title:
Twisting and Rieffel's deformation of locally compact quantum groups.
  Deformation of the Haar measure

abstract:
  We develop the twisting construction for locally compact quantum groups. A
new feature, in contrast to the previous work of M. Enock and the second
author, is a non-trivial deformation of the Haar measure. Then we construct
Rieffel's deformation of locally compact quantum groups and show that it is
dual to the twisting. This allows to give new interesting concrete examples of
locally compact quantum groups, in particular, deformations of the classical
$az+b$ group and of the Woronowicz' quantum $az+b$ group.


title: A locally compact quantum group of triangular matrices

abstract:
  We construct a one parameter deformation of the group of $2\times 2$ upper
triangular matrices with determinant 1 using the twisting construction. An
interesting feature of this new example of a locally compact quantum group is
that the Haar measure is deformed in a non-trivial way. Also, we give a
complete description of the dual $\cs$-algebra and the dual comultiplication.


title: Experimental disagreements with Extended Unitarity

abstract:
  In production processes, e.g. J/Psi -> omega-pi-pi or pbar-p -> 3pi, the
sigma and fo(980) overlap in the same partial wave. The conjecture of Extended
Unitarity (EU) states that the pi-pi pair should have the same phase variation
as pi-pi elastic scattering. This is an extension of Watson's theorem beyond
its original derivation, which stated only that the s-dependence of a single
resonance should be universal. The prediction of EU is that the deep dip
observed in pi-pi elastic scattering close to 1 GeV should also appear in
production data. Four sets of data disagree with this prediction. All require
different relative magnitudes of sigma and fo(980). That being so, a fresh
conjecture is to rewrite the 2-body unitarity relation for production in terms
of observed magnitudes. This leads to a prediction different to EU. Central
production data from the AFS experiment fit naturally to this hypothesis.


title: Effective resistance of random trees

abstract:
  We investigate the effective resistance $R_n$ and conductance $C_n$ between
the root and leaves of a binary tree of height $n$. In this electrical network,
the resistance of each edge $e$ at distance $d$ from the root is defined by
$r_e=2^dX_e$ where the $X_e$ are i.i.d. positive random variables bounded away
from zero and infinity. It is shown that
$\mathbf{E}R_n=n\mathbf{E}X_e-(\operatorname
{\mathbf{Var}}(X_e)/\mathbf{E}X_e)\ln n+O(1)$ and $\operatorname
{\mathbf{Var}}(R_n)=O(1)$. Moreover, we establish sub-Gaussian tail bounds for
$R_n$. We also discuss some possible extensions to supercritical Galton--Watson
trees.


title:
The origin of infinitely divisible distributions: from de Finetti's
  problem to Levy-Khintchine formula

abstract:
  The article provides an historical survey of the early contributions on
infinitely divisible distributions starting from the pioneering works of de
Finetti in 1929 up to the canonical forms developed in the thirties by
Kolmogorov, Levy and Khintchine. Particular attention is paid to single out the
personal contributions of the above authors that were published in Italian,
French or Russian during the period 1929-1938. In Appendix we report the
translation from the Russian into English of a fundamental paper by Khintchine
published in Moscow in 1937.


title:
The wetting problem of fluids on solid surfaces. Part 2: the contact
  angle hysteresis

abstract:
  In part 1, we proposed a model of dynamics of wetting for slow movements near
a contact line formed at the interface of two immiscible fluids and a solid
when viscous dissipation remains bounded. The contact line is not a material
line and a Young-Dupr\'e equation for the apparent dynamic contact angle taking
into account the line celerity was proposed. In this paper we consider a form
of the interfacial energy of a solid surface in which many small oscillations
are superposed on a slowly varying function. For a capillary tube, a scaling
analysis of the microscopic law associated with the Young-Dupr\'e dynamic
equation yields a macroscopic equation for the motion of the contact line. The
value of the deduced apparent dynamic contact angle yields for the average
response of the line motion a phenomenon akin to the stick-slip motion of the
contact line on the solid wall. The contact angle hysteresis phenomenon and the
modelling of experimentally well-known results expressing the dependence of the
apparent dynamic contact angle on the celerity of the line are obtained.
Furthermore, a qualitative explanation of the maximum speed of wetting (and
dewetting) can be given.


title: Large cardinals and gap-1 morasses

abstract:
  We present a new partial order for directly forcing morasses to exist that
enjoys a significant homogeneity property. We then use this forcing in a
reverse Easton iteration to obtain an extension universe with morasses at every
regular uncountable cardinal, while preserving all n-superstrong (0<n<omega+1),
hyperstrong and 1-extendible cardinals. In the latter case, a preliminary
forcing to make the GCH hold is required. Our forcing yields morasses that
satisfy an extra property related to the homogeneity of the partial order; we
refer to them as mangroves and prove that their existence is equivalent to the
existence of morasses. Finally, we exhibit a partial order that forces
universal morasses to exist at every regular uncountable cardinal, and use this
to show that universal morasses are consistent with n-superstrong, hyperstrong,
and 1-extendible cardinals. This all contributes to the second author's outer
model programme, the aim of which is to show that L-like principles can hold in
outer models which nevertheless contain large cardinals.


title:
Geometrical dynamics: spin as a result of rotation with superluminal
  speed

abstract:
  Dynamics is considered as a corollary of the space-time geometry. Evolution
of a particle in the space-time is described as a chain of connected equivalent
geometrical objects. Space-time geometry is determined uniquely by the world
function $\sigma $. Proper modification of the Minkowskian world function for
large space-time interval leads to wobbling of the chain, consisted of timelike
straight segments. Statistical description of the stochastic world chain
coincides with the quantum description by means of the Schr\"{o}dinger
equation. Proper modification of the Minkowskian world function for small
space-time interval may lead to appearance of a world chain, having a shape of
a helix with timelike axis. Links of the chain are spacelike straight segments.
Such a world chain describes a spatial evolution of a particle. In other words,
the helical world chain describes the particle rotation with superluminal
velocity. The helical world chain associated with the classical Dirac particle,
whose world line is a helix. Length of world chain link cannot be arbitrary. It
is determined by the space-time geometry and, in particular, by the elementary
length. There exists some discrimination mechanism, which can discriminate some
world chains.


title:
A closer look at the indications of q-generalized Central Limit Theorem
  behavior in quasi-stationary states of the HMF model

abstract:
  We give a closer look at the Central Limit Theorem (CLT) behavior in
quasi-stationary states of the Hamiltonian Mean Field model, a paradigmatic one
for long-range-interacting classical many-body systems. We present new
calculations which show that, following their time evolution, we can observe
and classify three kinds of long-standing quasi-stationary states (QSS) with
different correlations. The frequency of occurrence of each class depends on
the size of the system. The different microsocopic nature of the QSS leads to
different dynamical correlations and therefore to different results for the
observed CLT behavior.

categories: cond-mat.stat-mech astro-ph nucl-th physics.plasm-ph


title: Dynamical density functional theory with hydrodynamic interaction

abstract:
  This paper has been withdrawn by the author due to the incorrect application
of the divergence theorem to Eqs 7, 8 and 9.


title: Quantised Vortices in an Exciton-Polariton Fluid

abstract:
  One of the most striking quantum effects in a low temperature interacting
Bose gas is superfluidity. First observed in liquid 4He, this phenomenon has
been intensively studied in a variety of systems for its amazing features such
as the persistence of superflows and the quantization of the angular momentum
of vortices. The achievement of Bose-Einstein condensation (BEC) in dilute
atomic gases provided an exceptional opportunity to observe and study
superfluidity in an extremely clean and controlled environment. In the solid
state, Bose-Einstein condensation of exciton polaritons has now been reported
several times. Polaritons are strongly interacting light-matter
quasi-particles, naturally occurring in semiconductor microcavities in the
strong coupling regime and constitute a very interesting example of composite
bosons. Even though pioneering experiments have recently addressed the
propagation of a fluid of coherent polaritons, still no conclusive evidence is
yet available of its superfluid nature. In the present Letter, we report the
observation of spontaneous formation of pinned quantised vortices in the
Bose-condensed phase of a polariton fluid by means of phase and amplitude
imaging. Theoretical insight into the possible origin of such vortices is
presented in terms of a generalised Gross-Pitaevskii equation. The implications
of our observations concerning the superfluid nature of the non-equilibrium
polariton fluid are finally discussed.


title: Parton showers with quantum interference: leading color, spin averaged

abstract:
  We have previously described a mathematical formulation for a parton shower
based on the approximation of strongly ordered virtualities of successive
parton splittings. Quantum interference, including interference among different
color and spin states, is included. In this paper, we add the further
approximations of taking only the leading color limit and averaging over spins,
as is common in parton shower Monte Carlo event generators. Soft gluon
interference effects remain with this approximation. We find that the leading
color, spin averaged shower in our formalism is similar to that in other shower
formulations. We discuss some of the differences.


title: Stable Manifolds and the Transition to Turbulence in Pipe Flow

abstract:
  Lower-branch traveling waves and equilibria computed in pipe flow and other
shear flows appear intermediate between turbulent and laminar motions. We take
a step towards connecting these lower-branch solutions to transition by
deriving a numerical method for finding certain special disturbances of the
laminar flow in a short pipe. These special disturbances cause the disturbed
velocity field to approach the lower-branch solution by evolving along its
stable manifold. If the disturbance were slightly smaller, the flow would
relaminarize, and if slightly larger, it would transition to a turbulent state.


title:
Solutions to open problems in Neeb's recent survey on
  infinite-dimensional Lie groups

abstract:
  We solve three open problems concerning infinite-dimensional Lie groups posed
in a recent survey article by K.-H. Neeb:
  (1) There exists a subgroup of some infinite-dimensional Lie group G which
does not admit an initial Lie subgroup structure;
  (2) The pathology cannot occur if G is a direct limit of an ascending
sequence of finite-dimensional Lie groups;
  (3) Every such direct limit group is a ``topological group with Lie algebra''
in the sense of Hofmann and Morris.
  Moreover, we prove a version of Borel's Theorem announced in the survey,
ensuring the existence of compactly supported smooth diffeomorphisms with given
Taylor series around a fixed point p (provided the tangent map at p has
positive determinant).


