title: Spectral symmetries of zeta functions

abstract:
  We define, answering a question of Sarnak in his letter to Bombieri, a
symplectic pairing on the spectral interpretation (due to Connes and Meyer) of
the zeroes of Riemann's zeta function. This pairing gives a purely spectral
formulation of the proof of the functional equation due to Tate, Weil and
Iwasawa, which, in the case of a curve over a finite field, corresponds to the
usual geometric proof by the use of the Frobenius-equivariant Poincar\'e
duality pairing in etale cohomology. We give another example of a similar
construction in the case of the spectral interpretation of the zeroes of a
cuspidal automorphic $L$-function, but this time of an orthogonal nature. These
constructions are in adequation with Deninger's conjectural program and the
arithmetic theory of random matrices.


title:
Mechanical properties of the radio frequency field emitted by an antenna
  array

abstract:
  Angular momentum densities of electromagnetic beams are connected to helicity
(circular polarization) and topological charge (azimuthal phase shift and
vorticity). Computing the electromagnetic fields emitted by a circular antenna
array, analytic expressions are found for the densities of energy, linear and
angular momentum in terms of helicity and vorticity. It is found that the
angular momentum density can be separated into spin and orbital parts, a result
that is known to be true in a beam geometry. The results are of importance for
information-rich radio astronomy and space physics as well as novel radio,
radar, and wireless communication concepts.


title:
F-resolved Magneto-optical Resonances at D1 Excitation of Cesium:
  Experiment and Theory

abstract:
  Bright and dark nonlinear magneto-optical resonances associated with the
ground state Hanle effect have been studied experimentally and theoretically
for D1 excitation of atomic cesium. This system offers the advantage that the
separation between the different hyperfine levels exceeds the Doppler width,
and, hence, transitions between individual levels can be studied separately.
Experimental measurements for various laser power densities and transit
relaxation times are compared with a model based on the optical Bloch
equations, which averages over the Doppler contour of the absorption line and
simultaneously takes into account all hyperfine levels, as well as mixing of
magnetic sublevels in an external magnetic field. In contrast to previous
studies, which could not resolve the hyperfine transitions because of Doppler
broadening, in this study there is excellent agreement between experiment and
theory regarding the sign (bright or dark), contrast, and width of the
resonance. The results support the traditional theoretical interpretation,
according to which these effects are related to the relative strengths of
transition probabilities between different magnetic sublevels in a given
hyperfine transition.


title: Maps of Dipersions for Machining Processes

abstract:
  During the products design, the design office defines dimensional and
geometrical parameters according to the use criteria and the product
functionality. The manufacturing department must integrate the manufacturing
and the workpiece position dispersions during the choice of tools and machines
operating modes and parameters values to respect the functional constraints. In
this paper, we suggest to model the turning dispersions taking into account not
only geometrical specifications of position or orientation but also the
experience of method actors. A representation using the principle of know-how
maps in two or three dimensions is privileged. The most interesting aspect is
that these maps include tacit and explicit knowledge. An experimental study
realized on a machine tool (HES 300) allows to elaborate knowledge maps
especially for the turning process.


title:
Finite band inversion of ARPES in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in
  comparison with optics

abstract:
  Using a maximum entropy technique within a finite band Eliashberg formalism
we extract from recent high accuracy nodal direction angular resolved
photo-emission spectroscopy (ARPES) data in optimally doped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) a quasiparticle electron-boson
spectral density. Both normal and superconducting state with d-wave gap
symmetry are treated. Finite and infinite band results are considered and
contrasted. We compare with results obtained for the related transport spectral
density which follows from a similar inversion of optical data. We discuss the
implication of our results for quasiparticle renormalizations in the antinodal
direction.


title: Normal modes of layered elastic media and application to diffuse fields

abstract:
  The spectral decomposition of the elastic wave operator in a layered
isotropic half-space is derived by means of standard functional analytic
methods. Particular attention is paid to the coupled $P$-$SV$ waves. The
problem is formulated directly in terms of displacements which leads to a $2
\times 2$ Sturm-Liouville system. The resolvent kernel (Green function) is
expressed in terms of simple plane-wave solutions. Application of Stone's
formula leads naturally to eigenfunction expansions in terms of generalized
eigenvectors with oscillatory behavior at infinity. The generalized normal mode
expansion is employed to define a diffuse field as a white noise process in
modal space. By means of a Wigner transform, we calculate vertical to
horizontal kinetic energy ratios in layered media, as a function of depth and
frequency. Several illustrative examples are considered including energy ratios
near a free surface, in the presence of a soft layer. Numerical comparisons
between the generalized eigenfunction summation and a classical locked-mode
approximation demonstrate the validity of the approach. The impact of the local
velocity structure on the energy partitioning of a diffuse field is
illustrated.


title:
Singlet Ground State and Spin Gap in S=1/2 Kagome Antiferromagnet
  Rb$_2$Cu$_3$SnF$_{12}$

abstract:
  We investigated the crystal structure of Rb$_2$Cu$_3$SnF$_{12}$ and its
magnetic properties using single crystals. This compound is composed of Kagome
layers of corner-sharing CuF$_{6}$ octahedra with a 2a x 2a enlarged cell as
compared with the proper Kagome layer. Rb$_2$Cu$_3$SnF$_{12}$ is magnetically
described as an $S$=1/2 modified Kagome antiferromagnet with four kinds of
neighboring exchange interaction. From magnetic susceptibility and high-field
magnetization measurements, it was found that the ground state is a disordered
singlet with the spin gap, as predicted from a recent theory. Exact
diagonalization for a 12-site Kagome cluster was performed to analyze the
magnetic susceptibility, and individual exchange interactions were evaluated.


title:
Reading molecular messages from the intersections of high-order harmonic
  spectra at different orientations

abstract:
  We investigate the orientation dependence of high-order harmonic generation
(HHG) from H$_2^+$ with different internuclear distances irradiated by intense
laser fields both numerically and analytically. The calculated molecular HHG
spectra are found to be sensitive to molecular axis orientation relative to
incident laser field polarization and internuclear separation. In particular,
the spectra calculated for different orientation angles demonstrate a kind of
intersection, which is identified as arising due to intramolecular two-center
interference in the HHG. The striking "intersection" phenomenon can be used to
probe the molecular instantaneous structure.


title:
A generalized non-Hermitian oscillator Hamiltonian, N-fold supersymmetry
  and position-dependent mass models

abstract:
  A generalized non-Hermitian oscillator Hamiltonian is proposed that consists
of additional linear terms which break PT-symmetry explicitly. The model is put
into an equivalent Hermitian form by means of a similarity transformation and
the criterion of N-fold supersymmetry with a position-dependent mass is shown
to reside in it.


title:
Thermoelectric transport through a quantum dot coupled to a normal metal
  and BCS superconductor

abstract:
  I discuss thermoelectric properties of a quantum dot coupled to one normal
and one superconducting lead in the presence of Kondo effect and Andreev
scattering. I will focus on conductance, thermal conductance, thermopower and
related quantities like thermoelectric figure of merit which is a direct
measure of the usefulness of the system for applications and Wiedemann-Franz
ratio which indicates if the system is in the Fermi liquid state. I will show
that the superconductivity strongly modifies the thermal properties of the
system. In particular, the thermopower is strongly enhanced near the
superconducting transition temperature. Moreover, the Andreev reflections are
suppressed due to strong on-dot Coulomb repulsion. The suppression of the
Andreev reflections leads to a violation of the Wiedemann-Franz law and to a
non-Fermi liquid ground state.


title:
High-Order Harmonic Generation and Molecular Orbital Tomography:
  Characteristics of Molecular Recollision Electronic Wave Packets

abstract:
  We investigate the orientation dependence of molecular high-order harmonic
generation (HHG) both numerically and analytically. We show that the molecular
recollision electronic wave packets (REWPs) in the HHG are closely related to
the ionization potential as well as the particular orbital from which it
ionized. As a result, the spectral amplitude of the molecular REWP can be
significantly different from its reference atom (i.e., with the same ionization
potential as the molecule under study) in some energy regions due to the
interference between the atomic cores of the molecules. This finding is
important for molecular orbital tomography using HHG[Nature \textbf{432},
867(2004)].


title: Fine properties of self-similar solutions of the Navier-Stokes equations

abstract:
  We study the solutions of the nonstationary incompressible Navier--Stokes
equations in $\R^d$, $d\ge2$, of self-similar form $u(x,t)=\frac{1}{\sqrt
t}U\bigl(\frac{x}{\sqrt t}\bigr)$, obtained from small and homogeneous initial
data $a(x)$. We construct an explicit asymptotic formula relating the
self-similar profile $U(x)$ of the velocity field to its corresponding initial
datum $a(x)$.


title:
Iwasawa theory of totally real fields for certain non-commutative
  $p$-extensions

abstract:
  In this paper, we prove the Iwasawa main conjecture of totally real fields
for certain specific non-commutative $p$-adic Lie extensions, using the
integral logarithms introduced by Oliver and Taylor. Our result gives certain
generalization of Kazuya Kato's proof of the main conjecture for Galois
extensions of Heisenberg type.


title: Angular momentum and mass evolution of contact binaries

abstract:
  Various scenarios of contact binary evolution have been proposed in the past,
giving hints of (sometimes contradictory) evolutionary sequence connecting
A-type and W-type systems. As the components of close detached binaries
approach each other and contact binaries are formed, following evolutionary
paths transform them into systems of two categories: A-type and W-type. The
systems evolve in a similar way but under slightly different circumstances. The
mass/energy transfer rate is different, leading to quite different evolutionary
results. An alternative scenario of evolution in contact is presented and
discussed, based on the observational data of over a hundred low-temperature
contact binaries. It results from the observed correlations among contact
binary physical and orbital parameters. Theoretical tracks are computed
assuming angular momentum loss from a system via stellar wind, accompanied by
mass transfer from an advanced evolutionary secondary to the main sequence
primary. Good agreement is seen between the tracks and the observed graphs.
Independently of details of the evolution in contact and a relation between
A-type and W-type systems, the ultimate fate of contact binaries involves the
coalescence of both components into a single fast rotating star.


