title: Loss Fluctuations and Temporal Correlations in Network Queues

abstract:
  We consider data losses in a single node of a packet-switched Internet-like
network. We employ two distinct models, one with discrete and the other with
continuous one-dimensional random walks, representing the state of a queue in a
router. Both models {have} a built-in critical behavior with {a sharp}
transition from exponentially small to finite losses. It turns out that the
finite capacity of a buffer and the packet-dropping procedure give rise to
specific boundary conditions which lead to strong loss rate fluctuations at the
critical point even in the absence of such fluctuations in the data arrival
process.


title:
Mean-field approximations for the restricted solid-on-solid growth
  models

abstract:
  We study models for surface growth with a wetting and a roughening transition
using simple and pair mean-field approximations. The simple mean-field
equations are solved exactly and they predict the roughening transition and the
correct growth exponents in a region of the phase diagram. The pair mean-field
equations, which are solved numerically, show a better accordance with
numerical simulation and correctly predicts a growing interface with constant
velocity at the moving phase. Also, when detailed balance is fulfilled, the
pair mean field becomes the exact solution of the model.


title: Chiral Corrections and the Axial Charge of the Delta

abstract:
  Chiral corrections to the delta axial charge are determined using heavy
baryon chiral perturbation theory. Knowledge of this axial coupling is
necessary to assess virtual-delta contributions to nucleon and delta
observables. We give isospin relations useful for a lattice determination of
the axial coupling. Furthermore we detail partially quenched chiral
corrections, which are relevant to address partial quenching and/or mixed
action errors in lattice calculations of the delta axial charge.


title:
Quasinormal modes of black holes localized on the Randall-Sundrum
  2-brane

abstract:
  We investigate conformal scalar, electromagnetic, and massless Dirac
quasinormal modes of a brane-localized black hole. The background solution is
the four-dimensional black hole on a 2-brane that has been constructed by
Emparan, Horowitz, and Myers in the context of a lower dimensional version of
the Randall-Sundrum model. The conformally transformed metric admits a Killing
tensor, allowing us to obtain separable field equations. We find that the
radial equations take the same form as in the four-dimensional "braneless"
Schwarzschild black hole. The angular equations are, however, different from
the standard ones, leading to a different prediction for quasinormal
frequencies.


title:
Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the
  Polyakov loop

abstract:
  We present extensive studies on hot and dense quark matter with two light and
one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop
(so-called PNJL model). First we discuss prescription dependence in choosing
the Polyakov loop effective potential and propose a simple and rather sensible
ansatz. We look over quantitative comparison to the lattice measurement to
confirm that the model captures thermodynamic properties correctly. We then
analyze the phase structure with changing the temperature, quark chemical
potential, quark masses, and coupling constants. We particularly investigate
how the effective U_A(1) restoration and the induced vector-channel interaction
at finite density would affect the QCD critical point.


title: The Ponzano-Regge model

abstract:
  The definition of the Ponzano-Regge state-sum model of three-dimensional
quantum gravity with a class of local observables is developed. The main
definition of the Ponzano-Regge model in this paper is determined by its
reformulation in terms of group variables. The regularisation is defined and a
proof is given that the partition function is well-defined only when a certain
cohomological criterion is satisfied. In that case, the partition function may
be expressed in terms of a topological invariant, the Reidemeister torsion.
This proves the independence of our definition on the triangulation of the
3-manifold and on those arbitrary choices made in the regularisation. A further
corollary is that when the observable is a knot, the partition function (when
it exists) can be written in terms of the Alexander polynomial of the knot.
Various examples of observables in the three-sphere are computed explicitly.
Alternative regularisations of the Ponzano-Regge model by the simple cutoff
procedure and by the limit of the Turaev-Viro model are discussed, giving
successes and limitations of these approaches.


title:
Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills
  Theory

abstract:
  It is well known that there are no static non-Abelian monopole solutions in
pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions
exist in SU(N) gauge theory on the spaces R^2\times S^2 and R^1\times S^1\times
S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions
of pure Yang-Mills theory on T^1\times S^2, where T^1 is R^1 or S^1. Namely,
imposing SO(3)-invariance and some reality conditions, we consistently reduce
the Yang-Mills model on the above spaces to a non-Abelian analog of the \phi^4
kink model whose static solutions give SU(N) monopole (-antimonopole)
configurations on the space R^{1,1}\times S^2 via the above-mentioned
correspondence. These solutions can also be considered as instanton
configurations of Yang-Mills theory in 2+1 dimensions. The kink model on
R^1\times S^1 admits also periodic sphaleron-type solutions describing chains
of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They
correspond to chains of n static monopole-antimonopole pairs on the space
R^1\times S^1\times S^2 which can also be interpreted as instanton
configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature
(thermal time circle). We also describe similar solutions in Euclidean SU(N)
gauge theory on S^1\times S^3 interpreted as chains of n
instanton-antiinstanton pairs.