title:
Testing a Riemannian twisted solar loop model from EUV data and magnetic
  topology

abstract:
  Compact Riemannian solar twisted magnetic flux tube surfaces model are tested
against solar extreme ultraviolet (EUV) lines observations, allowing us to
compute the diameter and height of solar plasma loops. The relation between
magnetic and torsion energies is found for a nonplanar solar twisted
(torsioned) loop to be $10^{9}$, which shows that the contribution of torsion
energy to the solar loop is extremely weaker than the magnetic energy
contribution. In this case solar loops of up $5000 km$ in diameter can be
reached. The height of $220.000 km$ is used to obtain an estimate for torsion
based on the Riemannian flux tube surface, which yields ${\tau}_{0}=0.9{\times}
10^{-8} m^{-1}$ which coincides with one of the data of
$(0.9{\pm}0.4){\times}10^{-8}m^{-1}$ obtained by Lopez-Fuentes et al (2003).
This result tells us that the Riemannian flux tube model for plasma solar loops
is consistent with experimental results in solar physics. These results are
obtained for a homogeneous twisted solar loop. By making use of Moffatt-Ricca
theorem for the bounds on torsional energy of unknotted vortex filaments,
applied to magnetic topology, one places bounds on the lengths of EUV solar
loops. New results as the vorticity of the plasma flow along the tube is also
computed in terms of the flux tube twist.


title:
Fitting the luminosity data from type Ia supernovae in the frame of the
  Cosmic Defect theory

abstract:
  The Cosmic Defect (CD) theory is reviewed and used to fit the data for the
accelerated expansion of the universe, obtained from the apparent luminosity of
192 SnIa's. The fit from CD is compared with the one obtained by means of
$\Lambda $CDM. The results from both theories are in good agreement and the
fits are satisfactory. The correspondence between both approaches is discussed
and interpreted.


title: The Suprafroth (Superconducting Froth)

abstract:
  The structure and dynamics of froths have been subjects of intense interest
due to the desire to understand the behaviour of complex systems where
topological intricacy prohibits exact evaluation of the ground state. The
dynamics of a traditional froth involves drainage and drying in the cell
boundaries, thus it is irreversible. We report a new member to the froths
family: suprafroth, in which the cell boundaries are superconducting and the
cell interior is normal phase. Despite very different microscopic origin,
topological analysis of the structure of the suprafroth shows that statistical
von Neumann and Lewis laws apply. Furthermore, for the first time in the
analysis of froths there is a global measurable property, the magnetic moment,
which can be directly related to the suprafroth structure. We propose that this
suprafroth is a new, model system for the analysis of the complex physics of
two-dimensional froths.


title: Bi-Hermitian gray surfaces II

abstract:
  The aim of this paper is to classify bi-Hermitian compact surfaces $(M,g)$
whose Ricci tensor $\rho$ satisfies the relation $\nabla_X\rho(X,X)
=\frac13X\tau g(X,X)$.


title:
Positively and negatively excited random walks on integers, with
  branching processes

abstract:
  We consider excited random walks on the integers with a bounded number of
i.i.d. cookies per site which may induce drifts both to the left and to the
right. We extend the criteria for recurrence and transience by M. Zerner and
for positivity of speed by A.-L. Basdevant and A. Singh to this case and also
prove an annealed central limit theorem. The proofs are based on results from
the literature concerning branching processes with migration and make use of a
certain renewal structure.


title: A Framework for Designing Teleconsultation Systems in Africa

abstract:
  All of the countries within Africa experience a serious shortage of medical
professionals, particularly specialists, a problem that is only exacerbated by
high emigration of doctors with better prospects overseas. As a result, those
that remain in Africa, particularly those practicing in rural regions,
experience a shortage of specialists and other colleagues with whom to exchange
ideas. Telemedicine and teleconsultation are key areas that attempt to address
this problem by leveraging remote expertise for local problems. This paper
presents an overview of teleconsultation in the developing world, with a
particular focus on how lessons learned apply to Africa. By teleconsultation,
we are addressing non-real-time communication between health care professionals
for the purposes of providing expertise and informal recommendations, without
the real-time, interactive requirements typical of diagnosis and patient care,
which is impractical for the vast majority of existing medical practices. From
these previous experiences, we draw a set of guidelines and examine their
relevance to Ghana in particular. Based on 6 weeks of needs assessment, we
identify key variables that guide our framework, and then illustrate how our
framework is used to inform the iterative design of a prototype system.


title: Resonance Trapping in Protoplanetary Disks. I. Coplanar Systems

abstract:
  Mean-motion resonances (MMRs) are likely to play an important role both
during and after the lifetime of a protostellar gas disk. We study the
dynamical evolution and stability of planetary systems containing two giant
planets on circular orbits near a 2:1 resonance and closer. We find that by
having the outer planet migrate inward, the two planets can capture into either
the 2:1, 5:3, or 3:2 MMR. We use direct numerical integrations of ~1000 systems
in which the planets are initially locked into one of these resonances and
allowed to evolve for up to ~10^7 yr. We find that the final eccentricity
distribution in systems which ultimately become unstable gives a good fit to
observed exoplanets. Next, we integrate ~500 two-planet systems in which the
outer planet is driven to continuously migrate inward, resonantly capturing the
inner; the systems are evolved until either instability sets in or the planets
reach the star. We find that although the 5:3 resonance rapidly becomes
unstable under migration, the 2:1 and 3:2 are very stable. Thus the lack of
observed exoplanets in resonances closer than 2:1, if it continues to hold up,
may be a primordial signature of the planet formation process.


title: Asynchronous Remote Medical Consultation for Ghana

abstract:
  Computer-mediated communication systems can be used to bridge the gap between
doctors in underserved regions with local shortages of medical expertise and
medical specialists worldwide. To this end, we describe the design of a
prototype remote consultation system intended to provide the social,
institutional and infrastructural context for sustained, self-organizing growth
of a globally-distributed Ghanaian medical community. The design is grounded in
an iterative design process that included two rounds of extended design
fieldwork throughout Ghana and draws on three key design principles (social
networks as a framework on which to build incentives within a self-organizing
network; optional and incremental integration with existing referral
mechanisms; and a weakly-connected, distributed architecture that allows for a
highly interactive, responsive system despite failures in connectivity). We
discuss initial experiences from an ongoing trial deployment in southern Ghana.


title: Supersymmetry in Elementary Particle Physics

abstract:
  These lectures, presented at the 2006 TASI summer school, give a general
introduction to supersymmetry, emphasizing its application to models of
elementary particle physics at the 100 GeV energy scale. I discuss the
following topics: the construction of supersymmetric Lagrangians with scalars,
fermions, and gauge bosons, the structure and mass spectrum of the Minimal
Supersymmetric Standard Model (MSSM), the measurement of the parameters of the
MSSM at high-energy colliders, and the solutions that the MSSM gives to the
problems of electroweak symmetry breaking and dark matter.


title: The DNA Inequality in Non-Convex Regions

abstract:
  A simple plane closed curve $\Gamma$ satisfies the DNA Inequality if the
average curvature of any closed curve contained inside $\Gamma$ exceeds the
average curvature of $\Gamma$. In 1997 Lagarias and Richardson proved that all
convex curves satisfy the DNA Inequality and asked whether this is true for any
non-convex curve. They conjectured that the DNA Inequality holds for certain
L-shaped curves. In this paper, we disprove this conjecture for all L-Shapes
and construct a large class of non-convex curves for which the DNA Inequality
holds. We also give a polynomial-time procedure for determining whether any
specific curve in a much larger class satisfies the DNA Inequality.


title:
Tracking Down a Critical Halo Mass for Killing Galaxies through the
  Growth of the Red-Sequence

abstract:
  Red-sequence galaxies record the history of terminated star-formation in the
Universe and can thus provide important clues to the mechanisms responsible for
this termination. We construct composite samples of published cluster and field
galaxy photometry in order to study the build-up of galaxies on the
red-sequence, as parameterised by the dwarf-to-giant ratio (DGR). We find that
the DGR in clusters is higher than that of the field at all redshifts, implying
that the faint end of the red-sequence was established first in clusters. We
find that the DGR evolves with redshift for both samples, consistent with the
``down-sizing'' picture of star formation. We examine the predictions of
semi-analytic models for the DGR and find that neither the magnitude of its
environmental dependence nor its evolution is correctly predicted in the
models. Red-sequence DGRs are consistently too high in the models, the most
likely explanation being that the strangulation mechanism used to remove hot
gas from satellite galaxies is too efficient. Finally we present a simple toy
model including a threshold mass, below which galaxies are not strangled, and
show that this can predict the observed evolution of the field DGR.


title: Hebbian Inspecificity in the Oja Model

abstract:
  Recent work on Long Term Potentiation in brain slices shows that Hebb's rule
is not completely synapse-specific, probably due to intersynapse diffusion of
calcium or other factors. We extend the classical Oja unsupervised model of
learning by a single linear neuron to include Hebbian inspecificity, by
introducing an error matrix E, which expresses possible crosstalk between
updating at different connections. We show the modified algorithm converges to
the leading eigenvector of the matrix EC, where C is the input covariance
matrix. When there is no inspecificity, this gives the classical result of
convergence to the first principal component of the input distribution (PC1).
We then study the outcome of learning using different versions of E. In the
most biologically plausible case, arising when there are no intrinsically
privileged connections, E has diagonal elements Q and off- diagonal elements
(1-Q)/(n-1), where Q, the quality, is expected to decrease with the number of
inputs n. We analyze this error-onto-all case in detail, for both uncorrelated
and correlated inputs. We study the dependence of the angle theta between PC1
and the leading eigenvector of EC on b, n and the amount of input activity or
correlation. (We do this analytically and using Matlab calculations.) We find
that theta increases (learning becomes gradually less useful) with increases in
b, particularly for intermediate (i.e. biologically-realistic) correlation
strength, although some useful learning always occurs up to the trivial limit Q
= 1/n. We discuss the relation of our results to Hebbian unsupervised learning
in the brain.


title:
Strong decays $B_{s0} \to B_s \pi$ and $B_{s1} \to B^*_s \pi $ with
  light-cone QCD sum rules

abstract:
  In this article, we calculate the strong coupling constants $g_{B_{s0} B_s
\eta}$ and $g_{B_{s1} B^*_s \eta}$ with the light-cone QCD sum rules. Then we
take into account the small $\eta-\pi^0$ transition matrix according to
Dashen's theorem, and obtain the small decay widths for the isospin violation
processes $B_{s0}\to B_s\eta\to B_s\pi^0$ and $B_{s1}\to B_s^*\eta\to
B_s^*\pi^0$. We can search the strange-bottomed $(0^+,1^+)$ mesons $B_{s0}$ and
$B_{s1}$ in the invariant $B_s \pi^0$ and $B^*_s \pi^0$ mass distributions
respectively.