title: Deriving molecular bonding from macromolecular self-assembly

abstract:
  Macromolecules can form regular structures on inert surfaces. We have
developed a combined empirical and modeling approach to derive the bonding.
From experimental scanning tunneling microscopy (STM) images of structures
formed on Au(111) by melamine, by PTCDA, and by a 2:3 mixture of the two, we
determine the molecular bonding morphologies. Within these bonding morphologies
and recognizing the distinction between cohesive and adhesive molecular
interactions we simultaneously simulated different molecular structures using a
lattice Monte Carlo method. Within these bonding morphologies there is a
distinction between cohesive and adhesive molecular interactions. We have
simulated different molecular structures using a lattice Monte Carlo method.


title: Evaluation of machining dispersions for turning process

abstract:
  In this article we propose to extend the model of simulation of dispersions
in turning based on the geometrical specifications. Our study is articulated
around two trends of development: the first trend relates to the geometrical
model. The geometrical model suggested must allow a follow-up of the geometry
of the part during the simulation of machining. It is thus a question of
carrying out a systematic treatment of the whole dimensioning and tolerancing
process while being based on the principles of the \DeltaL method. We also
planned to integrate this type of specification in the model of simulation of
machining suggested. It is more generally a question of extending the
traditional model for better taking into account the multi axis specification
of coaxiality and perpendicularity on the turned workpieces. The second trend
of our study relates to the widening of the field of application of the model.
We propose to extend the field of application of the model by taking into
account the modifications of several parameters of the manufacturing process
plans, likely to involve variations of dispersions.


title: On-shell recursion relations for gravity

abstract:
  We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo
to show that graviton tree amplitudes are well behaved under large complex
deformations of the momenta of a pair of like-helicity gravitons. This shows
that BCFW recursion relations for gravity amplitudes can be constructed using
such shifts, providing an alternative proof to the recent one by Arkani-Hamed
and Kaplan. By using auxiliary recursion relations the cancellations which are
hidden when using covariant Feynman diagrams become manifest.


title:
Concern Regarding "A Non-Inflationary Solution to the Entropy Problem of
  Standard Cosmology."

abstract:
  We discuss the entropy and the size/homogeneity/horizon problems in power-law
expanding universes with one scale initial conditions. We set the minimal scale
$\Lambda = 10^{25}$ GeV at which a non-inflationary solution is possible and
show that the radiation dominated epoch alone technically is not able to
explain the issue. An earlier paper on the subject, [1], attempts a
multidimensional scenario. We review the scenario of the paper [1] in an
effective four dimensional Einstein frame. We find that during contraction of
extra dimensions, the residual bulk energy density is important and leads to a
scaling solution. The existence of this scaling solution is a new result. We
provide a numerical example which demonstrates the evolution of the scale
factor and the extra dimensions. In the whole, the validity of the effective
field theory calculations at the scale of $\Lambda = 10^{25}$ GeV is under
question and, hence, the final conclusion regarding the possibility of a
non-inflationary solution is preliminary.


title: Introduction to Monte Carlo methods for an Ising Model of a Ferromagnet

abstract:
  This discussion serves as an introduction to the use of Monte Carlo
simulations as a useful way to evaluate the observables of a ferromagnet. Key
background is given about the relevance and effectiveness of this stochastic
approach and in particular the applicability of the Metropolis-Hastings
algorithm. Importantly the potentially devastating effects of spontaneous
magnetization are highlighted and a means to avert this is examined.
  An Ising model is introduced and used to investigate the properties of a two
dimensional ferromagnet with respect to its magnetization and energy at varying
temperatures. The observables are calculated and a phase transition at a
critical temperature is also illustrated and evaluated. Lastly a finite size
scaling analysis is undertaken to determine the critical exponents and the
Curie temperature is calculated using a ratio of cumulants with differing
lattice sizes. The results obtained from the simulation are compared to exact
calculations to endorse the validity of this numerical process. A copy of the
code used, written in C++, is enclosed and is freely available for use and
modification under the General Public License.


title:
Angular variation of hard back-to-back hadron suppression in heavy-ion
  collisions

abstract:
  The basic idea of jet tomography is to infer information about the density
evolution of the medium created in heavy-ion (A-A) collisions by studying the
suppression of hard probes in an A-A environment as compared to the baseline
process known from p-p collisions. The suppression of back-to-back correlations
in heavy-ion collisions allows, due to a different geometrical bias, a view
into the medium which is qualitatively different from the one offered by single
hadron suppression. A control parameter for the suppression corresponding to a
systematic variation of in-medium pathlengths and density can be obtained by
studying collisions at finite impact parameter b. A systematic variation of
pathlength can then be introduced by studying the suppression pattern as a
function of the angle phi with the reaction plane. Using a 3-d hydrodynamical
evolution model for the medium and a Monte-Carlo model which has been shown to
successfully reproduce the measured suppression of back-to-back correlations in
central collisions of Au-Au at 200 AGeV, we compute the suppression as a
function of phi for b of 2.4 fm. 4.5 fm, 6.3 fm and 7.5 fm. Given that this
involves variations in both control parameters b and phi a comparison with data
should eventually allow to place strong constraints on the combination of
energy loss model and medium evolution model.


title: The order completion method for systems of nonlinear PDEs revisited

abstract:
  In this paper we presents further developments regarding the enrichment of
the basic Theory of Order Completion. In particular, spaces of generalized
functions are constructed that contain generalized solutions to all systems of
continuous, nonlinear PDEs. In terms of the existence and uniqueness results
previously obtained for such systems of equations, one may interpret the
existence of generalized solutions presented here as a regularity result.


title:
Detectability of neutral interstellar deuterium by a forthcoming SMEX
  mission IBEX

abstract:
  Context: Reconnaissance of feasibility of detection of interstellar neutral D
by the forthcoming NASA SMEX mission IBEX. Aims: To investigate by numerical
simulations the absolute density and flux at Earth orbit of neutral
interstellar D and to check its detectability by IBEX. Methods: The simulations
were performed with the use of the Warsaw 3D time-dependent test-particle model
of neutral interstellar gas in the inner heliosphere, specially adapted to the
case of D, and of the state-of-the-art models of the ionization field and
radiation pressure. The modeling returned density, bulk velocity, and flux of
interstellar D along at the Earth locations during the solar cycle. Particular
attention was paid to the time interval corresponding to the planned operations
of IBEX. Results: Simulations predict a large enhancement of D abundance at
Earth orbit with respect to the abundance at the termination shock. The energy
of the D atoms at IBEX will be within the energetic sensitivity band of its Lo
instrument except a short time interval between September and November each
year. Because of the specific observing geometry of IBEX, there will be one
opportunity each year to search for I/S D, when Earth is near ecliptic
longitude 136 deg, i.e. in February. Assuming the TS abundance of D identical
as in the Local Cloud equal to 1.56E-5, and the density of H at TS 0.11/cm2/s
one obtains the expected relative flux about 0.015/cm2/s, which corresponds to
the local absolute flux about 0.007/cm2/s. The dependence of the expected flux
on the phase of solar cycle is relatively weak. The flux scales proportionally
to the density of deuterium at the termination shock and depends only weakly on
the bulk velocity and temperature of the gas in this region.


title: Masses and Magnetic Moments of Charmed Baryons Using Hyper Central Model

abstract:
  Heavy flavour baryons containing one or two charm quarks with light flavour
combinations are studied using the hyper central description of the three-body
system. The confinement potential is assumed as hyper central coulomb plus
power potential with power index $\nu$. The ground state masses and the
magnetic moments of charmed, $J^P={1/2}^+$ and ${3/2}^+$ baryons are computed
for different power index, $ \nu$ starting from 0.5 to 2.0.


title:
Multiple bosonic mode coupling in the charge dynamics of the
  electron-doped superconductor (Pr$_{2-x}$Ce$_x$)CuO$_4$

abstract:
  We analyze optical spectroscopy data of the electron-doped superconductor
(Pr$_{2-x}$Ce$_x$)CuO$_4$ (PCCO) to investigate the coupling of the charge
carriers to bosonic modes. The method of analysis is the inversion of the
optical scattering rate $\tau^{-1}_{\rm op}(\omega,T)$ at different
temperatures $T$ by means of maximum entropy technique combined with Eliashberg
theory. We find that in the superconducting state the charge carriers couple to
two dominant modes one at $\sim 10 $meV and a second one at $\sim 45 $meV. The
low energy mode shows a strong temperature dependence and disappears at or
slightly above the critical temperature $T_c$. The high energy mode exists
above $T_c$ and moves towards higher energies with increasing temperatures. It
also becomes less prominent at temperatures $> 100 $K above which it evolves
into a typical spin-fluctuation background. In contrast to the hole-doped
High-$T_c$ superconductors PCCO proves to be a superconductor close to the
dirty limit.


title: The Harari-Shupe preon model and nonrelativistic quantum phase space

abstract:
  We propose that the whole algebraic structure of the Harari-Shupe rishon
model originates via a Dirac-like linearization of quadratic form x^2+p^2, with
position and momentum satisfying standard commutation relations. The scheme
does not invoke the concept of preons as spin-1/2 subparticles, thus evading
the problem of preon confinement, while fully explaining all symmetries emboded
in the Harari-Shupe model. Furthermore, the concept of quark colour is
naturally linked to the ordering of rishons. Our scheme leads to group
U(1)xSU(3) combined with SU(2), with two of the SU(2) generators not commuting
with reflections. An interpretation of intra-generation quark-lepton
transformations in terms of genuine rotations and reflections in phase space is
proposed.


title:
Dynamical Twisted Mass Fermions with Light Quarks: Simulation and
  Analysis Details

abstract:
  In a recent paper [hep-lat/0701012] we presented precise lattice QCD results
of our European Twisted Mass Collaboration (ETMC). They were obtained by
employing two mass-degenerate flavours of twisted mass fermions at maximal
twist. In the present paper we give details on our simulations and the
computation of physical observables. In particular, we discuss the problem of
tuning to maximal twist, the techniques we have used to compute correlators and
error estimates. In addition, we provide more information on the algorithm
used, the autocorrelation times and scale determination, the evaluation of
disconnected contributions and the description of our data by means of chiral
perturbation theory formulae.


title: Random hypergraphs and algorithmics

abstract:
  Hypergraphs are structures that can be decomposed or described; in other
words they are recursively countable. Here, we get exact and asymptotic
enumeration results on hypergraphs by means of exponential generating
functions. The number of hypergraph component is bounded, as a generalisation
of Wright inequalities for graphs: the proof is a combinatorial understanding
of the structure by inclusion exclusion. Asymptotic results are obtained,
thanks to generating functions proofs are at the end very easy to read, through
complex analysis by saddle point method. By this way, we characterized:
  - the components with a given number of vertices and of hyperedges by the
expected size of a random hypermatching in these structures.
  - the random hypergraphs (evolving hyperedge by hyperedge) according to the
expected number of hyperedges when the first cycle appears in the evolving
structure.
  This work is an open road to further works on random hypergraphs such as
threshold phenomenon, tools used here seem to be sufficient at first sight.