title: A connection whose curvature is the Lie bracket

abstract:
  Let G be a Lie group. On the trivial principal G-bundle over the Lie algebra
of G there is a natural connection whose curvature is the Lie bracket. The
exponential map is given by parallel transport of this connection. If G is the
diffeomorphism group of a manifold, the curvature of the natural connection is
the Lie bracket of vectorfields on the manifold. The motion of a ball rolling
on an oriented surface is the parallel transport of a similar connection on the
trivial SO(3)-bundle over the surface. If the surface is a plane or a sphere,
then the curvature of the connection is a scalar multiple of the Lie bracket in
the Lie algebra of SO(3).


title:
On Sp_4 modularity of Picard--Fuchs differential equations for
  Calabi--Yau threefolds (with an appendix by Vicentiu Pasol)

abstract:
  Motivated by the relationship of classical modular functions and
Picard--Fuchs linear differential equations of order 2 and 3, we present an
analogous concept for equations of order 4 and 5.


title: S-Z Power Spectra

abstract:
  There is some observational evidence for earlier evolution of clusters of
galaxies than predicted in the standard LambdaCDM model with a Gaussian
primordial density fluctuation field, and a low value for the mass variance
parameter sigma_8. Particularly difficult in this model is the interpretation
of possible excess CMB anisotropy on cluster scales as due to the
Sunyaev-Zeldovich (S-Z) effect. We have calculated S-Z power spectra in the
standard model, and in two alternative models which predict higher cluster
abundance - a model with non-Gaussian PDF, and an early dark energy model. As
anticipated, the levels of S-Z power in the latter two models are significantly
higher than in the standard model, and in good agreement with current
measurements of CMB anisotropy at high multipole values. Our results provide a
sufficient basis for testing the viability of the three models by futur high
quality measurements of cluster abundance and the anisotropy induced by the S-Z
effect.


title:
The BCS Critical Temperature for Potentials with Negative Scattering
  Length

abstract:
  We prove that the critical temperature for the BCS gap equation is given by
$T_c = \mu (8/\pi e^{\gamma -2} + o(1)) e^{\pi/(2\sqrt \mu a)}$ in the low
density limit $\mu\to 0$. The formula holds for a suitable class of interaction
potentials with negative scattering length $a$ in the absence of bound states.


title:
Unconventional pairing originating from disconnected Fermi surfaces in
  superconducting LaFeAsO$_{1-x}$F$_x$}

abstract:
  For a newly discovered iron-based high $T_c$ superconductor
LaFeAsO$_{1-x}$F$_x$, we have constructed a minimal model, where inclusion of
all the five Fe $d$ bands is found to be necessary. Random-phase approximation
is applied to the model to investigate the origin of superconductivity. We
conclude that the multiple spin fluctuation modes arising from the nesting
across the disconnected Fermi surfaces realize an extended s-wave pairing,
while d-wave pairing can also be another candidate.


title: Cocompact imbeddings and structure of weakly convergent sequences

abstract:
  Concentration compactness method is a powerful techniques for establishing
existence of minimizers for inequalities and of critical points of functionals
in general. The paper gives a functional-analytic formulation for the method in
Banach space, generalizing the Hilbert space case elaborated in \cite{ccbook}.
The key object is a dislocation space - a triple $(X,F,D)$, where $F$ is a
convex functional that defines a norm on Banach space $X$, and $D$ is a group
of isometries on $X$. Bounded sequences in dislocation spaces admit a
decomposition into an asymptotic sum "profiles" $w^{(n)}\in X$ dislocated by
actions of $D$, that is, a sum of the form $\sum_ng^{(n)}_kw^{(n)}$,
$g^{(n)}_k\in D$, while the remainder term converges weakly under actions of
any sequence $g_k\in D$ ({\em $D$-weak convergence}). This decomposition allows
to extend the weak convergence argument from variational problems with
compactness to problems where $X$ is {\em cocompactly} (relatively to the group
$D$) imbedded into a Banach space $Y$, that is, when every sequence $D$-weakly
convergent in $X$ is convergent in the norm of $Y$. We prove a general
statement on existence of minimizers in cocompact imbeddings that applies, in
particular to Sobolev imbeddings which lack compactness (unbounded domain,
critical exponent) including the subelliptic Sobolev spaces and spaces over
Riemannian manifolds.


