2,801 research outputs found
On multidegree of tame and wild automorphisms of C^3
In this note we show that the set mdeg(Aut(C^3)) mdeg(Tame(C^3)) is not
empty. Moreover we show that this set has infinitely many elements. Since for
the famous Nagata's example N of wild automorphism, mdeg N =(5,3,1) is an
element of mdeg(Tame(C^3)) and since for other known examples of wild
automorphisms the multidegree is of the form (1,d_2,d_3) (after permutation if
neccesary), then we give the very first exmple of wild automorphism F of C^3
such that mdeg F does not belong to mdeg(Tame(C^3)).
We also show that, if d_1,d_2 are odd numbers such that gcd (d_1,d_2) =1,
then (d_1,d_2,d_3) belongs to mdeg(Tame(C^3)) if and only if d_3 is a linear
combination of d_1,d_2 with natural coefficients. This a crucial fact that we
use in the proof of the main result
Regular Boardgames
We propose a new General Game Playing (GGP) language called Regular
Boardgames (RBG), which is based on the theory of regular languages. The
objective of RBG is to join key properties as expressiveness, efficiency, and
naturalness of the description in one GGP formalism, compensating certain
drawbacks of the existing languages. This often makes RBG more suitable for
various research and practical developments in GGP. While dedicated mostly for
describing board games, RBG is universal for the class of all finite
deterministic turn-based games with perfect information. We establish
foundations of RBG, and analyze it theoretically and experimentally, focusing
on the efficiency of reasoning. Regular Boardgames is the first GGP language
that allows efficient encoding and playing games with complex rules and with
large branching factor (e.g.\ amazons, arimaa, large chess variants, go,
international checkers, paper soccer).Comment: AAAI 201
Emerging singularities in the bouncing loop cosmology
In this paper we calculate corrections from holonomies
in the Loop Quantum Gravity, usually not taken into account. Allowance of the
corrections of this kind is equivalent with the choice of the new quatization
scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this
additional freedom and presented corrections are consistent with the standard
approach. We apply these corrections to the flat FRW cosmological model and
calculate the modified Friedmann equation. We show that the bounce appears in
the models with the standard quantization scheme is
shifted to the higher energies . Also
a pole in the Hubble parameter appears for corresponding to \emph{hyper-inflation/deflation} phases. This
pole represents a curvature singularity at which the scale factor is finite. In
this scenario the singularity and bounce co-exist. Moreover we find that an
ordinary bouncing solution appears only when quantum corrections in the lowest
order are considered. Higher order corrections can lead to the nonperturbative
effects.Comment: RevTeX4, 8 pages, 4 figures; v2 change of title, more discussion on
co-existence of singularity and bounc
Exact solutions for Big Bounce in loop quantum cosmology
In this paper we study the flat (k=0) cosmological FRW model with holonomy
corrections of Loop Quantum Gravity. The considered universe contains a
massless scalar field and the cosmological constant Lambda. We find analytical
solutions for this model in different configurations and investigate its
dynamical behaviour in the whole phase space. We show the explicit influence of
Lambda on the qualitative and quantitative character of solutions. Even in the
case of positive Lambda the oscillating solutions without the initial and final
singularity appear as a generic case for some quantisation schemes.Comment: 12 pages, 12 figures, added references and changed introduction and
summar
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