title: Subtraction-noise projection in gravitational-wave detector networks

abstract:
  In this paper, we present a successful implementation of a subtraction-noise
projection method into a simple, simulated data analysis pipeline of a
gravitational-wave search. We investigate the problem to reveal a weak
stochastic background signal which is covered by a strong foreground of
compact-binary coalescences. The foreground which is estimated by matched
filters, has to be subtracted from the data. Even an optimal analysis of
foreground signals will leave subtraction noise due to estimation errors of
template parameters which may corrupt the measurement of the background signal.
The subtraction noise can be removed by a noise projection. We apply our
analysis pipeline to the proposed future-generation space-borne Big Bang
Observer (BBO) mission which seeks for a stochastic background of primordial
GWs in the frequency range $\sim 0.1-1 $Hz covered by a foreground of
black-hole and neutron-star binaries. Our analysis is based on a simulation
code which provides a dynamical model of a time-delay interferometer (TDI)
network. It generates the data as time series and incorporates the analysis
pipeline together with the noise projection. Our results confirm previous ad
hoc predictions which say that BBO will be sensitive to backgrounds with
fractional energy densities below $\Omega=10^{-16}$


title:
Matches and mismatches in the descriptions of semi-inclusive processes
  at low and high transverse momentum

abstract:
  We investigate the transverse-momentum-dependence in semi-inclusive deep
inelastic leptoproduction of hadrons. There are two different theoretical
approaches to study this dependence, one for low and one for high transverse
momentum of the observed hadron. We systematically investigate their
connection, paying special attention to azimuthal distributions and to
polarization dependence. In the region of intermediate transverse momentum,
where both approaches are applicable, we find that their results match for
certain observables but not for others. Interpolating expressions are discussed
for the case where one has no matching. We then use power counting to determine
which mechanism is dominant in various azimuthal and spin asymmetries that are
integrated over the transverse momentum. Our findings have consequences for the
extension of transverse-momentum-dependent factorization beyond leading twist.
They also shed light on the problem of resumming logarithms of transverse
momentum for azimuthal distributions. Our results can be carried over to the
Drell-Yan process and to two-hadron production in e+e- annihilation.


title: Newtonian limit for weakly viscoelastic fluid flows of Olroyds' type

abstract:
  This paper is concerned with regular flows of incompressible weakly
viscoelastic fluids which obey a differential constitutive law of Oldroyd type.
  We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or
$\T^N$ for $N=2, 3$, when the Weissenberg number (relaxation time measuring the
elasticity effect in the fluid) tends to zero. More precisely, we prove that
the velocity field and the extra-stress tensor converge in their existence
spaces (we examine the Sobolev-$H^s$ theory and the Besov-$B^{s,1}_2$ theory to
reach the critical case $s= N/2$) to the corresponding newtonian quantities.
  These convergence results are established in the case of "ill-prepared"'
data.We deduce, in the two-dimensional case, a new result concerning the global
existence of weakly viscoelastic fluids flow. Our approach makes use of
essentially two ingredients : the stability of the null solution of the
viscoelastic fluids flow and the damping effect,on the difference between the
extra-stress tensor and the tensor of rate of deformation, induced by the
constitutive law of the fluid.


title:
Can We Constrain the Solar Interior Physics Studying the Gravity-Mode
  Asymptotic Signature?

abstract:
  Gravity modes are the best probes to infer the properties of the solar
radiative zone that represents 98% of the Sun's total mass. It is usually
assumed that high-frequency g modes give information about the structure of the
solar interior whereas low-frequency g modes are more sensitive to the solar
dynamics (the internal rotation). In this work, we develop a new methodology,
based on the analysis of the almost constant separation of the dipole gravity
modes, to introduce new constraints on the solar models. To validate this
analysis procedure, several solar models -- including different physical
processes and either old or new chemical abundances (from, respectively,
Grevesse and Noels (Origin and evolution of the elements. Cambridge, England,
199, 15, 1993) and Asplund, Grevesse, and Sauval (Astron. Soc. Pac. CS, San
Francisco, 36, 25, 2005)) -- have been compared to another model used as a
reference. The analysis clearly shows that this methodology has enough
sensitivity to distinguish between some of the models, in particular, between
those with different compositions. The comparison of the models with the g-mode
asymptotic signature detected in GOLF data favors the ones with old abundances.
Therefore, the physics of the core -- through the analysis of the g-mode
properties -- is in agreement with the results obtained in the previous studies
based on the acoustic modes, which are mostly sensitive to more external layers
of the Sun.


title: Discrete evolution for the zero-modes of the Quantum Liouville Model

abstract:
  The dynamical system for the zero modes of the Liouville Model, which is
separated from the full dynamics for the discrete shifts of time $ t \to t +
\pi $, is investigated. The structure of the modular double in quantum case is
introduced.


title: The Planck energy-mass source as an alternative to the Big Bang

abstract:
  The general theory of relativity is used to show that the total energy-mass
of the visible Universe could be produced by an energy-mass source with the
Planck power. The source was supposedly born at the phase of cosmic inflation
and acts continuously throughout the lifetime of our Universe. The model allows
one to treat dark energy as a real form of energy without using the hypothesis
of anti-gravity.


title:
Effective Field Theory of a Locally Noncommutative Space-Time and Extra
  Dimensions

abstract:
  We assume that the noncommutativity starts to be visible continuously from a
scale $\Lambda_{NC}$. According to this assumption, a two-loop effective action
is derived for noncommutative $\phi^{4}$ and $\phi^{3}$ theories from a
Wilsonian point of view. We show that these effective theories are free of
UV/IR mixing phenomena. We also investigate the positivity constraint on
coefficients of higher dimension operators present in the effective theory.
This constraint makes the low energy theory to be UV completion of a full
theory. Finally, we discuss noncommutativity and extra dimensions. In our
effective theories formulated on noncommutative extra dimensions, if the
campactification scale $\Lambda_{c}$ is less than the scale $\Lambda_{NC}$, the
theory will not suffer from UV/IR mixing.


title: Algebraic integrability of confluent Neumann system

abstract:
  In this paper we study the Neumann system, which describes the harmonic
oscillator (of arbitrary dimension) constrained to the sphere. In particular we
will consider the confluent case where two eigenvalues of the potential
coincide, which implies that the system has S^{1} symmetry. We will prove
complete algebraic integrability of confluent Neumann system and show that its
flow can be linearized on the generalized Jacobian torus of some singular
algebraic curve. The symplectic reduction of S^{1} action will be described and
we will show that the general Rosochatius system is a symplectic quotient of
the confluent Neumann system, where all the eigenvalues of the potential are
double. This will give a new mechanical interpretation of the Rosochatius
system.


title: Cutting Sequences and Palindromes

abstract:
  We give a unified geometric approach to some theorems about primitive
elements and palindromes in free groups of rank 2. The geometric treatment
gives new proofs of the theorems. Dedicated to Bill Harvey on his 65th
birthday.


title:
Self-Enrichment in Globular Clusters: Is There a Role for the
  Super-Asymptotic Giant Branch Stars?

abstract:
  In four globular clusters (GCs) a non negligible fraction of stars can be
interpreted only as a very helium rich population. The evidence comes from the
presence of a "blue" main sequence in $\omega$ Cen and NGC 2808, and from the
the very peculiar horizontal branch morphology in NGC 6441 and NGC 6388.
Although a general consensus is emerging on the fact that self--enrichment is a
common feature among GCs, the helium content required for these stars is
Y$\simgt$0.35, and it is difficult to understand how it can be produced without
any --or, for $\omega$ Cen, without a considerable--associated metal
enhancement. We examine the possible role of super--AGB stars, and show that
they may provide the required high helium. However, the ejecta of the most
massive super--AGBs show a global CNO enrichment by a factor of $\simeq$4, due
to the dredge--out process occurring at the second dredge up stage. If these
clusters show no evidence for this CNO enrichment, we can rule out that at
least the most massive super--AGBs evolve into O--Ne white dwarfs and take part
in the formation of the second generation stars. This latter hypothesis may
help to explain the high number of neutron stars present in GCs. The most
massive super--AGBs would in fact evolve into electron--capture supernovae.
Their envelopes would be easily ejected out of the cluster, but the remnant
neutron stars remain into the clusters, thanks to their small supernova natal
kicks.


title: Y-Formalism and Curved Beta-Gamma Systems

abstract:
  We adopt the Y-formalism to study beta-gamma systems on hypersurfaces. We
compute the operator product expansions of gauge-invariant currents and we
discuss some applications of the Y-formalism to model on Calabi-Yau spaces.


title: Monodromy Groups of Hurwitz-type Problems

abstract:
  We solve the Hurwitz monodromy problem for degree-4 covers. That is, the
Hurwitz space H_{4,g} of all simply branched covers of P^1 of degree 4 and
genus g is an unramified cover of the space P_{2g+6} of (2g+6)-tuples of
distinct points in P^1. We determine the monodromy of pi_1(P_{2g+6}) on the
points of the fiber. This turns out to be the same problem as the action of
pi_1(P_{2g+6}) on a certain local system of Z/2-vector spaces. We generalize
our result by treating the analogous local system with Z/N coefficients,
gcd(3,N)=1, in place of Z/2. This in turn allows us to answer a question of
Ellenberg concerning families of Galois covers of P^1 with deck group
(Z/N)^2:S_3.


title:
Damped harmonic oscillator interpretation of the soft-state power
  spectra of Cyg X-1

abstract:
  We develop a model of an accretion disc in which the variability induced at a
given radius is governed by a damped harmonic oscillator at the corresponding
epicyclic frequency. That variability induces both linear and non-linear
responses in the locally emitted radiation. The total observed variability of a
source is the sum of these contributions over the disc radius weighted by the
energy dissipation rate at each radius. It is shown that this simple model,
which effectively has only three parameters including the normalization, can
explain the range of the power spectra observed from Cyg X-1 in the soft state.
Although a degeneracy between the black hole mass and the strength of the
damping does not allow a unique determination of the mass, we can still
constrain it to <16--20 solar masses. We also show that our model preserves the
observed linear rms-flux relationship even in the presence of the non-linear
flux response.