title:
Killing-Yano Forms of a Class of Spherically Symmetric Space-Times I: A
  Unified Generation of Killing Vector Fields

abstract:
  Killing-Yano one forms (duals of Killing vector fields) of a class of
spherically symmetric space-times characterized by four functions are derived
in a unified and exhaustive way. For well-known space-times such as those of
Minkowski, Schwarzschild, Reissner-Nordstrom, Robertson-Walker and several
forms of de Sitter, these forms arise as special cases in a natural way.
Besides its two well-known forms, four more forms of de Sitter space-time are
also established with ten independent Killing vector fields for which four
different time evolution regimes can explicitly be specified by the symmetry
requirement. A family of space-times in which metric characterizing functions
are of the general form and admitting six or seven independent Killing vector
fields is presented.


title:
Killing-Yano Forms of a Class of Spherically Symmetric Space-Times II: A
  Unified Generation of Higher Forms

abstract:
  Killing-Yano (KY) two and three forms of a class of spherically symmetric
space-times that includes the well-known Minkowski, Schwarzschild,
Reissner-Nordstrom, Robertson-Walker and six different forms of de Sitter
space-times as special cases are derived in a unified and exhaustive manner. It
is directly proved that while the Schwarzschild and Reissner-Nordstrom
space-times do not accept any KY 3-form and they accept only one 2-form, the
Robertson-Walker space-time admits four KY 2-forms and only one KY 3-form.
Maximal number of KY-forms are obtained for Minkowski and all known forms of de
Sitter space-times. Complete lists comprising explicit expressions of KY-forms
are given.


title: Unbinding the Deuteron

abstract:
  We consider a description of the deuteron based on meson exchange potentials.
A key feature is the inclusion of the I=S=0 two-pion intermediate state
('sigma(600)') as a significant component of the inter-nucleon potential
energy. In this approach, deuteron binding is seen to be predominantly a
consequence of sigma(600) and omega(783) exchange, with a secondary tole played
by rho(770). We explore sensitivity of two-nucleon binding to changes in the
potential and thereby obtain an anthropic constraint -- that the deuteron
unbinds for a modest decrease (about 6%) in the attractive sigma(600)
potential.


title:
Matrix genetics, part 2: the degeneracy of the genetic code and the
  octave algebra with two quasi-real units (the genetic octave
  Yin-Yang-algebra)

abstract:
  Algebraic properties of the genetic code are analyzed. The investigations of
the genetic code on the basis of matrix approaches ("matrix genetics") are
described. The degeneracy of the vertebrate mitochondria genetic code is
reflected in the black-and-white mosaic of the (8*8)-matrix of 64 triplets, 20
amino acids and stop-signals. This mosaic genetic matrix is connected with the
matrix form of presentation of the special 8-dimensional Yin-Yang-algebra and
of its particular 4-dimensional case. The special algorithm, which is based on
features of genetic molecules, exists to transform the mosaic genomatrix into
the matrices of these algebras. Two new numeric systems are defined by these
8-dimensional and 4-dimensional algebras: genetic Yin-Yang-octaves and genetic
tetrions. Their comparison with quaternions by Hamilton is presented. Elements
of new "genovector calculation" and ideas of "genetic mechanics" are discussed.
These algebras are considered as models of the genetic code and as its possible
pre-code basis. They are related with binary oppositions of the Yin-Yang type
and they give new opportunities to investigate evolution of the genetic code.
The revealed fact of the relation between the genetic code and these genetic
algebras is discussed in connection with the idea by Pythagoras: "All things
are numbers". Simultaneously these genetic algebras can be utilized as the
algebras of genetic operators in biological organisms. The described results
are related with the problem of algebraization of bioinformatics. They take
attention to the question: what is life from the viewpoint of algebra?

categories: q-bio.QM math-ph math.MP q-bio.GN q-bio.OT


title: Variable range hopping in thin film with large dielectric constant

abstract:
  In a film with large dielectric constant $\kappa$ the electric field of an
electron spreads inside the film before exiting the film at large distances of
order of $\kappa d$ ($d$ is the film width). This leads to the logarithmic
Coulomb repulsion between electrons and modifies the shape of the Coulomb gap
in the density of localized states in a doped film. As a result the variable
range hopping conductivity in such a film has a peculiar temperature
dependence, where the domain of the $\ln \sigma (T) \propto (T_0/T)^{p}$
dependence, with the index $p \simeq 0.7$, is sandwiched between the two
domains with $p = 1/2$.


title: Moduli of twisted orbifold sheaves

abstract:
  We study stacks of slope-semistable twisted sheaves on orbisurfaces with
projective coarse spaces and prove that in certain cases they have many of the
asymptotic properties enjoyed by the moduli of slope-semistable sheaves on
smooth projective surfaces.


