pinecone/core-2020-05-10-deduplication huggingface dataset:
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
The NNLO gluon fusion Higgs production cross-section with many heavy
  quarks

We consider extensions of the Standard Model with a number of additional
heavy quarks which couple to the Higgs boson via top-like Yukawa interactions.
We construct an effective theory valid for a Higgs boson mass which is lighter
than twice the lightest heavy quark mass and compute the corresponding Wilson
coefficient through NNLO. We present numerical results for the gluon fusion
cross-section at the Tevatron for an extension of the Standard Model with a
fourth generation of heavy quarks. The gluon fusion cross-section is enhanced
by a factor of roughly 9 with respect to the Standard Model value. Tevatron
experimental data can place stringent exclusion limits for the Higgs mass in
this model.Comment: 14 pages, 1 tabl
Phase behaviour of polydisperse spheres: simulation strategies and an
  application to the freezing transition

The statistical mechanics of phase transitions in dense systems of
polydisperse particles presents distinctive challenges to computer simulation
and analytical theory alike. The core difficulty, namely dealing correctly with
particle size fractionation between coexisting phases, is set out in the
context of a critique of previous simulation work on such systems. Specialized
Monte Carlo simulation techniques and moment free energy method calculations,
capable of treating fractionation exactly, are then described and deployed to
study the fluid-solid transition of an assembly of repulsive spherical
particles described by a top-hat "parent" distribution of particle sizes. The
cloud curve delineating the solid-fluid coexistence region is mapped as a
function of the degree of polydispersity $\delta$, and the properties of the
incipient "shadow" phases are presented. The coexistence region is found to
shift to higher densities as $\delta$ increases, but does not exhibit the sharp
narrowing predicted by many theories and some simulations.Comment: 13 pages, 7 figure
A model colloidal fluid with competing interactions: bulk and
  interfacial properties

Using a simple mean-field density functional theory theory (DFT), we
investigate the structure and phase behaviour of a model colloidal fluid
composed of particles interacting via a pair potential which has a hard core of
diameter $\sigma$, is attractive Yukawa at intermediate separations and
repulsive Yukawa at large separations. We analyse the form of the asymptotic
decay of the bulk fluid correlation functions, comparing results from our DFT
with those from the self consistent Ornstein-Zernike approximation (SCOZA). In
both theories we find rich crossover behaviour, whereby the ultimate decay of
correlation functions changes from monotonic to long-wavelength damped
oscillatory decay on crossing certain lines in the phase diagram, or sometimes
from oscillatory to oscillatory with a longer wavelength. For some choices of
potential parameters we find, within the DFT, a $\lambda$-line at which the
fluid becomes unstable with respect to periodic density fluctuations. SCOZA
fails to yield solutions for state points near such a $\lambda$-line. The
propensity to clustering of particles, which is reflected by the presence of a
long wavelength $\gg \sigma$, slowly decaying oscillatory pair correlation
function, and a structure factor that exhibits a very sharp maximum at small
but non zero wavenumbers, is enhanced in states near the $\lambda$-line. We
present density profiles for the planar liquid-gas interface and for fluids
adsorbed at a planar hard wall. The presence of a nearby $\lambda$-transition
gives rise to pronounced long-wavelength oscillations in the one-body densities
at both types of interface.Comment: 14 pages, 11 figure
A class of quasi-linear equations in coframe gravity

We have shown recently that the gravity field phenomena can be described by a
traceless part of the wave-type field equation. This is an essentially
non-Einsteinian gravity model. It has an exact spherically-symmetric static
solution, that yields to the Yilmaz-Rosen metric. This metric is very close to
the Schwarzchild metric. The wave-type field equation can not be derived from a
suitable variational principle by free variations, as it was shown by Hehl and
his collaborates. In the present work we are seeking for another field equation
having the same exact spherically-symmetric static solution. The
differential-geometric structure on the manifold endowed with a smooth
orthonormal coframe field is described by the scalar objects of anholonomity
and its exterior derivative. We construct a list of the first and second order
SO(1,3)-covariants (one- and two-indexed quantities) and a quasi-linear field
equation with free parameters. We fix a part of the parameters by a condition
that the field equation is satisfied by a quasi-conformal coframe with a
harmonic conformal function. Thus we obtain a wide class of field equations
with a solution that yields the Majumdar-Papapetrou metric and, in
particularly, the Yilmaz-Rosen metric, that is viable in the framework of three
classical tests
Calculation of $K\to \pi$ matrix elements in quenched domain-wall QCD