title: Resonant spin-changing collisions in spinor Fermi gases

abstract:
  Spin-changing collisions in trapped Fermi gases may acquire a resonant
character due to the compensation of quadratic Zeeman effect and trap energy.
These resonances are absent in spinor condensates and pseudo-spin-1/2 Fermi
gases, being a characteristic feature of high-spin Fermi gases that allows
spinor physics at large magnetic fields. We analyze these resonances in detail
for the case of lattice spinor fermions, showing that they permit to
selectively target a spin-changing channel while suppressing all others. These
resonances allow for the controlled creation of non-trivial quantum
superpositions of many-particle states with entangled spin and trap degrees of
freedom, which remarkably are magnetic-field insensitive. Finally, we show that
the intersite tunneling may lead to a quantum phase transition described by an
effective quantum Ising model.


title: On the nature of Seyfert galaxies with high [OIII]5007 blueshifts

abstract:
  We have studied the properties of Seyfert galaxies with high [OIII]5007
blueshifts (`blue outliers'), originally identified because of their strong
deviation from the M_BH - sigma relation of normal, narrow-line Seyfert 1
(NLS1) and broad-line Seyfert 1 (BLS1) galaxies. These blue outliers turn out
to be important test-beds for models of the narrow-line region (NLR), for
mechanisms of driving large-scale outflows, for links between NLS1 galaxies and
radio galaxies, and for orientation-dependent NLS1 models. We report the
detection of a strong correlation of line blueshift with ionization potential
in each galaxy, including the measurement of coronal lines with radial
velocities up to 500--1000 km/s. All [OIII] blue outliers have narrow widths of
their broad Balmer lines and high Eddington ratios. While the presence of
non-shifted low-ionization lines signifies the presence of a classical outer
quiescent NLR in blue outliers, we also report the absence of any second,
non-blueshifted [OIII] component from a classical inner NLR. These results
place tight constraints on NLR models. We favor a scenario in which the NLR
clouds are entrained in a decelerating wind which explains the strong
stratification and the absence of a zero-blueshift inner NLR of blue outliers.
The origin of the wind remains speculative at this time (collimated radio
plasma, thermal winds, radiatively accelerated clouds). It is perhaps linked to
the high Eddington ratios of blue outliers. Similar, less powerful winds could
be present in all Seyfert galaxies, but would generally only affect the coronal
line region (CLR), or level off even before reaching the CLR. Similarities
between blue outliers in NLS1 galaxies and (compact) radio sources are briefly
discussed.


title:
Self-Stabilizing Pulse Synchronization Inspired by Biological Pacemaker
  Networks

abstract:
  We define the ``Pulse Synchronization'' problem that requires nodes to
achieve tight synchronization of regular pulse events, in the settings of
distributed computing systems. Pulse-coupled synchronization is a phenomenon
displayed by a large variety of biological systems, typically overcoming a high
level of noise. Inspired by such biological models, a robust and
self-stabilizing Byzantine pulse synchronization algorithm for distributed
computer systems is presented. The algorithm attains near optimal
synchronization tightness while tolerating up to a third of the nodes
exhibiting Byzantine behavior concurrently. Pulse synchronization has been
previously shown to be a powerful building block for designing algorithms in
this severe fault model. We have previously shown how to stabilize general
Byzantine algorithms, using pulse synchronization. To the best of our knowledge
there is no other scheme to do this without the use of synchronized pulses.


title: Moufang symmetry VII. Moufang transformations

abstract: Concept of a birepresentation for the Moufang loops is elaborated.


title: Moufang symmetry VIII. Reconstruction of Moufang loops

abstract: Reconstruction theorem for the Moufang loops is proved.


title:
Representation of mean-periodic functions in series of exponential
  polynomials

abstract:
  Let $\theta$ be a Young function and consider the space
$\mathcal{F}_{\theta}(\C)$ of all entire functions with $\theta$-exponential
growth. In this paper, we are interested in the solutions $f\in
\mathcal{F}_{\theta}(\C)$ of the convolution equation $T\star f=0$, called
mean-periodic functions, where $T$ is in the topological dual of
$\mathcal{F}_{\theta}(\C)$. We show that each mean-periodic function can be
represented in an explicit way as a convergent series of exponential
polynomials.


title: Quantum Phase Analysis of Extended Bose-Hubbard Model

abstract:
  We have obtained the quantum phase diagram of one dimensional extended
Bose-Hubbard model using the density-matrix renormalization group and Abelian
bosonization methods for different commensurabilities. We describe the nature
of different quantum phases at the charge degeneracy point. We find a direct
phase transition from Mott insulating phase to superconducting phase for
integer band fillings of bosons. We predict explicitly the presence of two
kinds of repulsive Luttinger liquid phases, apart from the charge density wave
and superconducting phases for half-integer band fillings. Our study reveals
that extended range interactions are necessary to get the correct phase
boundary of an one-dimensional interacting bosons system.


title: Unraveling duality violations in hadronic tau decays

abstract:
  There are some indications from recent determinations of the strong coupling
constant alpha_s and the gluon condensate that the Operator Product Expansion
may not be accurate enough to describe non-perturbative effects in hadronic tau
decays. This breakdown of the Operator Product Expansion is usually referred to
as being due to ``Duality Violations.'' With the help of a physically motivated
model, we investigate these duality violations. Based on this model, we argue
how they may introduce a non-negligible systematic error in the current
analysis, which employs finite-energy sum rules with pinched weights. In
particular, this systematic effect might affect the precision determination of
alpha_s from tau decays. With a view to a possible future application to real
data, we present an alternative method for determining the OPE coefficients
that might help estimating, and possibly even reducing, this systematic error.


title:
Time variation of the electron mass in the early universe and the
  Barrow-Magueijo model

abstract:
  We put limits on the time variation of the electron mass in the early
universe using observational primordial abundances of D, He4 and Li7, recent
data from the Cosmic Microwave Background and the 2dFGRS power spectrum.
Furthermore, we use these constraints together with other astronomical and
geophysical bounds from the late universe to test Barrow-Magueijo's model for
the variation in m_e. From our analysis we obtain -0.615 < G\omega/c^4 < -0.045
(3\sigma interval) in disagreement with the result obtained in the original
paper.


title: Networks become navigable as nodes move and forget

abstract:
  We propose a dynamical process for network evolution, aiming at explaining
the emergence of the small world phenomenon, i.e., the statistical observation
that any pair of individuals are linked by a short chain of acquaintances
computable by a simple decentralized routing algorithm, known as greedy
routing. Previously proposed dynamical processes enabled to demonstrate
experimentally (by simulations) that the small world phenomenon can emerge from
local dynamics. However, the analysis of greedy routing using the probability
distributions arising from these dynamics is quite complex because of mutual
dependencies. In contrast, our process enables complete formal analysis. It is
based on the combination of two simple processes: a random walk process, and an
harmonic forgetting process. Both processes reflect natural behaviors of the
individuals, viewed as nodes in the network of inter-individual acquaintances.
We prove that, in k-dimensional lattices, the combination of these two
processes generates long-range links mutually independently distributed as a
k-harmonic distribution. We analyze the performances of greedy routing at the
stationary regime of our process, and prove that the expected number of steps
for routing from any source to any target in any multidimensional lattice is a
polylogarithmic function of the distance between the two nodes in the lattice.
Up to our knowledge, these results are the first formal proof that navigability
in small worlds can emerge from a dynamical process for network evolution. Our
dynamical process can find practical applications to the design of spatial
gossip and resource location protocols.


title:
Interference and Shadow Effects in the Production of Light by Charged
  Particles in Optical Fibers

abstract:
  A charged particle passing through or near a narrow optical fiber induces, by
polarisation, coherent light guided by the fiber. In the limit of zero crossing
angle, the radiation tends towards a Cherenkov radiation with a discrete
spectrum, studied by different authors. If the particle crosses a bent fiber at
regularly spaced points, interference gives quasi-monochromatic lines. If the
particle passes near an end of the fiber, light is produced by the capture of
virtual photons through the end face. An alternative way consists in sticking a
metallic ball to the fiber: the passing particle induces plasmons which are
then evacuated as light in the fiber. Interferences can occur between lights
from several ends or balls. Applications of these various light signals to beam
diagnostics are discussed. The shadow effect, which reduces the photon yield
when the particle runs parallel to a row of balls, is pointed out and an upper
bound $-dE/dz\le C(Ze/b)^2$ for the particle energy loss is conjectured ($Ze$
is the particle charge, $b$ the impact parameter and $C$ a numerical constant).
This bound should also apply to other kinds of light sources, in particular to
Smith-Purcell radiation.


title: High energy gravitational scattering: a numerical study

abstract:
  The S-matrix in gravitational high energy scattering is computed from the
region of large impact parameters b down to the regime where classical
gravitational collapse is expected to occur. By solving the equation of an
effective action introduced by Amati, Ciafaloni and Veneziano we find that the
perturbative expansion around the leading eikonal result diverges at a critical
value signalling the onset of a new regime. We then discuss the main features
of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G
s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact
parameter. The nature of the singularity is studied with particular attention
to the scaling behaviour of various observables at the transition. The
numerical approach is validated by reproducing the known exact solution in the
axially symmetric case to high accuracy.


title:
Mid-infrared Properties and Color Selection for X-ray Detected AGN in
  the MUSYC ECDF-S field

abstract:
  We present the mid-infrared colors of X-ray-detected AGN and explore
mid-infrared selection criteria. Using a statistical matching technique, the
likelihood ratio, over 900 IRAC counterparts were identified with a new MUSYC
X-ray source catalog that includes ~1000 published X-ray sources in the Chandra
Deep Field-South and Extended Chandra Deep Field-South. Most X-ray-selected AGN
have IRAC spectral shapes consistent with power-law slopes, f_{nu} ~
nu^{alpha}, and display a wide range of colors, -2 < alpha < 2. Although X-ray
sources typically fit to redder (more negative alpha) power-laws than non-X-ray
detected galaxies, more than 50% do have flat or blue (galaxy-like) spectral
shapes in the observed 3-8 micron band. Only a quarter of the X-ray selected
AGN detected at 24 micron are well fit by featureless red power laws in the
observed 3.6-24 micron, likely the subset of our sample whose infrared spectra
are dominated by emission from the central AGN region. Most IRAC
color-selection criteria fail to identify the majority of X-ray-selected AGN,
finding only the more luminous AGN, the majority of which have broad emission
lines. In deep surveys, these color-selection criteria select 10-20% of the
entire galaxy population and miss many moderate luminosity AGN.


