15,421 research outputs found
Software for cut-generating functions in the Gomory--Johnson model and beyond
We present software for investigations with cut generating functions in the
Gomory-Johnson model and extensions, implemented in the computer algebra system
SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on
Mathematical Software 201
Rational quantum integrable systems of D_N type with polarized spin reversal operators
We study the spin Calogero model of D_N type with polarized spin reversal
operators, as well as its associated spin chain of Haldane-Shastry type, both
in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and
the partition function of the former model in closed form, from which we derive
an exact formula for the chain's partition function in terms of products of
partition functions of Polychronakos-Frahm spin chains of type A. Using a
recursion relation for the latter partition functions that we derive in the
paper, we are able to numerically evaluate the partition function, and thus the
spectrum, of the D_N-type spin chain for relatively high values of the number
of spins N. We analyze several global properties of the chain's spectrum, such
as the asymptotic level density, the distribution of consecutive spacings of
the unfolded spectrum, and the average degeneracy. In particular, our results
suggest that this chain is invariant under a suitable Yangian group, and that
its spectrum coincides with that of a Yangian-invariant vertex model with
linear energy function and dispersion relation.Comment: 26 pages, 5 figures, typeset in LaTe
Nutritional intervention and impact of polyphenol on glycohaemoglobin (HbA1c) in non-diabetic and type 2 diabetic subjects: systematic review and meta-analysis
Polyphenols have been extensively studied for their antioxidant and anti-inflammatory properties. Recently, their antiglycative actions by oxidative stress modulation have been linked to prevention of diabetes and associated complications. This paper assesses the evidence for polyphenol interventions on glycohaemoglobin (HbA1c) in non-diabetic, pre-diabetic and type 2 diabetes mellitus (T2DM) subjects. A systematic review of polyphenols clinical trials on HbA1c in humans was performed according to the Preferred Reporting Items for Systematic Review and Meta-Analysis. Thirty-six controlled randomized trials with HbA1c values were included. Polyphenols (extracts, supplements, foods), were supplemented (28 mg to 1.5g) for 0.7 to 12 months. Combining all subjects (n=1954, mean baseline HbA1c=7.03%, 53 mmol/mol), polyphenol supplementation significantly (p<0.001) lowered HbA1c% by -0.53±0.12 units (-5.79±0.13 mmol/mol). This reduction was significant (p<0.001) in T2DM subjects, specifically (n=1426, mean baseline HbA1c=7.44%, 58 mmol/mol), with HbA1c% lowered by -0.21±0.04 units (-2.29±0.4 mmol/mol). Polyphenol supplementation had no significant effect (p>0.21) in the non-diabetic (n=258, mean baseline HbA1c=5.47%, 36 mmol/mol) and the pre-diabetic subjects (n=270, mean baseline HbA1c=6.06%, 43 mmol/mol) strata: -0.39±0.27 HbA1c% units (-4.3±0.3 mmol/mol), and -0.38±0.31 units (-4.2±0.31 mmol/mol), respectively. In conclusion, polyphenols can successfully reduce HbA1c in T2DM, without any intervention at glycaemia, and could contribute to the prevention of diabetes complications
Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field
We consider a spin half particle in the external magnetic field which couples
to a harmonic oscillator through some pseudo-hermitian interaction. We find
that the energy eigenvalues for this system are real even though the
interaction is not PT invariant.Comment: Latex, no figs, 8 pages. (To appear in Mod. Phys. Lett. A
noise and integrable systems
An innovative test for detecting quantum chaos based on the analysis of the
spectral fluctuations regarded as a time series has been recently proposed.
According to this test, the fluctuations of a fully chaotic system should
exhibit 1/f noise, whereas for an integrable system this noise should obey the
1/f^2 power law. In this letter, we show that there is a family of well-known
integrable systems, namely spin chains of Haldane-Shastry type, whose spectral
fluctuations decay instead as 1/f^4. We present a simple theoretical
justification of this fact, and propose an alternative characterization of
quantum chaos versus integrability formulated directly in terms of the power
spectrum of the spacings of the unfolded spectrum.Comment: 5 pages, 3 figures, RevTe
Multi-parameter deformed and nonstandard Yangian symmetry in integrable variants of Haldane-Shastry spin chain
By using `anyon like' representations of permutation algebra, which pick up
nontrivial phase factors while interchanging the spins of two lattice sites, we
construct some integrable variants of Haldane-Shastry (HS) spin chain. Lax
equations for these spin chains allow us to find out the related conserved
quantities. However, it turns out that such spin chains also possess a few
additional conserved quantities which are apparently not derivable from the Lax
equations. Identifying these additional conserved quantities, and the usual
ones related to Lax equations, with different modes of a monodromy matrix, it
is shown that the above mentioned HS like spin chains exhibit multi-parameter
deformed and `nonstandard' variants of Yangian symmetry.Comment: 18 pages, latex, no figure
Formation and Collapse of Nonaxisymmetric Protostellar Cores in Planar Magnetic Interstellar Clouds: Formulation of the Problem and Linear Analysis
We formulate the problem of the formation and collapse of nonaxisymmetric
protostellar cores in weakly ionized, self-gravitating, magnetic molecular
clouds. In our formulation, molecular clouds are approximated as isothermal,
thin (but with finite thickness) sheets. We present the governing dynamical
equations for the multifluid system of neutral gas and ions, including
ambipolar diffusion, and also a self-consistent treatment of thermal pressure,
gravitational, and magnetic (pressure and tension) forces. The dimensionless
free parameters characterizing model clouds are discussed. The response of
cloud models to linear perturbations is also examined, with particular emphasis
on length and time scales for the growth of gravitational instability in
magnetically subcritical and supercritical clouds. We investigate their
dependence on a cloud's initial mass-to-magnetic-flux ratio (normalized to the
critical value for collapse), the dimensionless initial neutral-ion collision
time, and also the relative external pressure exerted on a model cloud. Among
our results, we find that nearly-critical model clouds have significantly
larger characteristic instability lengthscales than do more distinctly sub- or
supercritical models. Another result is that the effect of a greater external
pressure is to reduce the critical lengthscale for instability. Numerical
simulations showing the evolution of model clouds during the linear regime of
evolution are also presented, and compared to the results of the dispersion
analysis. They are found to be in agreement with the dispersion results, and
confirm the dependence of the characteristic length and time scales on
parameters such as the initial mass-to-flux ratio and relative external
pressure.Comment: 30 pages, 7 figures Accepted by Ap
Quantum finite automata and linear context-free languages: a decidable problem
We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. © 2013 Springer-Verlag
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