We explore the possibility for an evaluation of non-leptonic $\Delta S=1$ $K$
decay amplitudes through the calculation of $K\to\pi$ matrix elements using
domain-wall QCD. The relation between the physical $K\to\pi\pi$ matrix elements
and $K\to\pi$ matrix elements deduced from chiral perturbation theory is
recapitulated. Quenched numerical simulations are performed on an $16^3\times
32\times 16$ lattice at a lattice spacing $a^{-1}\approx 2$GeV for both the
standard plaquette gauge action and a renormalization-group improved gauge
action, and reasonable signals for $K\to\pi$ matrix elements are obtained.
Preliminary results are reported on the $K\to\pi\pi$ matrix elements, and
results from two actions are compared.Comment: Lattice 2000 (Hadronic Matrix Elements), 4 pages, 8 figures,
  Addresses of the author was revise
Affleck-Dine leptogenesis with triplet Higgs

We study an extension of the supersymmetric standard model including a pair
of electroweak triplet Higgs $\Delta$ and ${\bar \Delta}$. The neutrinos
acquire Majorana masses mediated by these triplet Higgs fields rather than the
right-handed neutrinos. The successful leptogenesis for baryogenesis can be
realized after the inflation through the Affleck-Dine mechanism on a flat
manifold consisting of $\Delta$, ${\bar \Delta}$, ${\tilde e}^c$
(anti-slepton), even if the triplet Higgs mass $M_\Delta$ is much larger than
the gravitino mass $m_{3/2} \sim 10^3 {\rm GeV}$. Specifically, due to the
effects of the potential terms provided with the superpotential terms $M_\Delta
{\bar \Delta} \Delta$, $(\lambda_{L /} / 2M) {\bar \Delta} {\bar \Delta} e^c
e^c$, $(\lambda_\Delta / 2M) {\bar \Delta} \Delta {\bar \Delta} \Delta$
($\lambda_{L /} / \lambda_\Delta \sim 0.3 - 3$), the phases of $\Delta$, ${\bar
\Delta}$, ${\tilde e}^c$ are rotated at the time with the Hubble parameter $H
\sim M_\Delta$, producing generally the asymmetry with fraction $\epsilon_L
\sim 0.1$. If $M_\Delta$ is large enough, this early leptogenesis can be
completed before the thermal effects take place.Comment: 11 pages, 2 figure
Higgs Boson Mass and Electroweak-Gravity Hierarchy from Dynamical
  Gauge-Higgs Unification in the Warped Spacetime

Dynamical electroweak symmetry breaking by the Hosotani mechanism in the
Randall-Sundrum warped spacetime is examined, relations among the W-boson mass
(m_W), the Kaluza-Klein mass scale (M_{KK}), and the Higgs boson mass (m_H)
being derived. It is shown that M_{KK}/m_W = (2 pi kR)^{1/2} (pi/theta_W) and
m_H /m_W = 0.058 kR (pi/theta_W), where k^2, R, and theta_W are the curvature
and size of the extra-dimensional space and the Wilson line phase determined
dynamically. For typical values kR = 12 and theta_W = (0.2 to 0.4) pi, one
finds that M_{KK} = (1.7 to 3.5) TeV, k = (1.3 to 2.6) x 10^{19} GeV, and m_H =
(140 to 280) GeV.Comment: 14 pages. The argument below (22) was elaborate
Comments on Hall transport from effective actions

We consider parity-odd transport in 2+1 dimensional charged fluids
restricting attention to the class of non-dissipative fluids. We show that
there is a two parameter family of such non-dissipative fluids which can be
derived from an effective action, in contradistinction with a four parameter
family that can be derived from an entropy current analysis. The effective
action approach allows us to extract the adiabatic transport data, in
particular the Hall viscosity and Hall conductivity amongst others, in terms of
the thermodynamic functions that enter as 'coupling constants'. Curiously, we
find that Hall viscosity is forced to vanish, whilst the Hall conductivity is
generically a non-vanishing function of thermodynamic data determined in terms
of the hydrodynamic couplings.Comment: 19 pages. v2: added refs and comments on connections with torsion.
  v3: typos fixed, published version. v4: added comment on Legendre transfor
Nucleon spin structure at very high-x