title: Secondary multiplication in Tate cohomology of certain p-groups

abstract:
  Let k be a field and let G be a finite group. By a theorem of D.Benson,
H.Krause and S.Schwede, there is a canonical element in the Hochschild
cohomology of the Tate cohomology HH^{3,-1} H*G with the following property:
Given any graded H*G-module X, the image of the canonical element in
Ext^{3,-1}(X,X) is zero if and only if X is isomorphic to a direct summand of
H*(G,M) for some kG-module M.
  We investigate this canonical element in certain special cases, namely that
of (finite) abelian p-groups and the quaternion group. In case of
non-triviality of the canonical element, we also give examples of
non-realizable modules X.


title: The constrained next-to-minimal supersymmetric standard model

abstract:
  We consider the fully constrained version of the next-to-minimal
supersymmetric extension of the standard model (cNMSSM) in which a singlet
Higgs superfield is added to the two doublets that are present in the minimal
extension (MSSM). Assuming universal boundary conditions at a high scale for
the soft supersymmetry-breaking gaugino, sfermion and Higgs mass parameters as
well as for the trilinear interactions, we find that the model is more
constrained than the celebrated minimal supergravity model. The
phenomenologically viable region in the parameter space of the cNMSSM
corresponds to a small value for the universal scalar mass m_0: in this case,
one single input parameter is sufficient to describe the phenomenology of the
model once the available constraints from collider data and cosmology are
imposed. We present the particle spectrum of this very predictive model and
discuss how it can be distinguished from the MSSM.


title:
Anisotropic Electron-Phonon Coupling and Dynamical Nesting on the
  Graphene Sheets in CaC6

abstract:
  Superconductivity in graphite intercalated compounds has been studied for
more than 40 years and it is still not fully understood, despite the recent
progress and the discovery of relatively high Tc superconductivity in CaC6 and
YbC6. Recent studies now suggest that the electron-phonon coupling is most
likely responsible for pairing and that the intercalant-derived electronic
states and vibrations play the dominant role. Here, we present the first
studies of electronic structure in CaC6, a superconductor with Tc=11.6 K. Using
angle-resolved photoemission spectroscopy, we find that, contrary to
theoretical models, the EPC on the graphene-derived Fermi sheets is
surprisingly strong, reflecting the interaction with high-frequency
graphene-derived vibrations. Thus, in addition to the amazing properties in the
charge-neutral state, graphene sheets also show surprises in the heavily doped
regime: they may support strong pairing interactions and lead to
superconductivity in compounds in which they are building blocks.


title: Brown-Rho Scaling in the Strong Coupling Lattice QCD

abstract:
  We examine the Brown-Rho scaling for meson masses in the strong coupling
limit of lattice QCD with one species of staggered fermion. Analytical
expression of meson masses is derived at finite temperature and chemical
potential. We find that meson masses are approximately proportional to the
equilibrium value of the chiral condensate, which evolves as a function of
temperature and chemical potential.


title:
Late-Time HST Photometry of SN 1994I: Hints of Positron Annihilation
  Energy Deposition

abstract:
  We present multicolor Hubble Space Telescope (HST) WFPC2 broadband
observations of the Type Ic SN 1994I obtained approximately 280 days after
maximum light. We measure the brightness of the SN and, relying on the detailed
spectroscopic database of SN 1994I, we transform the ground-based photometry
obtained at early times to the HST photometric system, deriving light curves
for the WFPC2 F439W, F555W, F675W, and F814W passbands that extend from 7 days
before to 280 days after maximum. We use the multicolor photometry to build a
quasi-bolometric light curve of SN 1994I, and compare it with similarly
constructed light curves of other supernovae. In doing so, we propose and test
a scaling in energy and time that allows for a more meaningful comparison of
the exponential tails of different events.
  Through comparison with models, we find that the late-time light curve of SN
1994I is consistent with that of spherically symmetric ejecta in homologous
expansion, for which the ability to trap the Gamma-rays produced by the
radioactive decay of 56Co diminishes roughly as the inverse of time squared. We
also find that by the time of the HST photometry, the light curve was
significantly energized by the annihilation of positrons.


title:
Early-type galaxies with neutral hydrogen in the Virgo cluster from the
  ALFALFA survey

abstract:
  We extend our published work on the neutral hydrogen content of early-type
galaxies in the Virgo cluster using the catalogue of detected sources from the
ALFALFA survey, by showing the 21cm spectra of all the detected galaxies and
discussing a deeper analysis of the ALFALFA datacubes, searching for lower S/N
sources. A view of the multiphase interstellar medium of M86 is also presented,
by comparing images of the cold, warm and hot phases.


title:
Evidence for the Discrete Asymptotically-Free BFKL Pomeron from HERA
  Data

abstract:
  We show that the next-to-leading-order renormalization-group-improved
asymptotically-free BFKL Pomeron provides a good fit to HERA data on virtual
photoproduction at small x and large Q^2. The leading discrete Pomeron pole
reproduces qualitatively the Q^2 dependence of the HERA data for x ~10^{-3},
and a fit using the three leading discrete singularities reproduces
quantitatively the Q^2 and x dependence of the HERA data for x < 10^{-2}. This
fit fixes the phase for all the BFKL wavefunctions at a chosen infrared scale.


title: Improvements in 3D Automated Shimming Techniques in High-Resolution NMR

abstract:
  Traditionally the improvement of static magnetic field homogeneity of the
magnet in Nuclear Magnetic Resonance (NMR) spectroscopy is performed manually,
which has many limitations. However, in recent years a number of automated
shimming techniques based on Fourier Imaging Technique have been proposed.
Existing 3D automated shimming methods require special, Pulsed Field Gradient
(PFG) hardware, which is not available on majority of high-resolution NMR
spectrometers. The modified technique, presented in this thesis uses the normal
NMR hardware provided with the majority of high-resolution NMR spectrometers.
The 3D shimming technique described was optimised for use with Varian UNITY
INOVA spectrometers and successfully tested with both protonated and deuterated
solvents. A method for calibrating linear transverse shim field gradients and
correcting any non-orthogonality and imbalance of strengths is proposed. The
effect of thermal convection on field mapping was observed and is reported here
for the first time.


title:
Intraband exciton relaxation in a biased lattice with long-range
  correlated disorder

abstract:
  We study numerically the intraband exciton relaxation in a one-dimensional
lattice with scale-free disorder, in the presence of a linear bias. Exciton
transport is considered as incoherent hoppings over the eigenstates of the
static lattice. The site potential of the unbiased lattice is
long-range-correlated with a power-law spectral density $S(k) \sim
1/k^{\alpha}$, $\alpha > 0$. The lattice supports a phase of extended states at
the center of the band, provided $\alpha$ is larger than a critical value
$\alpha_c$ [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. \textbf{81},
3735 (1998)]. When the bias is applied, the absorption spectrum displays clear
signatures of the Wannier-Stark ladder [E. D\'{\i}az \emph{et al.}, Phys. Rev.
B\textbf{73}, 172410 (2006)]. We demonstrate that in unbiased lattices and in
weakly correlated potentials the decay law is non-exponential. However, the
decay is purely exponential when the bias increases and $\alpha$ is large. We
relate this exponential decay to the occurrence of the Wannier-Stark ladder in
the exciton band.


title: Stability of multipeakons

abstract:
  The Camassa-Holm equation possesses well-known peaked solitary waves that are
called peakons. Their orbital stability has been established by Constantin and
Strauss (2000). We prove here the stability of ordered trains of peakons. We
also establish a result on the stability of multipeakons.


title:
Perturbative Yukawa theory at finite density: the role of masses and
  renormalization group flow at two loops

abstract:
  Yukawa theory at vanishing temperature provides (one of the ingredients for)
an effective description of the thermodynamics of a variety of cold and dense
fermionic systems. We study the role of masses and the renormalization group
flow in the calculation of the equation of state up to two loops within the
MSbar scheme. Two-loop integrals are computed analytically for arbitrary
fermion and scalar masses, and expressed in terms of well-known special
functions. The dependence of the renormalization group flow on the number of
fermion flavors is also discussed.


title:
Hamiltonian and Brownian systems with long-range interactions: V.
  Stochastic kinetic equations and theory of fluctuations

abstract:
  We develop a theory of fluctuations for Brownian systems with weak long-range
interactions. For these systems, there exists a critical point separating a
homogeneous phase from an inhomogeneous phase. Starting from the stochastic
Smoluchowski equation governing the evolution of the fluctuating density field,
we determine the expression of the correlation function of the density
fluctuations around a spatially homogeneous equilibrium distribution. In the
stable regime, we find that the temporal correlation function of the Fourier
components of the density fluctuations decays exponentially rapidly with the
same rate as the one characterizing the damping of a perturbation governed by
the mean field Smoluchowski equation (without noise). On the other hand, the
amplitude of the spatial correlation function in Fourier space diverges at the
critical point $T=T_{c}$ (or at the instability threshold $k=k_{m}$) implying
that the mean field approximation breaks down close to the critical point and
that the phase transition from the homogeneous phase to the inhomogeneous phase
occurs sooner. By contrast, the correlations of the velocity fluctuations
remain finite at the critical point (or at the instability threshold). We give
explicit examples for the Brownian Mean Field (BMF) model and for Brownian
particles interacting via the gravitational potential and via the attractive
Yukawa potential. We also introduce a stochastic model of chemotaxis for
bacterial populations generalizing the mean field Keller-Segel model by taking
into account fluctuations.


title:
Constraints on grain size and stable iron phases in the uppermost Inner
  Core from multiple scattering modeling of seismic velocity and attenuation

abstract:
  We propose to model the uppermost inner core as an aggregate of randomly
oriented anisotropic ``patches''. A patch is defined as an assemblage of a
possibly large number of crystals with identically oriented crystallographic
axes. This simple model accounts for the observed velocity isotropy of short
period body waves, and offers a reasonable physical interpretation for the
scatterers detected at the top of the inner core. From rigorous multiple
scattering modeling of seismic wave propagation through the aggregate, we
obtain strong constraints on both the size and the elastic constants of iron
patches. We perform a systematic search for iron models compatible with
measured seismic velocities and attenuations. An iron model is characterized by
its symmetry (cubic or hexagonal), elastic constants, and patch size.
Independent of the crystal symmetry, we infer a most likely size of patch of
the order of 400 m. Recent {\it bcc} iron models from the literature are in
very good agreement with the most probable elastic constants of cubic crystals
found in our inversion. Our study (1) suggests that the presence of melt may
not be required to explain the low shear wavespeeds in the inner core and (2)
supports the recent experimental results on the stability of cubic iron in the
inner core, at least in its upper part.


