73,028 research outputs found
On a total function which overtakes all total recursive functions
This paper discusses a function that is frequently presented as a simile or
look-alike of the so-called ``counterexample function to P=NP,'' that is, the
function that collects all first instances of a problem in NP where a poly
machine incorrectly `guesses' about the instance. We state and give in full
detail a crucial result on the computation of Goedel numbers for some families
of poly machines.Comment: LaTe
A lemma on a total function defined over the Baker-Gill-Solovay set of polynomial Turing machines
If we establish that the counterexample function for P=NP, if total,
overtakes all total recursive functions when extended over all Turing machines,
then what happens to the same counterexample function when defined over the
so-called Baker-Gill-Solovay (BGS) set of poly machines? We state and prove
here a lemma that tries to answer this query.Comment: LaTe
On the existence of certain total recursive functions in nontrivial axiom systems, I
We investigate the existence of a class of ZFC-provably total recursive unary
functions, given certain constraints, and apply some of those results to show
that, for -sound set theory, ZFC.Comment: LaTeX, 16 pages, no figures. This paper was submitted to a major
journal in the field and rejected. The referee somehow misundesrtood
Corollary 3.8 and wrongly concluded that the proof had either a gap or an
error. Can you find whether that error exists
On the consistency of with fragments of ZFC whose own consistency strength can be measured by an ordinal assignment
We formulate the hypothesis in the case of the satisfiability problem
as a sentence, out of which we can construct a partial recursive
function so that is total if and only if . We
then show that if is total, then it isn't --provably
total (where is a fragment of ZFC that adequately extends PA and
whose consistency is of ordinal order). Follows that the negation of ,
that is, , is consistent with those .Comment: LaTeX, 19 pages, no figure
Effects of entanglement and instanton suppression at finite temperature in a SU(2) EPNJL model with anomaly
We investigate the phase transitions characterized by deconfinement and
restoration of chiral and axial symmetries,at finite temperature, in the
framework of QCD inspired models. We compare the results obtained in the SU(2)
Polyakov-Nambu-Jona-Lasinio model with anomaly and in its extended version, the
Entangled Polyakov-Nambu-Jona-Lasinio model. In the last version, four-quark
vertices with entanglement between the chiral condensate and the Polyakov loop
are considered. The thermodynamics of the phase transitions, the meson
spectrum, and in particular the convergence of axial and chiral partners, will
be analyzed, as well as the topological susceptibility. We find that an
explicit temperature dependence of the coupling vertices is necessary in both
models in order to have effective restoration of the U(1) symmetry.Comment: 19 pages, 4 figures; PRD versio
Quantification of Einstein-Podolski-Rosen steering for two-qubit states
In the last few years, several criteria to identify Eistein-Podolski-Rosen
steering have been proposed and experimentally implemented. On the operational
side, however, the evaluation of the steerability degree of a given state has
shown to be a difficult task and only a few results are known. In this work, we
propose a measure of steering that is based on the maximal violation of well
established steering inequalities. Applying this approach to two-qubit states,
we managed to derive simple closed formulas for steering in the two- and
three-measurement scenarios. Among the options investigated, a measure has been
found that correctly satisfies the entanglement-steering-nonlocality hierarchy
and reproduces results reported so far.Comment: 5 pages, published versio
Pseudoscalar Mesons in Asymmetric Matter
The behavior of kaons and pions in hot non strange quark matter, simulating
neutron matter, is investigated within the SU(3) Nambu-Jona-Lasinio [NJL] and
in the Enlarged Nambu-Jona-Lasinio [ENJL] (including vector pseudo-vector
interaction) models. At zero temperature, it is found that in the NJL model,
where the phase transition is first order, low energy modes with K-, Pi+
quantum numbers, which are particle-hole excitations of the Fermi sea, appear.
Such modes are not found in the ENJL model and in NJL at finite temperatures.
The increasing temperature has also the effect of reducing the splitting
between the charge multiplets.Comment: 10 pages, 4 figures. Published in the Proc. of the workshop 'Quark
Matter in Astro- and Particle Physics', Rostock, November 200
Restoration of axial symmetry and its possible relation with restoration of chiral symmetry and deconfinement at finite temperature
The phase transitions characterized by deconfinement and restoration of
chiral symmetry as well as the restoration of axial symmetry, at finite
temperature, are investigated in the framework of SU(2)
Polyakov-Nambu-Jona-Lasinio (PNJL) models with the U(1) anomaly. The
thermodynamics of the phase transitions, the topological susceptibility, the
meson spectrum, and, in particular, the convergence of axial and chiral
partners are analyzed, in the framework of the ordinary PNJL model and in its
extension, the entangled Polyakov-Nambu-Jona-Lasinio (EPNJL) model. The latter
incorporates entanglement between restoration of chiral symmetry and
deconfinement.Comment: Contribution to the International Meeting "Excited QCD", Bjelasnica
Mountain, Sarajevo, 3-9 February 201
Thermodynamics and critical behavior in the Nambu-Jona-Lasinio model of QCD
We investigate the phase diagram of strongly interacting matter as a function
of temperature and baryonic density/chemical potential, within
Nambu--Jona-Lasinio type models. We perform a systematic study concerning the
existence, location, and properties of a critical end point/tricritical point,
both in SU(2) and SU(3) versions of the model. We verify that, for
and up to a critical strange quark mass, there is a tricritical point, which
becomes a critical end point in a world with realistic values of the current
quark masses. The properties of physical observables, such as the baryon number
susceptibility and the specific heat, are analyzed in the vicinity of the
critical end point, with special focus on their critical exponents. The
behavior of mesons in the plane is analyzed in connection
with possible signatures of partial and effective restoration of chiral
symmetry.Comment: 29 pages, 8 figures; PRD versio
Migrations, vaccinations and epidemic control
We consider three regions with different public health conditions. In the
absence of migration among these regions, the first two have good health
conditions and the disease free state is stable; for the third region, on the
other hand, the only stable state is the endemic one. When migration is
included in the model, we assume that the second region has a disease risk that
makes its inhabitants prone to accept to be vaccinated, while the population in
the first region tends to reject the vaccination, considered riskier that the
disease. Therefore, the second region is a "buffer zone" between the two
extremal regions. We study the basic reproductive ratio as a function of the
vaccination in all regions and migration among them. This problem is studied
numerically, showing explicit situations in which migration will have an
overall positive effect in the disease dynamics, with and without vaccinations.
We also find explicit formula in the limit of small ("closed borders") and high
migration ("open borders").Comment: 11 pages, 5 figure
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