Dyson-Schwinger equation treatments of the strong interaction show that the
presence and importance of nonpointlike diquark correlations within the nucleon
are a natural consequence of dynamical chiral symmetry breaking. Using this
foundation, we deduce a collection of simple formulae, expressed in terms of
diquark appearance and mixing probabilities, from which one may compute ratios
of longitudinal-spin-dependent u- and d-quark parton distribution functions on
the domain x =1. A comparison with predictions from other approaches plus a
consideration of extant and planned experiments shows that the measurement of
nucleon longitudinal spin asymmetries on x =1 can add considerably to our
capacity for discriminating between contemporary pictures of nucleon structure.Comment: 6 pages, 1 table, 3 figures. To appear in Phys. Lett.
A review of beam tomography research at Daresbury Laboratory

This is a review on beam tomography research at Daresbury. The research has
focussed on development of normalised phase space techniques. It starts with
the idea of sampling tomographic projections at equal phase advances and shows
that this would give the optimal reconstruction results. This idea has
influenced the design, construction and operation of the tomography sections at
the Photo Injector Test Facility at Zeuthen (PITZ) and at the Accelerator and
Laser in Combined Experiments (ALICE) at Daresbury. The theoretical
justification of this idea is later developed through simulations and analysis
of the measurements results at ALICE. The mathematical formalism is constructed
around the normalised phase space and the idea of equal phase advances become
the basis of this. This formalism is applied to a variety of experimental and
simulated situations and shown to be useful in improving resolution, increasing
reliability and providing diagnostic information. In this review, we also
present the simplifying concepts, formalisms and simulation tools that we have
developed
Liouville theorems for scaling invariant superlinear parabolic problems
  with gradient structure

We provide a simple method for obtaining new Liouville theorems for scaling
invariant superlinear parabolic problems with gradient structure. To illustrate
the method we prove Liouville theorems (guaranteeing nonexistence of positive
classical solutions) for the following model problems: the scalar nonlinear
heat equation $$ u_t-\Delta u=u^p \qquad\hbox{in}\ {\mathbb R}^n\times{\mathbb
R}, $$ its vector-valued generalization with a $p$-homogeneous nonlinearity and
the linear heat equation in ${\mathbb R}^n_+\times{\mathbb R}$ complemented by
nonlinear boundary conditions of the form $\partial u/\partial\nu=u^q$. Here
$\nu$ denotes the outer unit normal on the boundary of the halfspace ${\mathbb
R}^n_+$ and the exponents $p,q>1$ satisfy $p<n/(n-2)$ and $q<(n-1)/(n-2)$ if
$n>2$ (or $p<(n+2)/(n-2)$ and $q<n/(n-2)$ if $n>2$ and some symmetry of the
solutions is assumed). As a typical application of our nonexistence results we
provide optimal universal estimates for positive solutions of related problems
in bounded and unbounded domains
Gauge Field Emergence from Kalb-Ramond Localization

A new mechanism, valid for any smooth version of the Randall-Sundrum model,
of getting localized massless vector field on the brane is described here. This
is obtained by dimensional reduction of a five dimension massive two form, or
Kalb-Ramond field, giving a Kalb-Ramond and an emergent vector field in four
dimensions. A geometrical coupling with the Ricci scalar is proposed and the
coupling constant is fixed such that the components of the fields are
localized. The solution is obtained by decomposing the fields in transversal
and longitudinal parts and showing that this give decoupled equations of motion
for the transverse vector and KR fields in four dimensions. We also prove some
identities satisfied by the transverse components of the fields. With this is
possible to fix the coupling constant in a way that a localized zero mode for
both components on the brane is obtained. Then, all the above results are
generalized to the massive $p-$form field. It is also shown that in general an
effective $p$ and $(p-1)-$forms can not be localized on the brane and we have
to sort one of them to localize. Therefore, we can not have a vector and a
scalar field localized by dimensional reduction of the five dimensional vector
field. In fact we find the expression $p=(d-1)/2$ which determines what forms
will give rise to both fields localized. For $D=5$, as expected, this is valid
only for the KR field.Comment: Improved version. Some factors corrected and definitions added. The
  main results continue vali
Baryonic contributions to $e^{+}e^{-}$ yields in a hydrodynamic model of Pb + Au collisions at the SPS