title: Blind Fingerprinting

abstract:
  We study blind fingerprinting, where the host sequence into which
fingerprints are embedded is partially or completely unknown to the decoder.
This problem relates to a multiuser version of the Gel'fand-Pinsker problem.
The number of colluders and the collusion channel are unknown, and the
colluders and the fingerprint embedder are subject to distortion constraints.
  We propose a conditionally constant-composition random binning scheme and a
universal decoding rule and derive the corresponding false-positive and
false-negative error exponents. The encoder is a stacked binning scheme and
makes use of an auxiliary random sequence. The decoder is a {\em maximum
doubly-penalized mutual information decoder}, where the significance of each
candidate coalition is assessed relative to a threshold that trades off
false-positive and false-negative error exponents. The penalty is proportional
to coalition size and is a function of the conditional type of host sequence.
Positive exponents are obtained at all rates below a certain value, which is
therefore a lower bound on public fingerprinting capacity. We conjecture that
this value is the public fingerprinting capacity. A simpler threshold decoder
is also given, which has similar universality properties but also lower
achievable rates. An upper bound on public fingerprinting capacity is also
derived.


title: The logarithmic equation of state for superconducting cosmic strings

abstract:
  This investigation follows up the suggestion that the equation of state for
superconducting cosmic strings provided by Witten's prototype biscalar field
model can be well represented by an effective Lagrangian of simple logarithmic
form depending on only 3 independent parameters. The numerical work described
here confirms the validity of this approximation, and initiates the evaluation
of the 3 required parameters, as functions of the masses and other parameters
specifying the underlying U(1) x U(1) scalar field model in the limit for which
the relevant gauge coupling constants are small.In this limit, subject to
calibration of the relevant length and mass scales, the scalar field model is
characterised by just 3 dimensionless ratios which (in order to provide
conducting strings) must be subject to three inequalities (of which two have
obvious analytic expressions). It is found here that when all three of these
inequalities are satisfied by a reasonably large margin, there is a simple
empirical formula that can be used to provide a fairly accurate prescription
for the algebraic dependence on these 3 dimensionless ratios of the 3
parameters required for the logarithmic equation of state.


title:
Number of "udu" of a Dyck path and ad-nilpotent ideals of parabolic
  subalgebras of sl_{l+1}(C)

abstract:
  For an ad-nilpotent ideal $i$ of a Borel subalgebra of $sl_{l+1}(C)$, we
denote by $I_i$ the maximal subset $I$ of the set of simple roots such that $i$
is an ad-nilpotent ideal of the standard parabolic subalgebra $p_I$. We use the
bijection given by G.E. Andrews, C. Krattenthaler, L. Orsina and P. Papi
between the set of ad-nilpotent ideals of a Borel subalgebra in $sl_{l+1}(C)$
and the set of Dyck paths of length $2l+2$, to explicit a bijection between
ad-nilpotent ideals $i$ of the Borel subalgebra such that the cardinality of
$I_i$ is equal to $r$ and the Dyck paths of length $2l+2$ having $r$ occurence
"udu". We obtain also a duality between antichains of cardinality $p$ and $l-p$
in the set of positive roots.


title: The universe out of a breathing bubble

abstract:
  We consider the model of a false vacuum bubble with a thin wall where the
surface energy density is composed of two different components, "domain-wall"
type and "dust" type, with opposite signs. We find stably oscillating
solutions, which we call "breathing bubbles". By decay to a lower mass state,
such a breathing bubble could become either i) a child universe or ii) a bubble
that "eats up" the original universe, depending on the sign of the surface
energy of the "domain-wall" component. We also discuss the effect of the
finite-thickness corrections to the thin-wall approximation and possible
origins of the energy contents of our model.


title:
Optimal protocols for minimal work processes in underdamped stochastic
  thermodynamics

abstract:
  For systems in an externally controllable time-dependent potential, the
optimal protocol minimizes the mean work spent in a finite-time transition
between two given equilibrium states. For overdamped dynamics which ignores
inertia effects, the optimal protocol has been found to involve jumps of the
control parameter at the beginning and end of the process. Including the
inertia term, we show that this feature not only persists but that even delta
peak-like changes of the control parameter at both boundaries make the process
optimal. These results are obtained by analyzing two simple paradigmatic cases:
First, a Brownian particle dragged by a harmonic optical trap through a viscous
fluid and, second, a Brownian particle subject to an optical trap with
time-dependent stiffness. These insights could be used to improve free energy
calculations via either thermodynamic integration or "fast growth" methods
using Jarzynski's equality.


title: Autobiographical Numbers

abstract:
  I introduce autobiographical numbers as defined in A046043 (see Online
Encyclopedia of Integer Sequences). I continue by defining and analyzing
biographies, curricula vitae and complete life stories of numbers. I end with
the definition of mutually-praising number pairs.


title: Relation between chiral symmetry breaking and confinement in YM-theories

abstract:
  Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov
loop are thoroughly investigated. The approach by Gattringer is generalized to
mode sums which reconstruct the Polyakov loop locally. This opens the
possibility to study the mode sum approximation to the Polyakov loop
correlator. The approach is re-derived for the ab initio continuum formulation
of Yang-Mills theories, and the convergence of the mode sum is studied in
detail. The mode sums are then explicitly calculated for the Schwinger model
and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice
gauge theory, the IR dominated mode sums are considered and the mode sum
approximation to the static quark anti-quark potential is obtained numerically.
We find a good agreement between the mode sum approximation and the static
potential at large distances for the confinement and the high temperature
plasma phase.


title: High threshold universal quantum computation on the surface code

abstract:
  We present a comprehensive and self-contained simplified review of the
quantum computing scheme of Phys. Rev. Lett. 98, 190504 (2007), which features
a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate
approaching 1%, natural asymmetric and adjustable strength error correction and
low overhead arbitrarily long-range logical gates. These features make it by
far the best and most practical quantum computing scheme devised to date. We
restrict the discussion to direct manipulation of the surface code using the
stabilizer formalism, both of which we also briefly review, to make the scheme
accessible to a broad audience.


title:
Two--Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor
  Production to $O(\epsilon)

abstract:
  We calculate the $O(\alpha_s^2)$ massive operator matrix elements for the
twist--2 operators, which contribute to the heavy flavor Wilson coefficients in
unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$, up to the
$O(\epsilon)$ contributions. These terms contribute through the renormalization
of the $O(\alpha_s^3)$ heavy flavor Wilson coefficients of the structure
function $F_2(x,Q^2)$. The calculation has been performed using light--cone
expansion techniques without using the integration-by-parts method. We
represent the individual Feynman diagrams by generalized hypergeometric
structures, the $\epsilon$--expansion of which leads to infinite sums depending
on the Mellin variable $N$. These sums are finally expressed in terms of nested
harmonic sums using the general summation techniques implemented in the {\tt
Sigma} package.


title:
Comment on "Pygmy dipole response of proton-rich argon nuclei in
  random-phase approximation and no-core shell model"

abstract:
  In a recent article by C. Barbieri, E. Caurier, K. Langanke, and G.
Mart\'inez-Pinedo \cite{Bar.08}, low-energy dipole excitations were studied in
proton-rich $^{32,34}$Ar with random-phase approximation (RPA) and no-core
shell model (NCSM) using correlated realistic nucleon-nucleon interactions
obtained by the unitary correlation operator method (UCOM) \cite{Fel.98}. The
main objective of this Comment is to argue that the article \cite{Bar.08}
contains an inconsistency with respect to previous study of excitations in the
same UCOM-RPA framework using identical correlated Argonne V18 interaction
\cite{Paa.06}, it does not provide any evidence that the low-lying state
declared as pygmy dipole resonance in $^{32}$Ar indeed has the resonance-like
structure, and that prior to studying exotic modes of excitation away from the
valley of stability one should ensure that the model provides reliable
description of available experimental data on nuclear ground state properties
and excitations in nuclei. Although the authors aimed at testing the UCOM based
theory at the proton drip line, available experimental data that are used as
standard initial tests of theory frameworks at the proton drip line have not
been considered in the UCOM case (e.g., binding energies, one-proton separation
energies, two-proton separation energies).


title: Wetting problem for multi-component fluid mixtures

abstract:
  In this paper we propose an extension of the Cahn method to binary mixtures
and study the problem of wetting near a two-phase critical point without any
assumption on the form of intermolecular potentials. A comparison between
Cahn's method and later works by Sullivan, Evans et al is made. By using an
expression of the energy of interaction between solid surface and liquids
proposed recently by Gouin, we obtain the equations of density profiles and the
boundary conditions on a solid surface. In the case of a convex free energy, a
one-dimensional solution of a linear problem is proposed for the density
profiles between a bulk and on a solid wall. A non-linear model of binary
mixtures extending Cahn's results for simple fluids is also studied. For the
case of a purely attractive wall we have established a criterion of a first
order transition in terms of the structure of the level set of the homogeneous
part of the free energy. Additively, explicit expressions of density profiles
near the wall are proposed. They allow one to consider the adsorption of
mixture components by a solid wall.


title:
Hydromagnetic waves in a superfluid neutron star with strong vortex
  pinning

abstract:
  Neutron-star cores may be hosts of a unique mixture of a neutron superfluid
and a proton superconductor. Compelling theoretical arguments have been
presented over the years that if the proton superconductor is of type II, than
the superconductor fluxtubes and superfluid vortices should be strongly coupled
and hence the vortices should be pinned to the proton-electron plasma in the
core. We explore the effect of this pinning on the hydromagnetic waves in the
core, and discuss 2 astrophysical applications of our results: 1. We show that
even in the case of strong pinning, the core Alfven waves thought to be
responsible for the low-frequency magnetar quasi-periodic oscillations (QPO)
are not significantly mass-loaded by the neutrons. The decoupling of about 0.95
of the core mass from the Alfven waves is in fact required in order to explain
the QPO frequencies, for simple magnetic geometries and for magnetic fields not
greater than 10^{15} Gauss. 2. We show that in the case of strong vortex
pinning, hydromagnetic stresses exert stabilizing influence on the Glaberson
instability, which has recently been proposed as a potential source of
superfluid turbulence in neutron stars.


