition of what a chaotic solution is, it is gene...
In this paper, the quantum logical ‘or’ is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration...
We show that the second iterate H2(M) = H(H(M)) of a random oracle H cannot achieve strong security in the sense of indifferentiability from a random oracle. We do so by proving that indifferentiabili...
We construct an example of a hyperbolic group with a hyperbolic subgroup for which the Cannon-Thurston map does not exist. That is, inclusion does not induce a map of the boundaries.
We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of...
We consider the derived category of a specific non-Noetherian ring \Lambda, and show that there are objects in D(\Lambda) that are not Bousfield equivalent to any module. This answers a question posed...
Abstract: We show that Bergman completeness is not a quasi-conformal invariant for general Riemann surfaces.
Abstract: Answering an old question of M.Hata, we construct an example of a 1-dimensional Peano continuum which is not homeomorphic to an attractor of IFS.

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