title: Critical Review of Path Integral Formulation

abstract:
  The path integral formulation in quantum mechanics corresponds to the first
quantization since it is just to rewrite the quantum mechanical amplitude into
many dimensional integrations over discretized coordinates $x_n$. However, the
path integral expression cannot be connected to the dynamics of classical
mechanics, even though, superficially, there is some similarity between them.
Further, the field theory path integral in terms of many dimensional
integrations over fields does not correspond to the field quantization. We
clarify the essential difference between Feynman's original formulation of path
integral in QED and the modern version of the path integral method prevailing
in lattice field theory calculations, and show that the former can make a
correct second quantization while the latter cannot quantize fields at all and
its physical meaning is unknown.


title: Possible Knot-type Time-dependent Quantum-mechanically Dynamical System

abstract:
  We illustrate schematically a possible traversing along the path of
trefoil-type and $8_{18}$ knots during a specific time period by considering a
quantum-mechanic system which satisfies a specific kind of phase dynamics of
quantum mechanics. This result is relevant to the composite particle which is
present in the initial or final configuration.


title:
Slowly evolving early universe and a phenomenological model for
  time-dependent fundamental constants and the leptonic masses

abstract:
  A phenomenological model with an extreme accuracy is proposed for the cosmic
time variation of the primordial fundamental constants (e, h, G and c) and the
leptonic masses. The model is purely exploratory in that at the very early
times the light speed is purposely modeled to be negligibly small, indicating a
very slowly expanding universe around t=0. The impact of this idea in cosmology
and its modeling is overwhelming.


title: Continuum shell model: From Ericson to conductance fluctuations

abstract:
  We discuss an approach for studying the properties of mesoscopic systems,
where discrete and continuum parts of the spectrum are equally important. The
approach can be applied (i) to stable heavy nuclei and complex atoms near the
continuum threshold, (ii) to nuclei far from the region of nuclear stability,
both of the regions being of great current interest, and (iii) to mesoscopic
devices with interacting electrons. The goal is to develop a new consistent
version of the continuum shell model that simultaneously takes into account
strong interaction between fermions and coupling to the continuum. Main
attention is paid to the formation of compound resonances, their statistical
properties, and correlations of the cross sections. We study the Ericson
fluctuations of overlapping resonances and show that the continuum shell model
nicely describes universal properties of the conductance fluctuations.


title:
Absence of coexisting phase of quark-antiquark and diquark condensed
  phases in the extended Gross-Neveu model in $2 + 1$ dimensions

abstract:
  We show that the coexisting phase of quark-antiquark and diquark condensed
phases is absent in the cold quark matter in the $2 + 1$ dimensional extended
Gross-Neveu model, which is in sharp contrast to the case of $3 + 1$
dimensional Nambu--Jona-Lasinio model.


title: Artin formalism for Selberg zeta functions of co-finite Kleinian groups

abstract:
  Let $\Gamma\backslash\mathbb H^3$ be a finite-volume quotient of the
upper-half space, where $\Gamma\subset {\rm SL}(2,\mathbb C)$ is a discrete
subgroup. To a finite dimensional unitary representation $\chi$ of $\Gamma$ one
associates the Selberg zeta function $Z(s;\Gamma;\chi)$. In this paper we prove
the Artin formalism for the Selberg zeta function. Namely, if $\tilde\Gamma$ is
a finite index group extension of $\Gamma$ in ${\rm SL}(2,\mathbb C)$, and
$\pi={\rm Ind}_{\Gamma}^{\tilde\Gamma}\chi$ is the induced representation, then
$Z(s;\Gamma;\chi)=Z(s;\tilde\Gamma;\pi)$. In the second part of the paper we
prove by a direct method the analogous identity for the scattering function,
namely $\phi(s;\Gamma;\chi)=\phi(s;\tilde\Gamma;\pi)$, for an appropriate
normalization of the Eisenstein series.


title:
Probing of $Wtb$ Anomalous Couplings via the $tW$ Channel of Single Top
  Production

abstract:
  The potential of LHC for investigation of the $W$-$t$-$b$ vertex through the
$tW$ channel of single top quark production is studied. Unlike the other two
single top quark production processes ($t-$channel and $s-$channel), the $tW$
channel provides the possibility to study the $Wtb$ vertex without receiving
contamination from FCNC. This study has been done at parton level but is
involved the separation of signal from backgrounds when both $W$-bosons decay
to leptons. In this study $\mathcal{CP}$ is assumed to be conserved. The 68%
C.L. bounds on the non-Standard Model couplings are estimated.


title: Relation between quantum tomography and optical Fresnel transform

abstract:
  Corresponding to optical Fresnel transformation characteristic of ray
transfer matrix elements (A;B;C;D); AD-BC = 1, there exists Fresnel operator
F(A;B;C;D) in quantum optics, we show that under the Fresnel transformation the
pure position density |x><x| becomes the tomographic density |x>_rs,rs_<x|,
which is just the Radon transform of the Wigner operator, i.e.,
  F|x><x|F^(+) = |x>_rs,rs_<x|= \int dx'dp'delta[x-(Dx'-Bp')]*Wigner operator
where s, r are the complex-value expression of (A;B;C;D). So the probability
distribution for the Fresnel quadrature phase is the tomography (Radon
transform of Wigner function), and the tomogram of a state |phi> is just the
wave function of its Fresnel transformed state F|phi>, i.e. rs_<x||phi>=
<x|F^(+)|phi>. Similarly, we find F|p><p|F^(+) = |p>_rs,rs_<p|= \int
dx'dp'delta[x-(Ap'-Cx')]*Wigner operator.


title: Active Quantum Memory Using Oscillating Dark States

abstract:
  An active method for long time storage of quantum superposition state in
atomic system using the Oscillating Dark States (ODS) is presented. Quantum
state of a three-level $\Lambda$ configuration atomic system oscillates
periodically between two ground levels, when two pairs of classical detuning
laser fields driving the system into the ODS under evolving adiabatic
conditions. When considering another uploading/unloading adiabatic conditions
and applying the oscillation of the ODS to quantum state storage, surprisingly,
we can obtain the greatly suppressed decoherence of the system and high
fidelity of the retrieved state, even if decay factor of coherence term of the
system density matrix $\gamma_{21}$$\cdot$ $t$$ \gg$1. The storage time is not
limited by coherence decay time of the atomic system any longer, and can be
thousands of times longer than that in those passive schemes without additional
laser fields.


title:
On smooth curves endowed with a large automorphism $p$-group in
  characteristic $p>0$

abstract:
  Let $k$ be an algebraically closed field of characteristic $p>0$ and $C$ a
connected nonsingular projective curve over $k$ with genus $g \geq 2$. This
paper continues the work begun by Lehr and Matignon, namely the study of "big
actions", i.e. the pairs $(C,G)$ where $G$ is a $p$-subgroup of the
$k$-automorphism group of $C$ such that$\frac{|G|}{g} >\frac{2 p}{p-1}$. If
$G_2$ denotes the second ramification group of $G$ at the unique ramification
point of the cover $C \to C/G$, we display necessary conditions on $G_2$ for
$(C,G)$ to be a big action, which allows us to pursue the classification of big
actions. Our main source of examples comes from the construction of curves with
many rational points using ray class field theory for global function fields,
as initiated by J-P. Serre and followed by Lauter and Auer. In particular, we
obtain explicit examples of big actions with $G_2$ abelian of large exponent.


title:
On standard forms of 1--dominations between knots with same Gromov
  volumes

abstract:
  Let $k$ and $k'$ be two knots in 3-sphere. Say $k$ 1--dominates $k'$, if
there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of
$k_i$.
  Theorem: Suppose that any companion of $k$ is prime. If $k$ 1--dominates $k'$
with the same Gromov volume, then $k'$ can be obtained from $k$ by finitely
many de-satellizations.
  The condition of "same Gromov volume" clearly can not be removed. We also
give a new construction of 1-domination between knots with same Gromov volume
to show that the condition "any companion of $k$ is prime" can not be removed.


title:
Additional information decreases the estimated entanglement using the
  Jaynes principle

abstract:
  We study a particular example considered in {[Phys. Rev. A {\bf 59,} 1799
(1999)]}, concerning the statistical inference of quantum entanglement using
the Jaynes principle. Assume a Clauser-Horne-Simony-Holt (CHSH) Bell operator,
a sum of two operators $\sqrt{2}(X+Z)$. Given only an average of the Bell-CHSH
operator, we may overestimate entanglement. However, the estimated entanglement
is decreased (never increases) when we use the expectation value of the
operator $X$ as additional information. A minimum entanglement state is
obtained by minimizing the variance of the observable $X$.


title: Unconditional no-hidden-variables theorem

abstract:
  Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate
version of no-hidden-variables theorem. We derive a proposition concerning the
quantum theory under the existence of the Bloch sphere in a single spin-1/2
system. The existence of a single classical probability space for measurement
outcome within the formalism of von Neumann's projective measurement does not
coexist with the proposition concerning the quantum theory. We have to give up
the existence of such a classical probability space for measurement outcome in
the two-dimensional Hilbert space formalism of the quantum theory. The quantum
theory does not accept a hidden-variable interpretation in the two-dimensional
space.


title:
Finiteness of mapping degrees and ${\rm PSL}(2,{\R})$-volume on graph
  manifolds

abstract:
  For given closed orientable 3-manifolds $M$ and $N$ let $\c{D}(M,N)$ be the
set of mapping degrees from $M$ to $N$. We address the problem: For which $N$,
$\c{D}(M,N)$ is finite for all $M$? The answer is known in Thurston's picture
of closed orientable irreducible 3-manifolds unless the target is a non-trivial
graph manifold. We prove that for each closed non-trivial graph manifold $N$,
$\c{D}(M,N)$ is finite for all graph manifold $M$.
  The proof uses a recently developed standard forms of maps between graph
manifolds and the estimation of the $\widetilde{\rm PSL}(2,{\R})$-volume for
certain class of graph manifolds.


title: Efficient Matrix Product State Method for periodic boundary conditions

abstract:
  We introduce an efficient method to calculate the ground state of
one-dimensional lattice models with periodic boundary conditions. The method
works in the representation of Matrix Product States (MPS), related to the
Density Matrix Renormalization Group (DMRG) method. It improves on a previous
approach by Verstraete et al. We introduce a factorization procedure for long
products of MPS matrices, which reduces the computational effort from m^5 to
m^3, where m is the matrix dimension, and m ~ 100 - 1000 in typical cases. We
test the method on the S=1/2 and S=1 Heisenberg chains. It is also applicable
to non-translationally invariant cases. The new method makes ground state
calculations with periodic boundary conditions about as efficient as
traditional DMRG calculations for systems with open boundaries.


title: On the connected components of moduli spaces of finite flat models

abstract:
  We prove that the non-ordinary component is connected in the moduli spaces of
finite flat models of two-dimensional local Galois representations over finite
fields. This was conjectured by Kisin. As an application to global Galois
representations, we prove a theorem on the modularity comparing a deformation
ring and a Hecke ring.