title: On a New Alternative Mathematical Model for Special Relativity

abstract:
  In this paper, it is shown why Lorentz Transformation implies the general
case where observed events are not necessarily in the inertia frame of any
observer but assumes a special scenario when determining the length contraction
and time dilation factors. It is shown that this limitation has led to
mathematical and physical inconsistencies. The paper explains the conditions
for a successful theory of time dilation and length contraction, and provides a
simple proof to a new generalized transformation of coordinate systems as the
only possible solution that meets those conditions. It discusses
inconsistencies of Lorentz Transformation, and shows how the new generalized
transformation resolves those apparent inconsistencies. The new transformation
agrees with Special Relativity on its conclusions of time dilation and space
contraction, and yields the same law of addition of velocities as proposed in
Lorentz Transformation.


title:
A Monte Carlo study of the triangular lattice gas with the first- and
  the second-neighbor exclusions

abstract:
  We formulate a Swendsen-Wang-like version of the geometric cluster algorithm.
As an application,we study the hard-core lattice gas on the triangular lattice
with the first- and the second-neighbor exclusions. The data are analyzed by
finite-size scaling, but the possible existence of logarithmic corrections is
not considered due to the limited data. We determine the critical chemical
potential as $\mu_c=1.75682 (2)$ and the critical particle density as
$\rho_c=0.180(4)$. The thermal and magnetic exponents $y_t=1.51(1) \approx 3/2$
and $y_h=1.8748 (8) \approx 15/8$, estimated from Binder ratio $Q$ and
susceptibility $\chi$, strongly support the general belief that the model is in
the 4-state Potts universality class. On the other hand, the analyses of
energy-like quantities yield the thermal exponent $y_t$ ranging from $1.440(5)$
to $1.470(5)$. These values differ significantly from the expected value 3/2,
and thus imply the existence of logarithmic corrections.


title: Knuth Relations for the Hyperoctahedral Groups

abstract:
  C. Bonnaf{\'e}, M. Geck, L. Iancu, and T. Lam have conjectured a description
of one-sided cells in unequal parameter Hecke algebras of type $B$ which is
based on domino tableaux of arbitrary rank. In the integer case, this
generalizes the work of D. Garfinkle whose methods we adapt to construct a
family of operators which generate the conjectured combinatorial description.


title:
A nonlinear classical model for the decay widths of Isoscalar Giant
  Monopole Resonances

abstract:
  The decay of the Isoscalar Giant Monopole Resonance (ISGMR) in nuclei is
studied by means of a nonlinear classical model consisting of several
noninteracting nucleons (particles) moving in a potential well with an
oscillating nuclear surface (wall). The motion of the nuclear surface is
described by means of a collective variable which appears explicitly in the
Hamiltonian as an additional degree of freedom. The total energy of the system
is therefore conserved. Although the particles do not directly interact with
each other, their motions are indirectly coupled by means of their interaction
with the moving nuclear surface. We consider as free parameters in this model
the degree of collectivity and the fraction of nucleons that participate to the
decay of the collective excitation. Specifically, we have calculated the decay
width of the ISGMR in the spherical nuclei $^{208}\rm{Pb}$, $^{144}\rm{Sm}$,
$^{116}\rm{Sn}$ and $^{90}\rm{Zr}$. Despite its simplicity and its purely
classical nature, the model reproduces the trend of the experimental data which
show that with increasing mass number the decay width decreases. Moreover the
experimental results (with the exception of $^{90}\rm{Zr}$) can be well fitted
using appropriate values for the free parameters mentioned above. It is also
found that these values allow for a good description of the experimentally
measured $^{112}\rm{Sn}$ and $^{124}\rm{Sn}$ decay widths. In addition, we give
a prediction for the decay width of the exotic isotope $^{132}Sn$ for which
there is experimental interest. The agreement of our results with the
corresponding experimental data for medium-heavy nuclei is dictated by the
underlying classical mechanics i.e. the behaviour of the maximum Lyapunov
exponent as a function of the system size.


title: The Canonical Model of a Singular Curve

abstract:
  We give refined statements and modern proofs of Rosenlicht's results about
the canonical model C' of an arbitrary complete integral curve C. Notably, we
prove that C and C' are birationally equivalent if and only if C is
nonhyperelliptic, and that, if C is nonhyperelliptic, then C' is equal to the
blowup of C with respect to the canonical sheaf \omega. We also prove some new
results: we determine just when C' is rational normal, arithmetically normal,
projectively normal, and linearly normal.