title: General post-Minkowskian expansion of time transfer functions

abstract:
  Modeling most of the tests of general relativity requires to know the
function relating light travel time to the coordinate time of reception and to
the spatial coordinates of the emitter and the receiver. We call such a
function the reception time transfer function. Of course, an emission time
transfer function may as well be considered. We present here a recursive
procedure enabling to expand each time transfer function into a perturbative
series of ascending powers of the Newtonian gravitational constant $G$ (general
post-Minkowskian expansion). Our method is self-sufficient, in the sense that
neither the integration of null geodesic equations nor the determination of
Synge's world function are necessary. To illustrate the method, the time
transfer function of a three-parameter family of static, spherically symmetric
metrics is derived within the post-linear approximation.


title:
Crossover from ballistic to diffusive thermal transport in quantum
  Langevin dynamics study of a harmonic chain connected to self-consistent
  reservoirs

abstract:
  Through an exact analysis using quantum Langevin dynamics, we demonstrate the
crossover from ballistic to diffusive thermal transport in a harmonic chain
with each site connected to Ohmic heat reservoirs. The temperatures of the two
heat baths at the boundaries are specified from before whereas the temperatures
of the interior heat reservoirs are determined self-consistently by demanding
that in the steady state, on average, there is no heat current between any such
(self-consistent) reservoir and the harmonic chain. Essence of our study is
that the effective mean free path separating the ballistic regime of transport
from the diffusive one emerges naturally.


title: Baryons and the phase diagram for a large number of colors and flavors

abstract:
  We consider the possible phases of a non-Abelian gauge theory, as a function
of temperature and quark chemical potential, when both the number of colors and
flavors is very large. Generally, a large number of flavors washes out
deconfining phase transitions. We show, however, that the degeneracy of even
the lightest baryons is exponentially large. This implies that the baryon
number (or fluctuations thereof, at zero chemical potential) is an order
parameter in the limit of an infinite number of colors and flavors.


title: Tailored mixing inside a translating droplet

abstract:
  Tailored mixing inside individual droplets could be useful to ensure that
reactions within microscopic discrete fluid volumes, which are used as
microreactors in ``digital microfluidic'' applications, take place in a
controlled fashion. In this article we consider a translating spherical liquid
drop to which we impose a time periodic rigid-body rotation. Such a rotation
not only induces mixing via chaotic advection, which operates through the
stretching and folding of material lines, but also offers the possibility of
tuning the mixing by controlling the location and size of the mixing region.
Tuned mixing is achieved by judiciously adjusting the amplitude and frequency
of the rotation, which are determined by using a resonance condition and
following the evolution of adiabatic invariants. As the size of the mixing
region is increased, complete mixing within the drop is obtained.


title: Equilibrium boundary conditions, dynamic vacuum energy, and the Big Bang

abstract:
  The near-zero value of the cosmological constant \Lambda in an equilibrium
context may be due to the existence of a self-tuning relativistic vacuum
variable q. Here, a cosmological nonequilibrium context is considered with a
corresponding time-dependent cosmological parameter \Lambda(t) or vacuum energy
density \rho_V(t). A specific model of a closed Friedmann-Robertson-Walker
universe is presented, which is determined by equilibrium boundary conditions
at one instant of time (t=t_{eq}) and a particular form of vacuum-energy
dynamics (d\rho_V/dt \propto \rho_M). This homogeneous and isotropic model has
a standard Big Bang phase at early times (t << t_{eq}) and reproduces the main
characteristics of the present universe (t=t_0 < t_{eq}).


title: On a new definition of quantum entropy

abstract:
  It is proved here that, as a consequence of the unitary quantum evolution,
the expectation value of a properly defined quantum entropy operator (as
opposed to the non-evolving von Neumann entropy) can only increase during non
adiabatic transformations and remains constant during adiabatic ones. Thus
Clausius formulation of the second law is established as a theorem in quantum
mechanics, in a way that is equivalent to the previously established
formulation in terms of minimal work principle [A. E. Allahverdyan and T. M.
Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum
Mechanical Principle of Entropy Increase is then illustrated with an exactly
solvable example, namely the driven harmonic oscillator. Attention is paid to
both microcanonical and canonical initial condition. The results are compared
to their classical counterparts.


title: Bound State Inequality for High Mass Exchanges in a Scalar Field Model

abstract:
  Ladder diagrams are relevant for the study of bound states. The condition
upon the coupling strength for the existence of a bound state has been deduced
in a scalar field theory for the case of low mass exchanges. We apply this
approach to the case of very high mass exchanges.


title: Generalized Fourier Integral Operators on spaces of Colombeau type

abstract:
  Generalized Fourier integral operators (FIOs) acting on Colombeau algebras
are defined. This is based on a theory of generalized oscillatory integrals
(OIs) whose phase functions as well as amplitudes may be generalized functions
of Colombeau type. The mapping properties of these FIOs are studied as the
composition with a generalized pseudodifferential operator. Finally, the
microlocal Colombeau regularity for OIs and the influence of the FIO action on
generalized wave front sets are investigated. This theory of generalized FIOs
is motivated by the need of a general framework for partial differential
operators with non-smooth coefficients and distributional data.


title: Surprising properties of centralisers in classical Lie algebras

abstract:
  Let $g$ be a classical Lie algebra, i.e., either $gl_n$, $sp_n$, or $so_n$
and let $e\in g$ be a nilpotent element. We study various properties of
centralisers $g_e$. The first four sections deal with rather elementary
questions, like the centre of $g_e$, commuting varieties associated with $g_e$,
or centralisers of commuting pairs. The second half of the paper addresses
problems related to different Poisson structures on $g_e^*$ and symmetric
invariants of $g_e$.


title: Aspects of stable polynomials

abstract:
  This note is an introduction to the properties of stable polynomials in
several variables with real or complex coefficients. These polynomials are
defined in terms of where the polynomial is non-vanishing. We do not cover
well-known topics in one variable such as Routh-Hurwitz, the Edge theorem, and
Kharitonov theory.


title: Wild twistor D-modules

abstract:
  We propose a definition of (polarized) wild twistor D-modules, generalizing
to objects with irregular singularities that of (polarized) regular twistor
D-modules. We give a precise analysis in dimension one.


title: Electron transmission in normal/heavy-fermion superconductor junctions

abstract:
  The Andreev reflection between a normal metal (N) and a heavy-fermion
superconductor (HFS) is studied and the boundary conditions for the electron's
wave function in the two systems are established in the framework of a two band
model for the HFS. Hence we show in a simple and explicit way that the mass
enhancement factors in the heavy-fermion (HF) metal do not cause impedance at
the N/HFS interface, in accordance with arguments previously presented. We also
present an extension of the theory to a two-fluid model for the heavy-fermion,
as possibly applicable to, e.g., CeCoIn_5.


title:
Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic
  flows admit integrals quadratic in momenta

abstract:
  We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the
geodesic flow admits a nontrivial integral quadratic in velocities. We
construct local normal forms of such metrics. We show that these metrics have
certain useful properties similar to those of Riemannian Liouville metrics,
namely: 1) they admit geodesically equivalent metrics; 2) one can use them to
construct a big family of natural systems admitting integrals quadratic in
momenta; 3) the integrability of such systems can be generalized to the quantum
setting; 4) these natural systems are integrable by quadratures.


title:
Nontrivial lower bounds for the least common multiple of some finite
  sequences of integers

abstract:
  We present here a method which allows to derive a nontrivial lower bounds for
the least common multiple of some finite sequences of integers. We obtain
efficient lower bounds (which in a way are optimal) for the arithmetic
progressions and lower bounds less efficient (but nontrivial) for quadratic
sequences whose general term has the form $u_n = a n (n + t) + b$ with $(a, t,
b) \in {\mathbb{Z}}^3, a \geq 5, t \geq 0, \rm{gcd}(a, b) = 1$. From this, we
deduce for instance the lower bound: $\mathrm{lcm}\{1^2 + 1, 2^2 + 1, ..., n^2
+ 1\} \geq 0,32 (1,442)^n$ (for all $n \geq 1$).
  In the last part of this article, we study the integer $\mathrm{lcm}(n, n +
1, ..., n + k)$ $(k \in \mathbb{N}, n \in {\mathbb{N}}^*)$. We show that it has
a divisor $d_{n, k}$ simple in its dependence on $n$ and $k$, and a multiple
$m_{n, k}$ also simple in its dependence on $n$. In addition, we prove that
both equalities: $\mathrm{lcm}(n, n + 1, ..., n + k) = d_{n, k}$ and
$\mathrm{lcm}(n, n + 1, ..., n + k) = m_{n, k}$ hold for an infinitely many
pairs $(n, k)$.


title: D-branes at multicritical points

abstract:
  The moduli space of c=1 conformal field theories in two dimensions has a
multicritical point, where a circle theory is equivalent to an orbifold theory.
We analyse all the conformal branes in both descriptions of this theory, and
find convincing evidence that the full brane spectrum coincides. This shows
that the equivalence of the two descriptions at this multicritical point
extends to the boundary sector. We also perform the analogous analysis for one
of the multicritical points of the N=1 superconformal field theories at c=3/2.
Again the brane spectra are identical for both descriptions, however the
identification is more subtle.


title:
Quantum Games and the Relationships between Quantum Mechanics and Game
  Theory

abstract:
  Quantum games have proposed a new point of view for the solution of the
classical problems and dilemmas in game theory. Certain quantization
relationships can be proposed with the objective that a game can be generalized
into a quantum domain where the linear superposition of actions is allowed.
This quantization let us describe and solution problems originated by
conflicting or cooperative behaviors among the members of a system from the
point of view of quantum mechanical interactions. This leads us to interesting
aspects which only can be observed through the quantization of a game like the
possibility of the entanglement between players, the definition of a
socioeconomical temperature in a system, the collective welfare principle,the
analysis of a game through elements of quantum information theory and the
globalization process. The relationships between quantum mechanics and game
theory are also studied and its shown how although both systems analyzed are
described through two theories apparently different (quantum mechanics and game
theory) both are analogous and thus exactly equivalents.