title:
Possibility of using dual frequency to control chaotic oscillations of a
  spherical bubble

abstract:
  Acoustic cavitation bubbles are known to exhibit highly nonlinear and
unpredictable chaotic dynamics. Their inevitable role in applications like
sonoluminescence, sonochemistry and medical procedures suggests that their
dynamics be controlled. Reducing chaotic oscillations could be the first step
in controlling the bubble dynamics by increasing the predictability of the
bubble response to an applied acoustic field. One way to achieve this concept
is to perturb the acoustic forcing. Recently, due to the improvements
associated with using dual frequency sources, this method has been the subject
of many studies which have proved its applicability and advantages. Due to this
reason, in this paper, the oscillations of a spherical bubble driven by a dual
frequency source, were studied and compared to the ones driven by a single
source. Results indicated that using dual frequency had a strong impact on
reducing the chaotic oscillations to regular ones. The governing parameters
influencing its dynamics are the secondary frequency and its phase difference
with the fundamental frequency. Also using dual frequency forcing may arm us by
the possibility of generating oscillations of desired amplitudes. To our
knowledge the investigation of the ability of using a dual frequency forcing to
control chaotic oscillations are presented for the first time in this paper.


title:
Uniform asyptotic formulae for eigenfunctions of Sturm--Liouville
  operators with singular potentials

abstract:
  In this paper we study a Sturm--Liouville operator $Ly=-y''+q(x)y$ in the
space $L_2[0,\pi]$ with Direchlet boundary conditions. Here the potential $q$
is a fitst order distribution $q\in W_2^{-1}[0,\pi]$. Such operators were
defined in our previous papers. Here we study an asymptotic behaviour of
eigenfunctions with uniform estimates of rests. We obtain this estimates also
for potentials from Sobolev spaces $q\in W_2^{\theta-1}$, where
$\theta\in[0,1/2)$.


title:
Convexity and smoothness of scale functions and de Finetti's control
  problem

abstract:
  Under appropriate conditions, we obtain smoothness and convexity properties
of $q$-scale functions for spectrally negative L\'evy processes. Our method
appeals directly to very recent developments in the theory of potential
analysis of subordinators. As an application of the latter results to scale
functions, we are able to continue the very recent work of \cite{APP2007} and
\cite{Loe}. We strengthen their collective conclusions by showing, amongst
other results, that whenever the L\'evy measure has a density which is log
convex then for $q>0$ the scale function $W^{(q)}$ is convex on some half line
$(a^*,\infty)$ where $a^*$ is the largest value at which $W^{(q)\prime}$
attains its global minimum. As a consequence we deduce that de Finetti's
classical actuarial control problem is solved by a barrier strategy where the
barrier is positioned at height $a^*$.


title:
Phonon modulation of the spin-orbit interaction as a spin relaxation
  mechanism in InSb quantum dots

abstract:
  We calculate the spin relaxation rates in a parabolic InSb quantum dots due
to the spin interaction with acoustical phonons. We considered the deformation
potential mechanism as the dominant electron-phonon coupling in the
Pavlov-Firsov spin-phonon Hamiltonian. By studying suitable choices of magnetic
field and lateral dot size, we determine regions where the spin relaxation
rates can be practically suppressed. We analyze the behavior of the spin
relaxation rates as a function of an external magnetic field and mean quantum
dot radius. Effects of the spin admixture due to Dresselhaus contribution to
spin-orbit interaction are also discussed.


title: Predictability in Semi-Analytic Models of Galaxy Formation

abstract:
  We propose a general framework to scrutinize the performance of semi-analytic
codes of galaxy formation. The approach is based on the analysis of the outputs
from the model after a series of perturbations in the input parameters
controlling the baryonic physics. The perturbations are chosen in a way that
they do not change the results in the luminosity function or mass function of
the galaxy population. We apply this approach on a particular semi-analytic
model called GalICS. We chose to perturb the parameters controlling the
efficiency of star formation and the efficiency of supernova feedback. We keep
track of the baryonic and observable properties of the central galaxies in a
sample of dark matter halos with masses ranging from 10^{10} M_sol to 10^{13}
M_sol. We find very different responses depending on the halo mass. For small
dark matter halos its central galaxy responds in a highly predictable way to
small perturbation in the star formation and feedback efficiency. For massive
dark matter halos, minor perturbations in the input parameters can induce large
fluctuations on the properties of its central galaxy, at least $\sim 0.1$ in
(B-V) color or $\sim 0.5$ mag in U or r filter, in a seemingly random fashion.
We quantify this behavior through an objective scalar function we call
predictability. We argue that finding the origin of this behavior needs
additional information from other approximations and different semi-analytic
codes. Furthermore, the implementation of an scalar objective function, such as
the predictability, opens the door to quantitative benchmarking of
semi-analytic codes based on its numerical performance.


title: A General Relativistic Rotating Evolutionary Universe - Part II

abstract:
  As a sequel to (Berman, 2008a), we show that the rotation of the Universe can
be dealt by generalised Gaussian metrics, defined in this paper.
Robertson-Walker's metric has been employed with proper-time, in its standard
applications; the generalised Gaussian metric imply in the use of a
non-constant temporal metric coefficient modifying Robertson-Walker's standard
form. Experimental predictions are made


title: The Coarse Geometry of Merger Trees in \Lambda CDM

abstract:
  We introduce the contour process to describe the geometrical properties of
merger trees. The contour process produces a one-dimensional object, the
contour walk, which is a translation of the merger tree. We portray the contour
walk through its length and action. The length is proportional to to the number
of progenitors in the tree, and the action can be interpreted as a proxy of the
mean length of a branch in a merger tree.
  We obtain the contour walk for merger trees extracted from the public
database of the Millennium Run and also for merger trees constructed with a
public Monte-Carlo code which implements a Markovian algorithm. The trees
correspond to halos of final masses between 10^{11} h^{-1} M_sol and 10^{14}
h^{-1} M_sol. We study how the length and action of the walks evolve with the
mass of the final halo. In all the cases, except for the action measured from
Markovian trees, we find a transitional scale around 3 \times 10^{12} h^{-1}
M_sol. As a general trend the length and action measured from the Markovian
trees show a large scatter in comparison with the case of the Millennium Run
trees.


title: Emergence of a Helical Flux Rope Under an Active Region Prominence

abstract:
  Continuous observations were obtained of active region 10953 with the Solar
Optical Telescope (SOT) on board the \emph{Hinode} satellite during 2007 April
28 to May 9. A prominence was located over the polarity inversion line (PIL) in
the south-east of the main sunspot. These observations provided us with a time
series of vector magnetic fields on the photosphere under the prominence. We
found four features: (1) The abutting opposite-polarity regions on the two
sides along the PIL first grew laterally in size and then narrowed. (2) These
abutting regions contained vertically-weak, but horizontally-strong magnetic
fields. (3) The orientations of the horizontal magnetic fields along the PIL on
the photosphere gradually changed with time from a normal-polarity
configuration to a inverse-polarity one. (4) The horizontal-magnetic field
region was blueshifted. These indicate that helical flux rope was emerging from
below the photosphere into the corona along the PIL under the pre-existing
prominence. We suggest that this supply of a helical magnetic flux into the
corona is associated with evolution and maintenance of active-region
prominences.


title: Phase Space Factor for Two-Body Decay if One Product is a Stable Tachyon

abstract:
  We calculate the phase space factor for a two-body decay in which one of the
products is a tachyon. Two threshold conditions, a lower and an upper one, are
derived in terms of the masses of the particles and the speed of a preferred
frame. Implicit in the derivation is a consistently formulated quantum field
theory of tachyons in which spontaneous Lorentz symmetry breaking occurs. The
result is to be contrasted with a parallel calculation by Hughes and
Stephenson, which, however, implicitly adheres to strict Lorentz invariance of
the underlying quantum field theory and produces the conclusion that there is
no threshold for this process.


title: Coronal transverse magnetohydrodynamic waves in a solar prominence

abstract:
  Solar prominences are cool 10$^4$ Kelvin plasma clouds supported in the
surrounding 10$^6$ Kelvin coronal plasma by as-yet undetermined mechanisms.
Observations from \emph{Hinode} show fine-scale threadlike structures
oscillating in the plane of the sky with periods of several minutes. We suggest
these transverse magnetohydrodynamic waves may represent Alfv\'en waves
propagating on coronal magnetic field lines and these may play a role in
heating the corona.


title: Quantum Information Processing with Quantum Zeno Many-Body Dynamics

abstract:
  We show how the quantum Zeno effect can be exploited to control quantum
many-body dynamics for quantum information and computation purposes. In
particular, we consider a one dimensional array of three level systems
interacting via a nearest-neighbour interaction. By encoding the qubit on two
levels and using simple projective frequent measurements yielding the quantum
Zeno effect, we demonstrate how to implement a well defined quantum register,
quantum state transfer on demand, universal two-qubit gates and two-qubit
parity measurements. Thus, we argue that the main ingredients for universal
quantum computation can be achieved in a spin chain with an always-on and
constant many-body Hamiltonian. We also show some possible modifications of the
initially assumed dynamics in order to create maximally entangled qubit pairs
and single qubit gates.


title:
Magnetic shear-driven instability and turbulent mixing in magnetized
  protostellar disks

abstract:
  Observations of protostellar disks indicate the presence of the magnetic
field of thermal (or superthermal) strength. In such a strong magnetic field,
many MHD instabilities responsible for turbulent transport of the angular
momentum are suppressed. We consider the shear-driven instability that can
occur in protostellar disks even if the field is superthermal. This instability
is caused by the combined influence of shear and compressibility in a
magnetized gas and can be an efficient mechanism to generate turbulence in
disks. The typical growth time is of the order of several rotation periods.


title:
Ab initio calculations of electron affinity and ionization potential of
  carbon nanotubes

abstract:
  By combining ab initio all-electron localized orbital and pseudopotential
plane-wave approaches we report on calculations of the electron affinity (EA)
and the ionization potential (IP) of (5, 5) and (7, 0) single-wall carbon
nanotubes. The role played by finite-size effects and nanotube termination has
been analysed by comparing several hydrogen-passivated and not passivated
nanotube segments. The dependence of the EA and IP on both the quantum
confinement effect, due to the nanotube finite length, and the charge
accumulation on the edges, is studied in detail. Also, the EA and IP are
compared to the energies of the lowest unoccupied and highest occupied states,
respectively, upon increasing the nanotube length. We report a slow convergence
with respect to the number of atoms. The effect of nanotube packing in arrays
on the electronic properties is eventually elucidated as a function of the
intertube distance.