title: Performance Evaluation of Multiple TCP connections in iSCSI

abstract:
  Scaling data storage is a significant concern in enterprise systems and
Storage Area Networks (SANs) are deployed as a means to scale enterprise
storage. SANs based on Fibre Channel have been used extensively in the last
decade while iSCSI is fast becoming a serious contender due to its reduced
costs and unified infrastructure. This work examines the performance of iSCSI
with multiple TCP connections. Multiple TCP connections are often used to
realize higher bandwidth but there may be no fairness in how bandwidth is
distributed. We propose a mechanism to share congestion information across
multiple flows in ``Fair-TCP'' for improved performance. Our results show that
Fair-TCP significantly improves the performance for I/O intensive workloads.


title:
Universality and universal finite-size scaling functions in
  four-dimensional Ising spin glasses

abstract:
  We study the four-dimensional Ising spin glass with Gaussian and bond-diluted
bimodal distributed interactions via large-scale Monte Carlo simulations and
show via an extensive finite-size scaling analysis that four-dimensional Ising
spin glasses obey universality.


title:
Type ${\rm III_1}$ factors generated by regular representations of
  infinite dimensional nilpotent group $B_0^{\mathbb N}$

abstract:
  We study the von Neumann algebra, generated by the unitary representations of
infinite-dimensional groups nilpotent group $B_0^{\mathbb N}$. The conditions
of the irreducibility of the regular and quasiregular representations of
infinite-dimensional groups (associated with some quasi-invariant measures) are
given by the so-called Ismagilov conjecture (see [1,2,9-11]). In this case the
corresponding von Neumann algebra is type ${\rm I}_\infty$ factor. When the
regular representation is reducible we find the sufficient conditions on the
measure for the von Neumann algebra to be factor (see [13,14]). In the present
article we determine the type of corresponding factors. Namely we prove that
the von Neumann algebra generated by the regular representations of
infinite-dimensional nilpotent group $B_0^{\mathbb N}$ is type ${\rm III}_1$
hyperfinite factor. The case of the nilpotent group $B_0^{\mathbb Z}$ of
infinite in both directions matrices will be studied in [6].


title: Geometric Interpretation of Second Elliptic Integrable System

abstract:
  In this paper we give a geometrical interpretation of all the second elliptic
integrable systems associated to 4-symmetric spaces. We first show that a
4-symmetric space $G/G_0$ can be embedded into the twistor space of the
corresponding symmetric space $G/H$. Then we prove that the second elliptic
system is equivalent to the vertical harmonicity of an admissible twistor lift
$J$ taking values in $G/G_0 \hookrightarrow \Sigma(G/H)$. We begin the paper by
an example: $G/H=\R^4$. We study also the structure of 4-symmetric bundles over
Riemannian symmetric spaces.


title:
Origin of negative differential resistance in a strongly coupled single
  molecule-metal junction device

abstract:
  A new mechanism is proposed to explain the origin of negative differential
resistance (NDR) in a strongly coupled single molecule-metal junction. A
first-principles quantum transport calculation in a Fe-terpyridine linker
molecule sandwiched between a pair of gold electrodes is presented. Upon
increasing applied bias, it is found that a new phase in the broken symmetry
wavefunction of the molecule emerges from the mixing of occupied and unoccupied
molecular orbital. As a consequence, a non-linear change in the coupling
between molecule and lead is evolved resulting to NDR. This model can be used
to explain NDR in other class of metal-molecule junction device.


title:
Principal component analysis model for machine-part cell formation
  problem in group technology

abstract:
  In this paper, we consider the problem of forming machine cell in cellular
manufacturing (CM). The major problem in the design of a CM system is to
identify the part families and machine groups and consequently to form
manufacturing cells. The aim of this article is to formulate a multivariate
approach based on a correlation analysis for solving cell formation problem.
The proposed approach is carried out in two phases. In the first phase, the
correlation matrix is used as an original similarity coefficient matrix. In the
second phase, Principal Component Analysis (PCA) is applied to find the
eigenvalues and eigenvectors on the correlation similarity matrix. A scatter
plot analysis as a cluster analysis is applied to make machine groups while
maximizing correlation between elements. A numerical example for the design of
cell structures is provided in order to illustrate the proposed approach. The
results of a comparative study based on multiple performance criteria show that
the present approach is very effective, efficient and practical


title:
Alternative proofs of linear response for piecewise expanding unimodal
  maps

abstract:
  We give two new proofs that the SRB measure of a C^2 path f_t of unimodal
piecewise expanding C^3 maps is differentiable at 0 if f_t is tangent to the
topological class of f_0. The arguments are more conceptual than the one in our
previous paper, but require proving Holder continuity of the infinitesimal
conjugacy (a new result, of independent interest) and using spaces of bounded
p-variation. The first new proof gives differentiability of higher order if f_t
is smooth enough and stays in the topological class of f_0 and if the
observable smooth enough (a new result). In addition, this proof does not
require any information on the decomposition of the SRB measure into regular
and singular terms, making it potentially amenable to extensions to higher
dimensions. The second new proof allows us to recover the linear response
formula (i.e., the formula for the derivative at 0) obtained in our previous
paper and gives additional information on this formula.


