136 research outputs found
Undecidable properties of self-affine sets and multi-tape automata
We study the decidability of the topological properties of some objects
coming from fractal geometry. We prove that having empty interior is
undecidable for the sets defined by two-dimensional graph-directed iterated
function systems. These results are obtained by studying a particular class of
self-affine sets associated with multi-tape automata. We first establish the
undecidability of some language-theoretical properties of such automata, which
then translate into undecidability results about their associated self-affine
sets.Comment: 10 pages, v2 includes some corrections to match the published versio
A description of n-ary semigroups polynomial-derived from integral domains
We provide a complete classification of the n-ary semigroup structures
defined by polynomial functions over infinite commutative integral domains with
identity, thus generalizing G{\l}azek and Gleichgewicht's classification of the
corresponding ternary semigroups
Clones with finitely many relative R-classes
For each clone C on a set A there is an associated equivalence relation
analogous to Green's R-relation, which relates two operations on A iff each one
is a substitution instance of the other using operations from C. We study the
clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde
Role of baryonic resonances in the dilepton emission in nucleon-nucleon collisions
Within an effective Lagrangian model, we present calculations for cross
sections of the dilepton production in proton-proton and proton-neutron
collisions at laboratory kinetic energies in 1-5 GeV range. Production
amplitudes include contributions from the nucleon-nucleon bremsstrahlung as
well as from the mechanism of excitation, propagation, and radiative decay of
Delta(1232) and N*(1520) intermediate baryonic resonances. It is found that the
delta isobar terms dominate the cross sections in the entire considered beam
energy range. Our calculations are able to explain the data of the DLS
collaboration on the dilepton production in proton-proton collisions for beam
energies below 1.3 GeV. However, for incident energies higher than this the
inclusion of contributions from other dilepton sources like Dalitz decay of pi0
and eta mesons, and direct decay of rho and omega mesons is necessary to
describe the data.Comment: 22 pages, 7 figures, more details of the calculations added, version
to appear in Phys. Rev
Constructive Dimension and Turing Degrees
This paper examines the constructive Hausdorff and packing dimensions of
Turing degrees. The main result is that every infinite sequence S with
constructive Hausdorff dimension dim_H(S) and constructive packing dimension
dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) /
dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0,
then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness
extractor* that increases the algorithmic randomness of S, as measured by
constructive dimension.
A number of applications of this result shed new light on the constructive
dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to
hold for the Turing degree of any sequence S. A new proof is given of a
previously-known zero-one law for the constructive packing dimension of Turing
degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) =
dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive
Hausdorff and packing dimension equal to 1.
Finally, it is shown that no single Turing reduction can be a universal
constructive Hausdorff dimension extractor, and that bounded Turing reductions
cannot extract constructive Hausdorff dimension. We also exhibit sequences on
which weak truth-table and bounded Turing reductions differ in their ability to
extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems,
45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to
insufficient care with the choice of delta. This version modifies that proof
to fix the error
Dilepton production in heavy ion collisions at intermediate energies
We present a unified description of the vector meson and dilepton production
in elementary and in heavy ion reactions. The production of vector mesons
() is described via the excitation of nuclear resonances ().
The theoretical framework is an extended vector meson dominance model (eVMD).
The treatment of the resonance decays with arbitrary spin is
covariant and kinematically complete. The eVMD includes thereby excited vector
meson states in the transition form factors. This ensures correct asymptotics
and provides a unified description of photonic and mesonic decays. The
resonance model is successfully applied to the production in
reactions. The same model is applied to the dilepton production in elementary
reactions (). Corresponding data are well reproduced. However, when
the model is applied to heavy ion reactions in the BEVALAC/SIS energy range the
experimental dilepton spectra measured by the DLS Collaboration are
significantly underestimated at small invariant masses. As a possible solution
of this problem the destruction of quantum interference in a dense medium is
discussed. A decoherent emission through vector mesons decays enhances the
corresponding dilepton yield in heavy ion reactions. In the vicinity of the
-peak the reproduction of the data requires further a substantial
collisional broadening of the and in particular of the meson.Comment: 32 pages revtex, 19 figures, to appear in PR
production in reactions at SIS energies
Detailed predictions for dilepton production from reactions at SIS
energies are presented within a semi-classical BUU transport model that
includes the off-shell propagation of vector mesons nonperturbatively and
calculates the width of the vector mesons dynamically. Different scenarios of
in-medium modifications of vector mesons, such as collisional broadening and
dropping vector meson masses, are investigated and the possibilities for an
experimental observation of in-medium effects in reactions at 1--4 GeV
are discussed for a variety of nuclear targets.Comment: 38 pages, LaTeX, including 20 postscript figures, to be published in
Nucl. Phys.
Foundations for decision problems in separation logic with general inductive predicates
Abstract. We establish foundational results on the computational com-plexity of deciding entailment in Separation Logic with general induc-tive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment in the base language is ΠP2-complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed.
Periodicity Forcing Words
The Dual Post Correspondence Problem asks, for a given word α, if there exists a non-periodic morphism g and an arbitrary morphism h such that g(α) = h(α). Thus α satisfies the Dual PCP if and only if it belongs to a non-trivial equality set. Words which do not satisfy the Dual PCP are called periodicity forcing, and are important to the study of word equations, equality sets and ambiguity of morphisms. In this paper, a 'prime' subset of periodicity forcing words is presented. It is shown that when combined with a particular type of morphism it generates exactly the full set of periodicity forcing words. Furthermore, it is shown that there exist examples of periodicity forcing words which contain any given factor/prefix/suffix. Finally, an alternative class of mechanisms for generating periodicity forcing words is developed, resulting in a class of examples which contrast those known already
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