title: n-Monotone exact functionals

abstract:
  We study n-monotone functionals, which constitute a generalisation of
n-monotone set functions. We investigate their relation to the concepts of
exactness and natural extension, which generalise the notions of coherence and
natural extension in the behavioural theory of imprecise probabilities. We
improve upon a number of results in the literature, and prove among other
things a representation result for exact n-monotone functionals in terms of
Choquet integrals.


title: Asymptotics of semigroups generated by operator matrices

abstract:
  We survey some known results about operator semigroup generated by operator
matrices with diagonal or coupled domain. These abstract results are applied to
the characterization of well-/ill-posedness for a class of evolution equations
with dynamic boundary conditions on domains or metric graphs. In particular,
our ill-posedness results on the heat equation with general Wentzell-type
boundary conditions complement those previously obtained by, among others,
Bandle-von Below-Reichel and Vitillaro-V\'azquez.


title:
Enhance the Efficiency of Heuristic Algorithm for Maximizing Modularity
  Q

abstract:
  Modularity Q is an important function for identifying community structure in
complex networks. In this paper, we prove that the modularity maximization
problem is equivalent to a nonconvex quadratic programming problem. This result
provide us a simple way to improve the efficiency of heuristic algorithms for
maximizing modularity Q. Many numerical results demonstrate that it is very
effective.


title: Tunneling Anisotropic Magnetoresistance in Co/AlOx/Au Tunnel Junctions

abstract:
  We observe spin-valve-like effects in nano-scaled thermally evaporated
Co/AlOx/Au tunnel junctions. The tunneling magnetoresistance is anisotropic and
depends on the relative orientation of the magnetization direction of the Co
electrode with respect to the current direction. We attribute this effect to a
two-step magnetization reversal and an anisotropic density of states resulting
from spin-orbit interaction. The results of this study points to future
applications of novel spintronics devices involving only one ferromagnetic
layer.


title: Symmetry of models versus models of symmetry

abstract:
  A model for a subject's beliefs about a phenomenon may exhibit symmetry, in
the sense that it is invariant under certain transformations. On the other
hand, such a belief model may be intended to represent that the subject
believes or knows that the phenomenon under study exhibits symmetry. We defend
the view that these are fundamentally different things, even though the
difference cannot be captured by Bayesian belief models. In fact, the failure
to distinguish between both situations leads to Laplace's so-called Principle
of Insufficient Reason, which has been criticised extensively in the
literature.
  We show that there are belief models (imprecise probability models, coherent
lower previsions) that generalise and include the Bayesian belief models, but
where this fundamental difference can be captured. This leads to two notions of
symmetry for such belief models: weak invariance (representing symmetry of
beliefs) and strong invariance (modelling beliefs of symmetry). We discuss
various mathematical as well as more philosophical aspects of these notions. We
also discuss a few examples to show the relevance of our findings both to
probabilistic modelling and to statistical inference, and to the notion of
exchangeability in particular.


title: Projective embeddings of homogeneous spaces with small boundary

abstract:
  We study open equivariant projective embeddings of homogeneous spaces such
that the complement of the open orbit does not contain divisors. Criterions of
existence of such an embedding are considered and finiteness of isomorphism
classes of embeddings for a given homogeneous space is proved. Any embedding
with small boundary is realized as a GIT-quotient associated with a
linearization of the trivial line bundle on the space of the canonical
embedding. The generalized Cox's construction and the theory of bunched rings
allow us to describe basic geometric properties of embeddings with small
boundary in combinatorial terms.


title:
3d-electron induced magnetic phase transition in half-metallic
  semi-Heusler alloys

abstract:
  We study the effect of the non-magnetic 3\textit{d} atoms on the magnetic
properties of the half-metallic (HM) semi-Heusler alloys Co$_{1-x}$Cu$_{x}$MnSb
and Ni$_{1-x}$Cu$_{x}$MnSb ($0 \leq x \leq 1$) using first-principles
calculations. We determine the magnetic phase diagram of both systems at zero
temperature and obtain a phase transition from a ferromagnetic to an
antiferromagnetic state. For low Cu concentrations the ferromagnetic RKKY-like
exchange mechanism is dominating, while the antiferromagnetic superexchange
coupling becomes important for larger Cu content leading to the observed
magnetic phase transition. A strong dependence of the magnetism in both systems
on the position of the Fermi level within the HM gap is obtained. Obtained
results are in good agreement with the available experimental data.


title: Families index for manifolds with hyperbolic cusp singularities

abstract:
  Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds
with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's
treatment of Dirac-type operators associated to these metrics by weaking the
hypotheses on the boundary families through the use of Fredholm perturbations
as in the family index theorem of Melrose and Piazza and by treating the index
of families of such operators. We also extend the index theorem of Moroianu and
Leichtnam-Mazzeo-Piazza to families of perturbed Dirac-type operators
associated to fibered cusp metrics (sometimes known as fibered boundary
metrics).


title: Vector meson cross sections at HERA

abstract:
  Inelastic and elastic (exclusive) cross section measurements of vector meson
production at HERA are discussed.


title:
Comment on "Direct space-time observation of pulse tunneling in an
  electromagnetic band gap"

abstract:
  The investigation presented by Doiron, Hache, and Winful [Phys. Rev. A 76,
023823 (2007)] is not valid for the tunneling process as claimed in the paper.


title:
Intertwining relations and extended eigenvalues for analytic Toeplitz
  operators

abstract:
  We study the intertwining relations between analytic Toeplitz operators
induced on the Hardy space H^2 by analytic functions bounded on the open unit
disc. Our work centers on the connection between intertwining between the
Toeplitz operators the image containment between their symbols, as well as on
the nature of the intertwining operator. We use our results to study the
"extended eigenvalues" of analytic Toeplitz operators, i.e., the special case
where the operator is intertwined with a scalar multiple of itself.


title:
A non-universal transition to asymptotic freedom in low-energy quantum
  gravity

abstract:
  The model of low-energy quantum gravity by the author has the property of
asymptotic freedom at very short distances. The character of transition to
asymptotic freedom is studied here. It is shown that this transition is not
universal, but the one obeys the scaling rule: the range of this transition in
units of $r/E^{1/2}$, where $r$ is a distance between particles and $E$ is an
energy of the screening particle, is the same for any micro-particle. This
range for a proton is between $10^{-11} - 10^{-13}$ meter, while for an
electron it is approximately between $10^{-13} - 10^{-15}$ meter.


title: Central Exclusive Diffractive MSSM Higgs-Boson Production at the LHC

abstract:
  The prospects for central exclusive diffractive (CED) production of MSSM
Higgs bosons at the LHC are reviewed. It is shown that the CED channels, making
use of forward proton detectors at the LHC installed at 220 m and 420 m
distance around ATLAS and / or CMS, can provide important information on the
Higgs sector of the MSSM. In particular, CED production of the neutral CP-even
Higgs bosons h and H and their decays into bottom quarks has the potential to
probe interesting regions of the M_A--tan_beta parameter plane of the MSSM and
may give access to the bottom Yukawa couplings of the Higgs bosons up to masses
of M_H \approx 250 GeV.


title:
Nonrelativistic Multiferroicity in the Nonstoichiometric Spin s=1/2
  Spiral Chain Cuprate LiCu2O2

abstract:
  We argue for a recently observed puzzling multiferroic behavior in s=1/2 1D
chain cuprate LiCu2O2 with edge-shared arrangement of CuO4 plaquettes and
incommensurate spiral spin ordering can be consistently explained if one takes
into account the nonrelativistic exchange-induced electric polarization on the
Cu2+ centers substituting for the positions native for the Cu1+ ions. These
substituent centers are proved to be an effective probe of the spin
incommensurability and magnetic field effects.


title: An Enumerative Function

abstract:
  We define an enumerative function F(n,k,P,m) which is a generalization of
binomial coefficients. Special cases of this function are also power function,
factorials, rising factorials and falling factorials.
  The first section of the paper is an introduction.
  In the second section we derive an explicit formula for F. From the
expression for the power function we obtain a number theory result.
  Then we derive a formula which shows that the case of arbitrary m may be
reduced to the case m=0. This formula extends Vandermonde convolution.
  In the second section we describe F by the series of recurrence relations
with respect to each of arguments k, n, and P. As a special case of the first
recurrence relation we state a binomial identity. As a consequence of the
second recurrence relation we obtain relation for coefficients of Chebyshev
polynomial of both kind. This means that these polynomials might be defined in
pure combinatorial way.


title:
Space Weather Application Using Projected Velocity Asymmetry of Halo
  CMEs

abstract:
  Halo coronal mass ejections (HCMEs) originating from regions close to the
center of the Sun are likely to be responsible for severe geomagnetic storms.
It is important to predict geo-effectiveness of HCMEs using observations when
they are still near the Sun. Unfortunately, coronagraphic observations do not
provide true speeds of CMEs due to the projection effects. In the present
paper, we present a new technique allowing estimate the space speed and
approximate source location using projected speeds measured at different
position angles for a given HCME (velocity asymmetry). We apply this technique
to HCMEs observed during 2001-2002 and find that the improved speeds are better
correlated with the travel times of HCMEs to Earth and with the magnitudes
ensuing geomagnetic storms.


title: Conductivity of dielectric and thermal atom-wall interaction

abstract:
  We compare the experimental data of the first measurement of a temperature
dependence of the Casimir-Polder force by Obrecht et al. [Phys. Rev. Lett. {\bf
98}, 063201 (2007)] with the theory taking into account small, but physically
real, static conductivity of the dielectric substrate. The theory is found to
be inconsistent with the data. The conclusion is drawn that the conductivity of
dielectric materials should not be included in the model of the dielectric
response in the Lifshitz theory. This conclusion obtained from the long
separation measurement is consistent with related but different results
obtained for semiconductors and metals at short separations.


title: Minimum Leaf Out-branching and Related Problems

abstract:
  Given a digraph $D$, the Minimum Leaf Out-Branching problem (MinLOB) is the
problem of finding in $D$ an out-branching with the minimum possible number of
leaves, i.e., vertices of out-degree 0. We prove that MinLOB is polynomial-time
solvable for acyclic digraphs. In general, MinLOB is NP-hard and we consider
three parameterizations of MinLOB. We prove that two of them are NP-complete
for every value of the parameter, but the third one is fixed-parameter
tractable (FPT). The FPT parametrization is as follows: given a digraph $D$ of
order $n$ and a positive integral parameter $k$, check whether $D$ contains an
out-branching with at most $n-k$ leaves (and find such an out-branching if it
exists). We find a problem kernel of order $O(k^2)$ and construct an algorithm
of running time $O(2^{O(k\log k)}+n^6),$ which is an `additive' FPT algorithm.
We also consider transformations from two related problems, the minimum path
covering and the maximum internal out-tree problems into MinLOB, which imply
that some parameterizations of the two problems are FPT as well.