title: The value of Repeated Games with an informed controller

abstract:
  We consider the general model of zero-sum repeated games (or stochastic games
with signals), and assume that one of the players is fully informed and
controls the transitions of the state variable. We prove the existence of the
uniform value, generalizing several results of the literature. A preliminary
existence result is obtained for a certain class of stochastic games played
with pure strategies.


title: Counting points of homogeneous varieties over finite fields

abstract:
  Let $X$ be an algebraic variety over a finite field $\bF_q$, homogeneous
under a linear algebraic group. We show that the number of rational points of
$X$ over $\bF_{q^n}$ is a periodic polynomial function of $q^n$ with integer
coefficients. Moreover, the shifted periodic polynomial function, where $q^n$
is formally replaced with $q^n + 1$, is shown to have non-negative
coefficients.


title: Cohomologie De Hochschild Des Surfaces De Klein

abstract:
  Given a mechanical system $(M, \mathcal{F}(M))$, where $M$ is a Poisson
manifold and $\mathcal{F}(M)$ the algebra of regular functions on $M$, it is
important to be able to quantize it, in order to obtain more precise results
than through classical mechanics. An available method is the deformation
quantization, which consists in constructing a star-product on the algebra of
formal power series $\mathcal{F}(M)[[\hbar]]$. A first step toward study of
star-products is the calculation of Hochschild cohomology of $\mathcal{F}(M)$.
The aim of this article is to determine this Hochschild cohomology in the case
of singular curves of the plane -- so we rediscover, by a different way, a
result proved by Fronsdal and make it more precise -- and in the case of Klein
surfaces. The use of a complex suggested by Kontsevich and the help of
Gr\"obner bases allow us to solve the problem.


title: Entropy Moments Characterization of Statistical Distributions

abstract:
  This letter reports two moment extensions of the entropy of a distribution.
By understanding the traditional entropy as the average of the original
distribution up to a random variable transformation, the traditional moments
equation become immediately applicable to entropy. We also suggest an
alternative family of entropy moments. The discriminative potential of such
entropy moment extensions is illustrated with respect to different types of
distributions with otherwise undistinguishable traditional entropies.


title: Differential operators and Cherednik algebras

abstract:
  We establish a link between two geometric approaches to the representation
theory of rational Cherednik algebras of type A: one based on a noncommutative
Proj construction, used in [GS]; the other involving quantum hamiltonian
reduction of an algebra of differential operators, used in [GG].
  In the present paper, we combine these two points of view by showing that the
process of hamiltonian reduction intertwines a naturally defined geometric
twist functor on D-modules with the shift functor for the Cherednik algebra.
That enables us to give a direct and relatively short proof of the key result,
[GS, Theorem 1.4] without recourse to Haiman's deep results on the n! theorem.
We also show that the characteristic cycles defined independently in these two
approaches are equal, thereby confirming a conjecture from [GG].


title:
Hyperfine Mixing and the Semileptonic Decays of Double-Heavy Baryons in
  a Quark Model

abstract:
  The semileptonic decays of the lowest-lying double-heavy baryons is treated
in a quark model. For the $\Xi_{bb}$, hyperfine mixing in the spin wave
function leaves the total rate for decay into the lowest lying daughter baryons
essentially unchanged, but changes the relative rates into the $\Xi_{bc}$ and
$\Xi_{bc}^\prime$. The same pattern is obtained in the decays of the
$\Omega_{bb}$. For the $\Xi_{bc}$, this mixing leads to factor of about 17
suppression in the decay rate to the $\Xi_{cc}^*$, and a factor of two
suppression in the total decay rate. For the $\Omega_{bc}$, the decay to the
$\Omega_{cc}^*$ is suppressed by a factor of more than 30 from the unmixed
case, and the total decay rate is decreased to about 40% of the decay rate
obtained when mixing is ignored.


title:
Actions of F_\infty whose II_1 factors and orbit equivalence relations
  have prescribed fundamental group

abstract:
  We show that given any subgroup F of R_+ which is either countable or belongs
to a certain "large" class of uncountable subgroups, there exist continuously
many free ergodic probability measure preserving actions \sigma_i of the free
group with infinitely many generators such that their associated group measure
space II_1 factors M_i and orbit equivalence relations R_i have fundamental
group equal to F and with M_i (respectively R_i) stably non-isomorphic.
Moreover, these actions can be taken so that R_i has no outer automorphisms and
any automorphism of M_i is unitary conjugate to an automorphism that acts
trivially on $L^\infty(X_i) \subset M_i$.


