3,801,423 research outputs found
The origin of ultra high energy cosmic rays
We briefly discuss some open problems and recent developments in the
investigation of the origin and propagation of ultra high energy cosmic rays
(UHECRs).Comment: Invited Review Talk at TAUP 2005 (Zaragoza - September 10-14, 2005).
7 page
Functional boundedness of balleans
We pose some open problems related to boundedness of real-valued functions on
balleans and coarse spaces. Also we prove that the Bergman property of groups
is a coarse invariant. A special attention is payed to balleans on groups.Comment: 14 page
The Continuous Skolem-Pisot Problem: On the Complexity of Reachability for Linear Ordinary Differential Equations
We study decidability and complexity questions related to a continuous
analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity of
a linear recurrent sequence. In particular, we show that the continuous version
of the nonnegativity problem is NP-hard in general and we show that the
presence of a zero is decidable for several subcases, including instances of
depth two or less, although the decidability in general is left open. The
problems may also be stated as reachability problems related to real zeros of
exponential polynomials or solutions to initial value problems of linear
differential equations, which are interesting problems in their own right.Comment: 14 pages, no figur
Reconfiguration in bounded bandwidth and treedepth
We show that several reconfiguration problems known to be PSPACE-complete
remain so even when limited to graphs of bounded bandwidth. The essential step
is noticing the similarity to very limited string rewriting systems, whose
ability to directly simulate Turing Machines is classically known. This
resolves a question posed open in [Bonsma P., 2012]. On the other hand, we show
that a large class of reconfiguration problems becomes tractable on graphs of
bounded treedepth, and that this result is in some sense tight.Comment: 14 page
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