title: Charm and bottom baryons in nonperturbative quark dynamics

abstract:
  We use the Field Correlator Method in QCD to calculate the masses of
$\Sigma_c$, $\Xi_c$ and recently observed $\Sigma_b$, $\Xi_b$ baryons and their
orbital excitations.


title: Neighboring Fractions in Farey Subsequences

abstract:
  We present explicit formulas for the computation of the neighbors of several
elements of Farey subsequences.


title:
Inward and Outward Node Accessibility in Complex Networks as Revealed by
  Non-Linear Dynamics

abstract:
  In this work, the outward and inward accessibilities of individual nodes are
defined and their potential for application is illustrated with respect to the
investigation of 6 different types of networks. The outward accessibility
quantifies the potential of an individual node for accessing other nodes
through random walks. The inward accessibility measures the potential of a
given node of being accessed by other nodes. Both the inward and outward
accessibilities are measured with respect to successive time steps along the
walks, providing an interesting means for the characterization of the transient
non-linear dynamics of accessibility. Self-avoiding walks are considered here
because they are more purposive and necessarily finite (unlike traditional
random walks). The results include the identification of the fact that the
inward values tend to be much smaller than the outward values, the tendency of
the inward accessibility to be highly correlated with the node degree while the
outward values are mostly uncorrelated with that measurements, the distinct
behavior of the accessibility in geographical networks, the dominance of hubs
in scale free networks, as well as the enhanced uniformity of the
accessibilities for the path-regular model. Also investigated was the
possibility to predict the accessibility of a given node in terms of its
respective degree. The concepts of inward and outward accessibility, as well as
the several obtained results, have several implications and potential for
applications to several real-time problems including disease spreading, WWW
surfing, protein interaction, cortical networks and network attacks, among
others.


title:
Exponential estimates for plurisubharmonic functions and stochastic
  dynamics

abstract:
  We prove exponential estimates for plurisubharmonic functions with respect to
Monge-Ampere measures with Holder continuous potential. As an application, we
obtain several stochastic properties for the equilibrium measures associated to
holomorphic maps on projective spaces. More precisely, we prove the exponential
decay of correlations, the central limit theorem for general d.s.h.
observables, and the large deviations theorem for bounded d.s.h. observables
and Holder continuous observables.


title:
A Decisive test to confirm or rule out the existence of dark matter
  emulators using gravitational wave observations

abstract:
  We consider stable modified theories of gravity that reproduce galactic
rotation curves and the observed amount of weak lensing without dark matter. In
any such model gravity waves follow a different geodesic from that of other
massless particles. For a specific class of models which we call "dark matter
emulators," over cosmological distances this results in an easily detectable
and difference between the arrival times of the pulse of gravity waves from
some cosmic event and those of photons or neutrinos. For a repeat of SN 1987a
(which took place in the Large Magellanic Cloud) the time lag is in the range
of days. For the recent gamma ray burst, GRB 070201 (which seems to have taken
place on the edge of the Andromeda galaxy) the time lag would be in the range
of about two years.


title: Generalizing TeVeS Cosmology

abstract:
  I consider an extented version of Bekenstein's Tensor-Vector-Scalar theory
where the action of the vector field is of a general Einstein-Ether form. This
work presents the cosmological equations of this theory, both at the background
and perturbed level, for scalar, vector and tensor perturbation modes. By
solving the background equations in the radiation era analytically, to an
excellent approximation, I construct the primordial adiabatic perturbation for
a general family of scalar field kinetic functions.


title: Ultra High-Energy Cosmic Ray Observations

abstract:
  The year 2007 has furnished us with outstanding results about the origin of
the most energetic cosmic rays: a flux suppression as expected from the
GZK-effect has been observed in the data of the HiRes and Auger experiments and
correlations between the positions of nearby AGN and the arrival directions of
trans-GZK events have been observed by the Pierre Auger Observatory. The latter
finding marks the beginning of ultra high-energy cosmic ray astronomy and is
considered a major breakthrough starting to shed first light onto the sources
of the most extreme particles in nature. This report summarizes those
observations and includes other major advances of the field, mostly presented
at the 30th International Cosmic Ray Conference held in Merida, Mexico, in July
2007. With increasing statistics becoming available from current and even
terminated experiments, systematic differences amongst different experiments
and techniques can be studied in detail which is hoped to improve our
understanding of experimental techniques and their limitations.


title:
A Nearly Linear-Time PTAS for Explicit Fractional Packing and Covering
  Linear Programs

abstract:
  We give an approximation algorithm for packing and covering linear programs
(linear programs with non-negative coefficients). Given a constraint matrix
with n non-zeros, r rows, and c columns, the algorithm computes feasible primal
and dual solutions whose costs are within a factor of 1+eps of the optimal cost
in time O((r+c)log(n)/eps^2 + n).


title: Online variants of the cross-entropy method

abstract:
  The cross-entropy method is a simple but efficient method for global
optimization. In this paper we provide two online variants of the basic CEM,
together with a proof of convergence.


title:
Density functional methods for polymers: a coil-globule transition case
  study

abstract:
  We consider a free energy functional on the monomer density function that is
suitable for the study of coil-globule transition. We demonstrate, with
explicitly stated assumptions, why the entropic contribution is in the form of
the Kullback-Leibler distance, and that the energy contribution is given by
two-body and three-body terms. We then solve for the free energy analytically
on a set of trial density functions, and reproduce de Gennes' classical theory
on polymer coil-globule transition. We then discuss how our formalism can be
applied to study polymer dynamics from the perspective of dynamical density
function theory.


title:
Effects of inhomogeneities and thermal fluctuations on the spectral
  function of a model d-wave superconductor

abstract:
  We compute the spectral function $A({\bf k}, \omega)$ of a model
two-dimensional high-temperature superconductor, at both zero and finite
temperatures $T$. We assume that an areal fraction $c_{\beta}$ of the
superconductor has a large gap $\Delta$ ($\beta$ regions), while the rest has a
smaller $\Delta$ ($\alpha$ regions), both of which are randomly distributed in
space. We find that $A({\bf k}, \omega)$ is most strongly affected by
inhomogeneity near the point $\mathbf k = (\pi, 0)$ (and the symmetry-related
points). For $c_\beta\simeq 0.5$, $A({\bf k}, \omega)$ exhibits two double
peaks (at positive and negative energy) near this k-point if the difference
between $\Delta_\alpha$ and $\Delta_\beta$ is sufficiently large in comparison
to the hopping integral. The strength of the inhomogeneity required to produce
a split spectral function peak suggests that inhomogeneity is unlikely to be
the cause of a second branch in the dispersion relation. Thermal fluctuations
also affect $A({\bf k}, \omega)$ most strongly near $\mathbf k = (\pi,0)$.
Typically, peaks that are sharp at $T = 0$ become reduced in height, broadened,
and shifted toward lower energies with increasing $T$; the spectral weight near
$\mathbf k = (\pi, 0)$ becomes substantial at zero energy for $T$ greater than
the phase-ordering temperature.


title:
Energy gaps, magnetism, and electric field effects in bilayer graphene
  nanoribbons

abstract:
  Using a first principles density functional electronic structure method, we
study the energy gaps and magnetism in bilayer graphene nanoribbons as a
function of the ribbon width and the strength of an external electric field
between the layers. We assume AB (Bernal) stacking and consider both armchair
and zigzag edges and two edge alignments distinguished by a 60$^o$ rotation of
one layer with respect to the other. Armchair ribbons exhibit three classes of
bilayer gaps which decrease with increasing ribbon width. An external electric
field between the layers increases the gap in narrow ribbons and decreases the
gap for wide ribbons, a property which can be understood semi-analytically
using a $\pi$-band tight-binding model and perturbation theory. The magnetic
properties of zigzag edge ribbons are different for the two different edge
alignments, and not robust for all exchange-correlation approximations
considered. Bilayer ribbon gaps are sensitive to the presence or absence of
magnetism.


title: C*-algebras of labelled graphs II - Simplicity results

abstract:
  We prove simplicity and pure infiniteness results for a certain class of
labelled graph $C^*$-algebras. We show, by example, that this class of unital
labelled graph $C^*$-algebras is strictly larger than the class of unital graph
$C^*$-algebras.


title: On the characterization of expansion maps for self-affine tilings

abstract:
  We consider self-affine tilings in $\R^n$ with expansion matrix $\phi$ and
address the question which matrices $\phi$ can arise this way. In one
dimension, $\lambda$ is an expansion factor of a self-affine tiling if and only
if $|\lambda|$ is a Perron number, by a result of Lind. In two dimensions, when
$\phi$ is a similarity, we can speak of a complex expansion factor, and there
is an analogous necessary condition, due to Thurston: if a complex $\lambda$ is
an expansion factor of a self-similar tiling, then it is a complex Perron
number. We establish a necessary condition for $\phi$ to be an expansion matrix
for any $n$, assuming only that $\phi$ is diagonalizable over the complex
numbers. We conjecture that this condition on $\phi$ is also sufficient for the
existence of a self-affine tiling.


title:
Variation of fundamental constants in space and time: theory and
  observations

abstract:
  Review of recent works devoted to the temporal and spatial variation of the
fundamental constants and dependence of the fundamental constants on the
gravitational potential (violation of local position invariance) is presented.
  We discuss the variation of the fine structure constant $\alpha=e^2/\hbar c$,
strong interaction and fundamental masses (Higgs vacuum), e.g. the
electron-to-proton mass ratio $\mu=m_e/M_p$ or $X_e=m_e/\Lambda_{QCD}$ and
$X_q=m_q/\Lambda_{QCD}$. We also present new results from Big Bang
nucleosynthesis and Oklo natural nuclear reactor data and propose new
measurements of enhanced effects in atoms, nuclei and molecules, both in quasar
and laboratory spectra.


title:
The Dependence of Galaxy Morphology and Structure on Environment and
  Stellar Mass

abstract:
  From the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5), we extract a
sample of 4594 galaxies at redshifts 0.02<z<0.03, complete down to a stellar
mass of M=10^10 Msol. We quantify their structure (Sersic index), morphology
(Sersic index + ``Bumpiness''), and local environment. We show that morphology
and structure are intrinsically different galaxy properties, and we demonstrate
that this is a physically relevant distinction by showing that these properties
depend differently on galaxy mass and environment. Structure mainly depends on
galaxy mass whereas morphology mainly depends on environment. This is driven by
variations in star formation activity, as traced by color, which only weakly
affects the structure of a galaxy but strongly affects its morphological
appearance. The implication of our results is that the existence of the
morphology-density relation is intrinsic and not just due to a combination of
more fundamental, underlying relations. Our findings have consequences for
high-redshift studies, which often use some measure of structure as a proxy for
morphology. A direct comparison with local samples selected through visually
classified morphologies may lead to biases in the inferred evolution of the
morphological mix of the galaxy population, and misinterpretations in terms of
how galaxy evolution depends on mass and environment.