title: Inexistence of Zeeman's fine topology

abstract:
  The family of topologies that induce the Euclidean metric space on every time
axis and every space axis exhibits no maximal element when partially ordered by
the relation ``finer than'', as demonstrated in this article. One conclusion
and two reflections emerge and are addressed herein:
  Conclusion: a. Zeeman's fine topology [1] and G\"{o}bel's extension to
arbitrary spacetimes [2] do not exist. Reflections: a. Both authors' attempts
may be classified as type-2 strategies, within the taxonomy of [3]. b. How
could these inexistent topologies be used for decades?


title: On strongly $g(x)$-clean rings

abstract:
  Let $R$ be an associative ring with identity, $C(R)$ denote the center of
$R$, and $g(x)$ be a polynomial in the polynomial ring $C(R)[x]$. $R$ is called
strongly $g(x)$-clean if every element $r \in R$ can be written as $r=s+u$ with
$g(s)=0$, $u$ a unit of $R$, and $su=us$. The relation between strongly
$g(x)$-clean rings and strongly clean rings is determined, some general
properties of strongly $g(x)$-clean rings are given, and strongly $g(x)$-clean
rings generated by units are discussed.


title: A Payne-Weinberger eigenvalue estimate for wedge domains on spheres

abstract:
  A Faber-Krahn type argument gives a sharp lower estimate for the first
Dirichlet eigenvalue for subdomains of wedge domains in spheres, generalizing
the inequality in the plane, found by Payne and Weinberger. An application is
an alternative proof to the finiteness of a Brownian motion capture time
estimate.


title:
On the zeta function of divisors for projective varieties with higher
  rank divisor class group

abstract:
  Given a projective variety X defined over a finite field, the zeta function
of divisors attempts to count all irreducible, codimension one subvarieties of
X, each measured by their projective degree. When the dimension of X is greater
than one, this is a purely p-adic function, convergent on the open unit disk.
Four conjectures are expected to hold, the first of which is p-adic meromorphic
continuation to all of C_p.
  When the divisor class group (divisors modulo linear equivalence) of X has
rank one, then all four conjectures are known to be true. In this paper, we
discuss the higher rank case. In particular, we prove a p-adic meromorphic
continuation theorem which applies to a large class of varieties. Examples of
such varieties are projective nonsingular surfaces defined over a finite field
(whose effective monoid is finitely generated) and all projective toric
varieties (smooth or singular).


title:
Sea-quark flavor asymmetry in the nucleon from a relativistic analysis
  of the Drell-Yan scattering off nuclei

abstract:
  It is shown that accounting for the relativistic structure of the deuteron
allows to explain the ratio of the Drell-Yan pair production cross-section at
the low Bjorken $x$ off the deuteron and the proton. Thus, the sea quark
distributions in the nucleon should be studied with accounting for the effects
of the relativistic structure of the deuteron. The suggested approach reduces
theoretical uncertainty in extracting the ratio $\bar u/\bar d$ from the data
and it is important for the clarification of the nature of the sea quark
asymmetry in the nucleon.


title:
The Keck Planet Search: Detectability and the Minimum Mass and Orbital
  Period Distribution of Extrasolar Planets

abstract:
  We analyze 8 years of precise radial velocity measurements from the Keck
Planet Search, characterizing the detection threshold, selection effects, and
completeness of the survey. We carry out a systematic search for planets by
assessing the false alarm probability associated with Keplerian orbit fits to
the data. This allows us to understand the detection threshold for each star in
terms of the number and time baseline of the observations, and size of
measurement errors and stellar jitter. We show that all planets with orbital
periods <2000 days, velocity amplitudes >20 m/s, and eccentricities <0.6 have
been announced, and summarize the candidates at lower amplitudes and longer
orbital periods. For the remaining stars, we calculate upper limits on the
velocity amplitude of a companion, typically 10 m/s, and use the non-detections
to derive completeness corrections at low amplitudes and long orbital periods.
We give the fraction of stars with a planet as a function of planet mass and
orbital period, and extrapolate to long period orbits and low planet masses. A
power law fit for planet masses >0.3 Jupiter masses and periods <2000 days
gives a mass-period distribution dN=C M^\alpha P^\beta dlnM dlnP with
\alpha=-0.31 \pm 0.2, \beta=0.26\pm 0.1, and the normalization constant C such
that 10.5% of solar type stars have a planet with mass in the range 0.3-10
Jupiter masses and orbital period 2-2000 days. The orbital period distribution
shows an increase in the planet fraction by a factor of 5 for orbital periods
beyond 300 days. Extrapolation gives 17-20% of stars having gas giant planets
within 20 AU. Finally, taking into account differences in detectability, we
find that M dwarfs are 3 to 10 times less likely to harbor a Jupiter mass
planet than solar type stars.