We analyze e+e- yields from matter containing baryons in addition to mesons using a hydrodynamic approach to describe Pb+Au collisions at 158 A GeV/c. We use two distinctly different e+e- production rates to provide contrast. Although the presence of baryons leads to significant enhancement of e+e- emission relative to that from mesons-only matter, the calculated results fall below the data in the range 400 < M/MeV < 600. The calculated results are, however, only 1.3-1.5 standard deviations below the data, which may not be statistically significant
New Results on N=4 SuperYang-Mills Theory

The N=4 SuperYang--Mills theory is covariantly determined by a U(1) \times
SU(2) \subset SL(2,R) \times SU(2) internal symmetry and two scalar and one
vector BRST topological symmetry operators. This determines an off-shell closed
sector of N=4 SuperYang-Mills, with 6 generators, which is big enough to fully
determine the theory, in a Lorentz covariant way. This reduced algebra derives
from horizontality conditions in four dimensions. The horizontality conditions
only depend on the geometry of the Yang-Mills fields. They also descend from a
genuine horizontality condition in eight dimensions. In fact, the SL(2,R)
symmetry is induced by a dimensional reduction from eight to seven dimensions,
which establishes a ghost-antighost symmetry, while the SU(2) symmetry occurs
by dimensional reduction from seven to four dimensions. When the four
dimensional manifold is hyperKahler, one can perform a twist operation that
defines the N=4 supersymmetry and its SL(2,H)\sim SU(4) R-symmetry in flat
space. (For defining a TQFT on a more general four manifold, one can use the
internal SU(2)-symmetry and redefine a Lorentz SO(4) invariance). These results
extend in a covariant way the light cone property that the N=4 SuperYang-Mills
theory is actually determined by only 8 independent generators, instead of the
16 generators that occur in the physical representation of the superPoincare
algebra. The topological construction disentangles the off-shell closed sector
of the (twisted) maximally supersymmetric theory from the (irrelevant) sector
that closes only modulo equations of motion. It allows one to escape the
question of auxiliary fields in N=4 SuperYang-Mills theory.Comment: 14 page
G/H M-branes and AdS_{p+2} Geometries

We prove the existence of a new class of BPS saturated M-branes. They are in
one-to-one correspondence with the Freund--Rubin compactifications of M-theory
on either (AdS_4) x (G/H) or (AdS_7) x (G/H), where G/H is the seven (or four)
dimensional Einstein coset manifolds classified long ago in the context of
Kaluza Klein supergravity. The G/H M-branes are solitons that interpolate
between flat space at infinity and the old Kaluza-Klein compactifications at
the horizon. They preserve N/2 supersymmetries where N is the number of Killing
spinors of the (AdS) x (G/H) vacuum. A crucial ingredient in our discussion is
the identification of a solvable Lie algebra parametrization of the Lorentzian
non compact coset SO(2,p+1)/SO(1,p+1) corresponding to anti de Sitter space
AdS_{p+2} . The solvable coordinates are those naturally emerging from the near
horizon limit of the G/H p-brane and correspond to the Bertotti Robinson form
of the anti-de-Sitter metric. The pull-back of anti-de-Sitter isometries on the
p-brane world-volume contain, in particular, the broken conformal
transformations recently found in the literature.Comment: 1 LaTeX file, 29 pages, misprint in the Freund-Rubin parameter
  formula (61) correcte
Exact solutions of two complementary 1D quantum many-body systems on the
  half-line

We consider two particular 1D quantum many-body systems with local
interactions related to the root system $C_N$. Both models describe identical
particles moving on the half-line with non-trivial boundary conditions at the
origin, and they are in many ways complementary to each other. We discuss the
Bethe Ansatz solution for the first model where the interaction potentials are
delta-functions, and we find that this provides an exact solution not only in
the boson case but even for the generalized model where the particles are
distinguishable. In the second model the particles have particular momentum
dependent interactions, and we find that it is non-trivial and exactly solvable
by Bethe Ansatz only in case the particles are fermions. This latter model has
a natural physical interpretation as the non-relativistic limit of the massive
Thirring model on the half-line. We establish a duality relation between the
bosonic delta-interaction model and the fermionic model with local momentum
dependent interactions. We also elaborate on the physical interpretation of
these models. In our discussion the Yang-Baxter relations and the Reflection
equation play a central role.Comment: 15 pages, a mistake corrected changing one of our conclusion
Measurement and CFD Prediction of Heat Transfer in Air-Cooled Disc-Type Electrical Machines