title:
Modeling Porous Dust Grains with Ballistic Aggregates I: Geometry and
  Optical Properties

abstract:
  We investigate the scattering and absorption of light by random ballistic
aggregates of spherical monomers. We present a general measure for the porosity
of an irregular particle. Three different classes of ballistic aggregates are
considered, with different degrees of porosity. Scattering and absorption cross
sections are calculated, using the discrete dipole approximation (DDA), for
grains of three compositions (50% silicate and 50% graphite; 50% silicate and
50% amorphous carbon; and 100% silicate), for wavelengths from 0.1 micron to 4
micron. For fixed particle mass, increased porosity increases the extinction at
short wavelengths, but decreases the extinction at wavelengths long compared to
the overall aggregate size. Scattering and absorption cross sections are
insensitive to monomer size as long as the constituent monomers are small
compared with the incident wavelength. We compare our accurate DDA results with
two other approximations: the analytical multi-layer sphere (MLS) model and
effective medium theory (EMT). For high porosity and/or absorptive materials,
the MLS model does not provide a good approximation for scattering and
absorption by ballistic aggregates. The EMT method provides a much better
approximation than the MLS model for these aggregates, with a typical
difference less than 20% in extinction and scattering cross sections compared
with DDA results, for all types, compositions and wavelengths probed in this
study.


title:
An upper bound for the lower central series quotients of a free
  associative algebra

abstract:
  Feigin and Shoikhet conjectured in math/0610410 that successive quotients
$B_m(A_n)$ of the lower central series filtration of a free associative algebra
$A_n$ have polynomial growth. In this paper we give a proof of this conjecture,
using the structure of $W_n$-representation on $B_m(A_n)$ which was defined in
math/0610410 . We also prove that the number of squares in a Young diagram $D$
corresponding to an irreducible $W_n$-module in the Jordan-Holder series of
$B_m(A_n)$ is bounded above by the integer $(m-1)^2+2[(n-2)/2](m-1)$. This
bound combined with MAGMA computations by Rains in math/0610410 allows us to
confirm the $W_n$-module structure of $B_3(A_3)$ conjectured in math/0610410 .


title: Backlund transformations for integrable lattice equations

abstract:
  We give new Backlund transformations (BTs) for some known integrable (in the
sense of being multidimensionally consistent) quadrilateral lattice equations.
As opposed to the natural auto-BT inherent in every such equation, these BTs
are of two other kinds. Specifically, it is found that some equations admit
additional auto-BTs (with Backlund parameter), whilst some pairs of apparently
distinct equations admit a BT which connects them.


title:
Decay for the wave and Schroedinger evolutions on manifolds with conical
  ends, Part I

abstract:
  Global in time dispersive estimates for the Schroedinger and wave evolutions
are obtained on manifolds with conical ends whose Hamiltonian flow exhibits
trapping. This paper deals with the case of initial data with "zero angular
momentum".


title:
Elastic parton scattering and non-statistical event-by-event mean-pt
  fluctuations in Au + Au collisions at RHIC

abstract:
  Non-statistical event-by-event mean-pt fluctuations in Au + Au collisions at
sqrt(s_NN) = 130 and 200 GeV are analyzed in AMPT with string-melting, and the
results are compared with STAR data. The analysis suggests that in-medium
elastic parton scattering may contribute greatly to the mean-p_t fluctuations
in relativistic heavy-ion collisions. Furthermore, it is demonstrated that
non-statistical event-by-event mean-pt fluctuations can be used to probe the
initial partonic dynamics in these collisions. The comparison shows that with
an in-medium elastic parton scattering cross section sigma_p=10 mb, AMPT with
string-melting can well reproduce sqrt(s_NN) = 130 GeV data on the centrality
dependence of non-statistical event-by-event mean-pt fluctuations. The
comparison also shows that the fluctuation data for sqrt(s_NN) = 200 GeV Au +
Au collisions can be well reproduced with sigma_p between 6 and 10 mb.


title:
Decay for the wave and Schroedinger evolutions on manifolds with conical
  ends, Part II

abstract:
  Global in time dispersive estimates for the Schroedinger and wave evolutions
are obtained on manifolds with conical ends whose Hamiltonian flow exhibits
trapping. This paper deals with the case of initial data with fixed "nonzero
angular momentum".


title: Efimov states embedded in the three-body continuum

abstract:
  We consider a multichannel generalization of the Fermi pseudopotential to
model low-energy atom-atom interactions near a magnetically tunable Feshbach
resonance, and calculate the adiabatic hyperspherical potential curves for a
system of three such interacting atoms. In particular, our model suggests the
existence of a series of quasi-bound Efimov states attached to excited
three-body thresholds, far above open channel collision energies. We discuss
the conditions under which such states may be supported, and identify which
interaction parameters limit the lifetime of these states. We speculate that it
may be possible to observe these states using spectroscopic methods, perhaps
allowing for the measurement of multiple Efimov resonances for the first time.


title:
The early-type galaxies NGC 1407 and NGC 1400 - I: spatially resolved
  radial kinematics and surface photometry

abstract:
  This is the first paper of a series focused on investigating the star
formation and evolutionary history of the two early-type galaxies NGC 1407 and
NGC 1400. They are the two brightest galaxies of the NGC 1407 (or Eridanus-A)
group, one of the 60 groups studied as part of the Group Evolution
Multi-wavelength Study (GEMS). Here we present new high signal-to-noise
long-slit spectroscopic data obtained at the ESO 3.6m telescope and
high-resolution multi-band imaging data from the HST/ACS and wide-field imaging
from Subaru Suprime-Cam. We spatially resolved integrated spectra out to 0.6
(NGC 1407) and 1.3 (NGC 1400) effective radii. The radial profiles of the
kinematic parameters v(rot), sigma, h3 and h4 are measured. The surface
brightness profiles are fitted to different galaxy light models and the colour
distributions analysed. The multi-band images are modelled to derive isophotal
shape parameters and residual galaxy images. The parameters from the surface
brightness profile fitting are used to estimate the mass of the possible
central supermassive black hole in NGC 1407. The galaxies are found to be
rotationally supported and to have a flat core in the surface brightness
profiles. Elliptical isophotes are observed at all radii and no fine structures
are detected in the residual galaxy images. From our results we can also
discard a possible interaction between NGC 1400, NGC 1407 and the group
intergalactic medium. We estimate a mass of 1.03x10^9 M(sun) for the
supermassive black hole in NGC 1407 galaxy.


title: The Application of kd-tree in Astronomy

abstract:
  The basic idea of the kd-tree algorithm is to recursively partition a point
set P by hyperplanes, and to store the obtained partitioning in a binary tree.
Due to its immense popularity, many applications in astronomy have been
implemented. The algorithm can been used to solve a near neighbor problem for
cross-identification of huge catalogs and realize the classification of
astronomical objects. Since kd-tree can speed up query and partition spaces,
some approaches based on it have been applied for photometric redshift
measurement. We give the case studies of kd-tree in astronomy to show its
importance and performance.


title:
The early-type galaxies NGC 1407 and NGC 1400 - II: star formation and
  chemical evolutionary history

abstract:
  We present a possible star formation and chemical evolutionary history for
two early-type galaxies NGC 1407 and NGC 1400. They are the two brightest
galaxies of the NGC 1407 (or Eridanus-A) group, one of the 60 groups studied as
part of the Group Evolution Multi-wavelength Study (GEMS). Our analysis is
based on new high signal-to-noise spatially resolved integrated spectra
obtained at the ESO 3.6m telescope, out to 0.6 (NGC 1407) and 1.3 (NGC 1400)
effective radii. Using Lick/IDS indices we estimate luminosity-weighted ages,
metallicities and $\alpha$-element abundance ratios. Colour radial
distributions from HST/ACS and Subaru Suprime-Cam multi-band wide-field imaging
are compared to colours predicted from spectroscopically determinated ages and
metallicities using single stellar population models. The galaxies formed over
half of their mass in a single short-lived burst of star formation (> 100
M(sun)/year) at redshift z>5. This likely involved an outside-in mechanism with
supernova-driven galactic winds, as suggested by the flatness of the
alpha-element radial profiles and the strong negative metallicity gradients.
Our results support the predictions of the revised version of the monolithic
collapse model for galaxy formation and evolution. We speculate that, since
formation the galaxies have evolved quiescently and that we are witnessing the
first infall of NGC 1400 in the group.


title: Geometry and rigidity of mapping class groups

abstract:
  We study the large scale geometry of mapping class groups MCG(S), using
hyperbolicity properties of curve complexes. We show that any self
quasi-isometry of MCG(S) (outside a few sporadic cases) is a bounded distance
away from a left-multiplication, and as a consequence obtain quasi-isometric
rigidity for MCG(S), namely that groups quasi-isometric to MCG(S) are virtually
equal to it. (The latter theorem was proved by Hamenstadt using different
methods). As part of our approach we obtain several other structural results: a
description of the tree-graded structure on the asymptotic cone of MCG(S); a
characterization of the image of the curve-complex projection map from MCG(S)
to the product of the curve complexes of essential subsurfaces of S; and a
construction of Sigma-hulls in MCG(S), an analogue of convex hulls.


title:
Reconstruction of Gas Temperature and Density Profiles of the Galaxy
  Cluster RX J1347.5-1145

abstract:
  We use observations of Sunyaev-Zel'dovich effect and X-ray surface brightness
to reconstruct the radial profiles of gas temperature and density under the
assumption of a spherically symmetric distribution of the gas. The method of
reconstruction, first raised by Silk & White, depends directly on the
observations of the Sunyaev-Zel'dovich effect and the X-ray surface brightness,
without involving additional assumptions such as the equation of state of the
gas or the conditions of hydrostatic equilibrium. We applied this method to the
cluster RX J1347.5-1145, which has both the Sunyaev-Zel'dovich effect and X-ray
observations with relative high precision. It is shown that it will be an
effective method to obtain the gas distribution in galaxy clusters. Statistical
errors of the derived temperature and density profiles of gas were estimated
according to the observational uncertainties.