title:
X-ray absorption and x-ray magnetic dichroism study on Ca3CoRhO6 and
  Ca3FeRhO6

abstract:
  Using x-ray absorption spectroscopy at the Rh-L_2,3, Co-L_2,3, and Fe-L_2,3
edges, we find a valence state of Co^2+/Rh^4+ in Ca3CoRhO6 and of Fe^3+/Rh^3+
in Ca3FeRhO6. X-ray magnetic circular dichroism spectroscopy at the Co-L_2,3
edge of Ca3CoRhO6 reveals a giant orbital moment of about 1.7mu_B, which can be
attributed to the occupation of the minority-spin d_0d_2 orbital state of the
high-spin Co^2+ (3d^7) ions in trigonal prismatic coordination. This active
role of the spin-orbit coupling explains the strong magnetocrystalline
anisotropy and Ising-like magnetism of Ca3CoRhO6.


title: Topological tunneling with Dynamical overlap fermions

abstract:
  Tunneling between different topological sectors with dynamical chiral
fermions is difficult because of a poor mass scaling of the pseudo-fermion
estimate of the determinant. For small fermion masses it is virtually
impossible using standard methods. However, by projecting out the small Wilson
eigenvectors from the overlap operator, and treating the correction determinant
exactly, we can significantly increase the rate of topological sector tunneling
and reduce substantially the auto-correlation time. We present and compare a
number of different approaches, and advocate a method which allows topological
tunneling even at low mass with little addition to the computational cost.


title:
Subtle Signatures of Multiplicity in Late-type Dwarf Spectra: The
  Unresolved M8.5 + T5 Binary 2MASS J03202839-0446358

abstract:
  Evidence is presented that 2MASS J03202839-0446358, a late-type dwarf with
discrepant optical (M8:) and near-infrared (L1) spectral types, is an as-yet
unresolved stellar/brown dwarf binary with late-type M dwarf and T dwarf
components. This conclusion is based on low-resolution, near-infrared
spectroscopy that reveals a subtle but distinctive absorption feature at 1.6
micron. The feature, which is also present in the combined light spectrum of
the M8.5 + T6 binary SCR 1845-6357, arises from the combination of FeH
absorption from an M8.5 primary and pseudo-continuum flux from a T5+/-1
secondary, as ascertained from binary spectral templates constructed from
empirical data. The binary templates provide a far superior match to the
overall near-infrared spectral energy distribution of 2MASS J0320-0446 than any
single comparison spectra. Laser guide star adaptive optics (LGS AO) imaging
observations, including the first application of LGS AO aperture mask
interferometry, fail to resolve a faint companion, restricting the projected
separation of the system to less than 8.3 AU at the time of observation. 2MASS
J0320-0446 is the second very low mass binary to be identified from unresolved,
low-resolution, near-infrared spectroscopy, a technique that complements
traditional high resolution imaging and spectroscopic methods.


title:
HST FGS astrometry - the value of fractional millisecond of arc
  precision

abstract:
  In a few years astrometry with the venerable combination of Hubble Space
Telescope and Fine Guidance Sensor will be replaced by SIM, GAIA, and
long-baseline interferometry. Until then we remain a resource of choice for
sub-millisecond of arc precision optical astrometry. As examples we discuss 1)
the uses which can be made of our parallaxes of galactic Cepheids, and 2) the
determination of perturbation orbital elements for several exoplanet host
stars, yielding true companion masses.


title: Hodge correlators

abstract:
  Hodge correlators are complex numbers given by certain integrals assigned to
a smooth complex curve. We show that they are correlators of a Feynman
integral, and describe the real mixed Hodge structure on the pronilpotent
completion of the fundamental group of the curve. We introduce motivic
correlators, which are elements of the motivic Lie algebra and whose periods
are the Hodge correlators. They describe the motivic fundamental group of the
curve. We describe variations of real mixed Hodge structures on a variety by
certain connections on the product of the variety by an afine line. We call
them twistor connections. Generalising this, we suggest a DG enhancement of the
subcategory of Saito's Hodge complexes with smooth cohomology. We show that
when the curve varies, the Hodge correlators are the coefficients of the
twistor connection describing the corresponding variation of real MHS. Examples
of the Hodge correlators include classical and elliptic polylogarithms, and
their generalizations. The simplest Hodge correlators on the modular curves are
the Rankin-Selberg integrals. Examples of the motivic correlators include
Beilinson's elements in the motivic cohomology, e.g. the ones delivering the
Beilinson - Kato Euler system on modular curves.


title:
Spectral measures on toric varieties and the asymptotic expansion of
  Tian-Yau-Zelditch

abstract:
  We extend a recent result of Burns, Guillemin and Uribe on the asymptotics of
the spectral measure for the reduction metric on a toric variety to any toric
metric on a toric variety. We show how this extended result together with the
Tian-Yau-Zelditch asymptotic expansion can be used to deduce Abreu's formula
for the scalar curvature of a toric metric on a toric variety in terms of
polytope data.


title: Two and four-level systems in magnetic fields restricted in time

abstract:
  We describe some new exact solutions for two- and four-level systems. In all
the cases, external fields have a restricted behavior in time. First, we
consider two types of new solutions for one-spin equation, one of them is in a
external magnetic field that acts during a finite time interval. A new solution
for two interacting spins is found in the case when the field difference
between the external fields in each spin vary adiabatically, vanishing on the
time infinity. The latter system can be identified with a quantum gate realized
by two coupled quantum dots. The probability of the Swap operation for such a
gate can be explicitly expressed in terms of special functions. Using the
obtained expressions, we construct plots for the Swap operation for some
parameters of the external magnetic field and interaction function.


title: Proca Equation for Attosecond Electron Pulses

abstract:
  In this paper the heat transport of attosecond electron pulses is
investigated. It is shown that attosecond electrons can propagate as thermal
waves or diffused as particle conglommerates, Proca equation as type equation
for the thermal transport of the attosecond electron pulsem is formulated


title: Thermodynamic restrictions on statistics of molecular random walks

abstract:
  It is shown that time reversibility of Hamiltonian microscopic dynamics and
Gibbs canonical statistical ensemble of initial conditions for it together
produce an exact virial expansion for probability distribution of path of
molecular Brownian particle in a fluid. This expansion leads to inequality
connecting logarithmic derivative of the distribution with respect to fluid
density and characteristic volume occupied by pair statistical correlation
between the path and fluid molecules. Due to the inequality, finiteness of this
volume means that asymptotic of the distribution is essentially non-Gaussian.
For principal case when fluid is dilute gas it is demonstrated that the pair
correlation volume is actually finite and bounded above. Therefore even under
the Boltzmann-Grad limit the path distribution possess power-law long tails
(cut off at distances of ballistic flight).


title: Counting Defective Parking Functions

abstract:
  Suppose that $n$ drivers each choose a preferred parking space in a linear
car park with $m$ spaces. Each driver goes to the chosen space and parks there
if it is free, and otherwise takes the first available space with larger number
(if any). If all drivers park successfully, the sequence of choices is called a
parking function. In general, if $k$ drivers fail to park, we have a
\emph{defective parking function} of \emph{defect} $k$. Let $\cp(n,m,k)$ be the
number of such functions.
  In this paper, we establish a recurrence relation for the numbers
$\cp(n,m,k)$, and express this as an equation for a three-variable generating
function. We solve this equation using the kernel method, and extract the
coefficients explicitly: it turns out that the cumulative totals are partial
sums in Abel's binomial identity. Finally, we compute the asymptotics of
$\cp(n,m,k)$. In particular, for the case $m=n$, if choices are made
independently at random, the limiting distribution of the defect (the number of
drivers who fail to park), scaled by the square root of $n$, is the Rayleigh
distribution. On the other hand, in case $m=\omega(n)$, the probability that
all spaces are occupied tends asymptotically to one.


title:
Mixing internal and spacetime transformations: some examples and
  counterexamples

abstract:
  This note addresses the question whether in a gauge theory coupled to gravity
internal and spacetime transformation can be mixed. It is shown that if the VEV
of the gauge field is flat, the symmetry group is always a product of internal
and spacetime symmetries. On the other hand, if the VEV of the gauge field is
not flat it is impossible to properly define the notion of a ``spacetime''
transformation; as a consequence, if the symmetry group is nontrivial, mixing
generically occurs.


title: Remarks on the faithfulness of the Jones representations

abstract:
  We consider the linear representations of the mapping class group of an
n-punctured 2-sphere constructed by V. F. R. Jones using Iwahori-Hecke algebras
of type A. We show that their faithfulness is equivalent to that of certain
related Iwahori-Hecke algebra representation of Artin's braid group of n-1
strands. In the case of n=6, we provide a further restriction for the kernel
using our previous result, as well as a certain relation to the Burau
representation of degree 4.


title:
The link between the masses and central stellar populations of S0
  galaxies

abstract:
  Using high signal-to-noise ratio VLT/FORS2 long-slit spectroscopy, we have
studied the properties of the central stellar populations and dynamics of a
sample of S0 galaxies in the Fornax Cluster. The central absorption-line
indices in these galaxies correlate well with the central velocity dispersions
(Sigma0) in accordance with what previous studies found for elliptical
galaxies. However, contrary to what it is usually assumed for cluster
ellipticals, the observed correlations seem to be driven by systematic age and
alpha-element abundance variations, and not changes in overall metallicity. We
also found that the observed scatter in the Index-Sigma0 relations can be
partially explained by the rotationally-supported nature of these systems.
Indeed, even tighter correlations exist between the line indices and the
maximum circular velocity of the galaxies. This study suggests that the
dynamical mass is the physical property driving these correlations, and for S0
galaxies such masses have to be estimated assuming a large degree of rotational
support. The observed trends imply that the most massive S0s have the shortest
star-formation timescales and the oldest stellar populations.


title:
Anisotropic behaviors of massless Dirac fermions in graphene under
  periodic potential

abstract:
  Charge carriers of graphene show neutrino-like linear energy dispersions as
well as chiral behavior near the Dirac point. Here we report highly unusual and
unexpected behaviors of these carriers in applied external periodic potentials,
i.e., in graphene superlattices. The group velocity renormalizes highly
anisotropically even to a degree that it is not changed at all for states with
wavevector in one direction but is reduced to zero in another, implying the
possibility that one can make nanoscale electronic circuits out of graphene not
by cutting it but by drawing on it in a non-destructive way. Also, the type of
charge carrier species (e.g. electron, hole or open orbit) and their density of
states vary drastically with the Fermi energy, enabling one to tune the Fermi
surface-dominant properties significantly with gate voltage. These results
address the fundamental question of how chiral massless Dirac fermions
propagate in periodic potentials and point to a new possible path for nanoscale
electronics.