Accurate thermal analysis of axial flux permanent magnet (AFPM) machines is crucial in predicting maximum power output. Stator convective heat transfer is one of the most important and least investigated heat transfer mechanisms and is the focus of this paper. Experimental measurements were undertaken using a thin-film electrical heating method, providing radially resolved steady state heat transfer data from an experimental rotor-stator system designed as a geometric mockup of a through-flow ventilated AFPM machine. The measurements are compared with computational fluid dynamics (CFD) simulations using both 2D axisymmetric and 3D models. These were found to give a conservative estimate of heat transfer, with inaccuracies near the edge and in the transitional flow regime. Predicted stator heat transfer was found to be relatively insensitive to the choice of turbulence model used in the CFD simulations
New Phase Transitions in Chern-Simons Matter Theory

Applying the machinery of random matrix theory and Toeplitz determinants we
study the level $k$, $U(N)$ Chern-Simons theory coupled with fundamental matter
on $S^2\times S^1$ at finite temperature $T$. This theory admits a discrete
matrix integral representation, i.e. a unitary discrete matrix model of
two-dimensional Yang-Mills theory. In this study, the effective partition
function and phase structure of the Chern-Simons matter theory, in a special
case with an effective potential namely the Gross-Witten-Wadia potential, are
investigated. We obtain an exact expression for the partition function of the
Chern-Simons matter theory as a function of $k,N,T,$ for finite values and in
the asymptotic regime. In the Gross-Witten-Wadia case, we show that ratio of
the Chern-Simons matter partition function and the continuous two-dimensional
Yang-Mills partition function, in the asymptotic regime, is the Tracy-Widom
distribution. Consequently, using the explicit results for free energy of the
theory, new second-order and third-order phase transitions are observed.
Depending on the phase, in the asymptotic regime, Chern-Simons matter theory is
represented either by a continuous or discrete two-dimensional Yang-Mills
theory, separated by a third-order domain wall.Comment: 26 pages, 1 figure, references added, some parts rewritten and
  extended. To appear in Nucl. Phys.
Super-solar metallicity at the position of the ultra-long GRB130925A

Over the last decade there has been immense progress in the follow-up of
short and long GRBs, resulting in a significant rise in the detection rate of
X-ray and optical afterglows, in the determination of GRB redshifts, and of the
identification of the underlying host galaxies. Nevertheless, our theoretical
understanding on the progenitors and central engines powering these vast
explosions is lagging behind, and a newly identified class of `ultra-long' GRBs
has fuelled speculation on the existence of a new channel of GRB formation. In
this paper we present high signal-to-noise X-shooter observations of the host
galaxy of GRB130925A, which is the fourth unambiguously identified ultra-long
GRB, with prompt gamma-ray emission detected for ~20ks. The GRB line of sight
was close to the host galaxy nucleus, and our spectroscopic observations cover
both this region along the bulge/disk of the galaxy, in addition to a bright
star-forming region within the outskirts of the galaxy. From our broad
wavelength coverage we obtain accurate metallicity and dust-extinction
measurements at both the galaxy nucleus, and an outer star-forming region, and
measure a super-solar metallicity at both locations, placing this galaxy within
the 10-20% most metal-rich GRB host galaxies. Such a high metal enrichment has
implications on the progenitor models of both long and ultra-long GRBs,
although the edge-on orientation of the host galaxy does not allow us to rule
out a large metallicity variation along our line of sight. The spatially
resolved spectroscopic data presented in this paper offer important insight
into variations in the metal and dust abundance within GRB host galaxies. They
also illustrate the need for IFU observations on a larger sample of GRB host
galaxies at varies metallicities to provide a more quantitative view on the
relation between the GRB circumburst and the galaxy-whole properties.Comment: 9 pages, 3 figures, A&A in press, matches published versio