title:
Viscous dissipative Chaplygin gas dominated homogenous and isotropic
  cosmological models

abstract:
  The generalized Chaplygin gas, which interpolates between a high density
relativistic era and a non-relativistic matter phase, is a popular dark energy
candidate. We consider a generalization of the Chaplygin gas model, by assuming
the presence of a bulk viscous type dissipative term in the effective
thermodynamic pressure of the gas. The dissipative effects are described by
using the truncated Israel-Stewart model, with the bulk viscosity coefficient
and the relaxation time functions of the energy density only. The corresponding
cosmological dynamics of the bulk viscous Chaplygin gas dominated universe is
considered in detail for a flat homogeneous isotropic
Friedmann-Robertson-Walker geometry. For different values of the model
parameters we consider the evolution of the cosmological parameters (scale
factor, energy density, Hubble function, deceleration parameter and luminosity
distance, respectively), by using both analytical and numerical methods. In the
large time limit the model describes an accelerating universe, with the
effective negative pressure induced by the Chaplygin gas and the bulk viscous
pressure driving the acceleration. The theoretical predictions of the
luminosity distance of our model are compared with the observations of the type
Ia supernovae. The model fits well the recent supernova data. From the fitting
we determine both the equation of state of the Chaplygin gas, and the
parameters characterizing the bulk viscosity. The evolution of the scalar field
associated to the viscous Chaplygin fluid is also considered, and the
corresponding potential is obtained. Hence the viscous Chaplygin gas model
offers an effective dynamical possibility for replacing the cosmological
constant, and to explain the recent acceleration of the universe.


title: On Limit Aperiodic G-Sets

abstract:
  We prove that the property to be limit aperiodic is preserved by the standard
construction with groups like extension, HNN extension and free product. We
also construct a non-limit aperiodic G-space.


title: Contracting an element from a cocircuit

abstract:
  We consider the situation that M and N are 3-connected matroids such that
|E(N)| > 3 and C* is a cocircuit of M with the property that M/y has an N-minor
for some y in C*. We show that either there is an element x in C* such that
si(M/x) or co(si(M/x)) is 3-connected with an N-minor, or there is a
four-element fan of M that contains two elements of C* and an element x such
that si(M/x) is 3-connected with an N-minor.


title: Same-sign single dilepton productions at the LHC

abstract:
  We examine the same-sign single dilepton productions of
$\ell_i^{\pm}\ell_j^{\pm} (\ell_{i,j}=e,\mu)$ in high-energy proton-proton
collisions at the Large Hadron Collider (LHC) in models with doubly charged
Higgs scalars as well as heavy Majorana neutrinos. We demonstrate that these
spectacular productions can be detected at the LHC for a class model in which
the doubly charged Higgs scalars couple only to the right-handed charged
leptons. The ranges of the possible doubly charged Higgs masses and mixings to
observe the processes at the LHC are discussed.


title:
The linear flows in the space of Krichever-Lax matrices over an
  algebraic curve

abstract:
  In \cite{kri02}, I. M. Krichever invented the space of matrices parametrizing
the cotangent bundle of moduli space of stable vector bundles over a compact
Riemann surface, which is named as the Hitchin system after the investigation
\cite{hit87}. We study a necessary and sufficient condition for the linearity
of flows on the space of Krichever-Lax matrices in a Lax representation in
terms of cohomological classes using the similar technique and analysis from
the work \cite{grif85} by P. A. Griffiths.


title: Huygens' principle and anomalously small radiation tails

abstract:
  This is a short account of recent joint work with T. Chmaj and A.
Rostworowski on asymptotic behavior of linear and nonlinear waves, as presented
at the conference devoted to Myron Mathisson held at the Banach Center, Warsaw
2007.


title: Meet homological mirror symmetry

abstract:
  In this paper, we introduce the interested reader to homological mirror
symmetry. After recalling a little background knowledge, we tackle the simplest
cases of homological mirror symmetry: curves of genus zero and one. We close by
outlining the current state of the field and mentioning what homo- logical
mirror symmetry has to say about other aspects of mirror symmetry.


title:
Early Formation of Dust in the Ejecta of Type Ib SN 2006jc and
  Temperature and Mass of the Dust

abstract:
  SN 2006jc is a peculiar supernova (SN), in which the formation of dust has
been confirmed at an early epoch of ~50 days after the explosion. We
investigate the possibility of such an earlier formation of dust grains in the
expanding ejecta of SN 2006jc, applying the Type Ib SN model that is developed
to reproduce the observed light curve. We find that the rapid decrease of the
gas temperature in SN 2006jc enables the condensation of C grains in the C-rich
layer at 40-60 days after the explosion, which is followed by the condensation
of silicate and oxide grains until ~200 days. The average radius of each grain
species is confined to be less than 0.01 micron due to the low gas density at
the condensation time. The calculated total dust mass reaches ~1.5 Msun, of
which C dust shares 0.7 Msun. On the other hand, based on the calculated dust
temperature, we show that the dust species and mass evaluated to reproduce the
spectral energy distribution observed by AKARI and MAGNUM at day 200 are
different from those obtained by the dust formation calculations; the dust
species contributing to the observed flux are hot C and FeS grains with masses
of $5.6 \times 10^{-4}$ Msun and $2.0 \times 10^{-3}$ Msun, respectively,
though we cannot defy the presence of a large amount of cold dust such as
silicate and oxide grains up to 0.5 Msun. One of the physical processes
responsible for the difference between calculated and evaluated masses of C and
FeS grains could be considered to be the destruction of small-sized clusters by
energetic photons and electrons prevailing within the ejecta at the earlier
epoch.


title: Impact of Dynamical Fermions on QCD Vacuum Structure

abstract:
  We examine how dynamical fermions affect both the UV and infrared structure
of the QCD vacuum. We consider large $28^3 \times 96$ lattices from the MILC
collaboration, using a gluonic definition of the topological charge density,
founded on a new over-improved stout-link smearing algorithm. The algorithm
reproduces established results from the overlap formalism and is designed to
preserve nontrivial topological objects including instantons. At short
distances we focus on the topological charge correlator, $<q(x) q(0) >$, where
negative values at small $x$ reveal a sign-alternating layered structure to the
topological-charge density of the QCD vacuum. We find that the magnitudes of
the negative dip in the $<q(x)q(0)>$ correlator and the positive $<q(0)^2>$
contact term are both increased with the introduction of dynamical fermion
degrees of freedom. This is in accord with expectations based on charge
renormalization and the vanishing of the topological susceptibility in the
chiral limit. At large distances we examine the extent to which instanton-like
objects are found on the lattice, and how their distributions vary between
quenched and dynamical gauge fields. We show that dynamical gauge fields
contain more instanton-like objects with an average size greater than in the
quenched vacuum. Finally, we directly visualize the topological charge density
in order to investigate the effects of dynamical sea-quark degrees of freedom
on topology.


title: Scalar Field Dark Energy Perturbations and their Scale Dependence

abstract:
  We estimate the amplitude of perturbation in dark energy at different length
scales for a quintessence model with an exponential potential. It is shown that
on length scales much smaller than hubble radius, perturbation in dark energy
is negligible in comparison to that in in dark matter. However, on scales
comparable to the hubble radius ($\lambda_{p}>1000\mathrm{Mpc}$) the
perturbation in dark energy in general cannot be neglected. As compared to the
$\Lambda$CDM model, large scale matter power spectrum is suppressed in a
generic quintessence dark energy model. We show that on scales $\lambda_{p} <
1000\mathrm{Mpc}$, this suppression is primarily due to different background
evolution compared to $\Lambda$CDM model. However, on much larger scales
perturbation in dark energy can effect matter power spectrum significantly.
Hence this analysis can act as a discriminator between $\Lambda$CDM model and
other generic dark energy models with $w_{de} \neq -1$.


title:
Two-Zero Symmetric Neutrino Mass Matrices in Minimal Supersymmetric
  SO(10)

abstract:
  The phenomenological neutrino mass matrix for two-zero symmetric texture has
been obtained and used to rule out all possible two-zero symmetric neutrino
mass matrices obtained from Yukawa couplings to $\mathbf{10}$ and
$\mathbf{126}$ Higgs representations within the framework of minimal
supersymmetric SO(10).


title: CESAM: a free code for stellar evolution calculations

abstract:
  The Cesam code is a consistent set of programs and routines which perform
calculations of 1D quasi-hydrostatic stellar evolution including microscopic
diffusion of chemical species and diffusion of angular momentum. The solution
of the quasi-static equilibrium is performed by a collocation method based on
piecewise polynomials approximations projected on a B-spline basis; that allows
stable and robust calculations, and the exact restitution of the solution, not
only at grid points, even for the discontinuous variables. Other advantages are
the monitoring by only one parameter of the accuracy and its improvement by
super-convergence. An automatic mesh refinement has been designed for adjusting
the localisations of grid points according to the changes of unknowns. For
standard models, the evolution of the chemical composition is solved by stiffly
stable schemes of orders up to four; in the convection zones mixing and
evolution of chemical are simultaneous. The solution of the diffusion equation
employs the Galerkin finite elements scheme; the mixing of chemicals is then
performed by a strong turbulent diffusion. A precise restoration of the
atmosphere is allowed for.


title:
Induced Gravity in Deconstructed Space at Finite Temperature --
  Self-consistent Einstein Universe

abstract:
  We study self-consistent cosmological solutions for an Einstein Universe in a
graph-based induced gravity model. The graph-based field theory has been
proposed by the present authors to generalize dimensional deconstruction. In
this paper, we consider self-consistent Einstein equations for a ``graph theory
space''. Especially, we demonstrate specific results for cycle graphs.


title: Additive properties of product sets in an arbitrary finite field

abstract:
  It is proved that for any two subsets $A$ and $B$ of an arbitrary finite
field $\Fq$ such that $|A||B|>q$ the identity $16AB=\Fq$ holds. Moreover, it is
established that for every subsets $X, Y\subset \Fq$ with the property
$|X||Y|\geqslant 2q$ the equality $8XY=\Fq$ holds.


title: Stars in the age of micro-arc-second astrometry

abstract:
  The understanding and modeling of the structure and evolution of stars is
based on statistical physics as well as on hydrodynamics. Today, a precise
identification and proper description of the physical processes at work in
stellar interiors are still lacking (one key point being that of transport
processes) while the comparison of real stars to model predictions, which
implies conversions from the theoretical space to the observational one,
suffers from uncertainties in model atmospheres. That results in uncertainties
on the prediction of stellar properties needed for galactic studies or
cosmology (as stellar ages and masses). In the next decade, progress is
expected from the theoretical, experimental and observational sides. I
illustrate some of the problems we are faced with when modeling stars and the
possible tracks towards their solutions. I discuss how future observational
ground-based or spatial programs (in particular those dedicated to
micro-arc-second astrometry, asteroseismology and interferometry) will provide
precise determinations of the stellar parameters and contribute to a better
knowledge of stellar interiors and atmospheres in a wide range of stellar
masses, chemical compositions and evolution stages.