title:
Spitzer observations of the Massive star forming complex S254-S258:
  structure and evolution

abstract:
  We present Spitzer-IRAC, NOAO 2.1meter-Flamingos, Keck-NIRC, and
FCRAO-SEQUOIA observations of the massive star forming complex S254-S258,
covering an area of 25x20 arc-minutes. Using a combination of the IRAC and NIR
data, we identify and classify the young stellar objects (YSO) in the complex.
We detect 510 sources with near or mid IR-excess, and we classify 87 Class I,
and 165 Class II sources. The YSO are found in clusters surrounded by isolated
YSO in a low-density distributed population. The ratio of clustered to total
YSO is 0.8. We identify six new clusters in the complex. One of them,
G192.63-00, is located around the ionizing star of the HII region S255. We
hypothesize that the ionizing star of S255 was formed in this cluster. We also
detect a southern component of the cluster in HII region S256. The cluster
G192.54-0.15, located inside HII region S254 has a VLSR of 17 km/s with respect
to the main cloud, and we conclude that it is located in the background of the
complex. The structure of the molecular cloud is examined using 12CO and 13CO,
as well as a near-IR extinction map. The main body of the molecular cloud has
VLSR between 5 and 9 km/s. The arc-shaped structure of the molecular cloud,
following the border of the HII regions, and the high column density in the
border of the HII regions support the idea that the material has been swept up
by the expansion of the HII regions.


title: Adiabatic Condition and Quantum Geometric Potential

abstract:
  In this paper, we present a U(1)-invariant expansion theory of the adiabatic
process. As its application, we propose and discuss new sufficient adiabatic
approximation conditions. In the new conditions, we find a new invariant
quantity referred as quantum geometric potential (QGP) contained in all
time-dependent processes. Furthermore, we also give detailed discussion and
analysis on the properties and effects of QGP.


title: Asymptotics of input-constrained binary symmetric channel capacity

abstract:
  We study the classical problem of noisy constrained capacity in the case of
the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs
are sequences chosen from a constrained set. Motivated by a result of
Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop
(2004) 117--122], we derive an asymptotic formula (when the noise parameter is
small) for the entropy rate of a hidden Markov chain, observed when a Markov
chain passes through a BSC. Using this result, we establish an asymptotic
formula for the capacity of a BSC with input process supported on an
irreducible finite type constraint, as the noise parameter tends to zero.


title: The centers of Iwahori-Hecke algebras are filtered

abstract:
  We show that the center of the Iwahori--Hecke algebra of the symmetric group
$S_n$ carries a natural filtered algebra structure, and that the structure
constants of the associated graded algebra are independent of $n$. A series of
conjectures and open problems are also included.


title:
Correlation functions for a di-neutron condensate in asymmetric nuclear
  matter

abstract:
  Recent calculations with an effective isospin dependent contact interaction
show the possibility of the crossover from superfluidity of neutron Cooper
pairs in $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of
di-neutron bound states in dilute nuclear matter. The density and spin
correlation functions are calculated for a di-neutron condensate in asymmetric
nuclear matter with the aim to find the possible features of the BCS-BEC
crossover. It is shown that the zero-momentum transfer spin correlation
function satisfies the sum rule at zero temperature. In symmetric nuclear
matter, the density correlation function changes sign at low momentum transfer
across the BCS-BEC transition and this feature can be considered as a signature
of the crossover. At finite isospin asymmetry, this criterion gives too large
value for the critical asymmetry $\alpha_c^d\sim0.9$, at which the BEC state is
quenched. Therefore, it can be trusted for the description of the
density-driven BCS-BEC crossover of neutron pairs only at small isospin
asymmetry.
  This result generalizes the conclusion of the study in Phys. Rev. Lett. {\bf
95}, 090402 (2005), where the change of sign of the density correlation
function at low momentum transfer in two-component quantum fermionic atomic gas
with the balanced populations of fermions of different species was considered
as an unambiguous signature of the BCS-BEC transition.


title: Node discovery in a networked organization

abstract:
  In this paper, I present a method to solve a node discovery problem in a
networked organization. Covert nodes refer to the nodes which are not
observable directly. They affect social interactions, but do not appear in the
surveillance logs which record the participants of the social interactions.
Discovering the covert nodes is defined as identifying the suspicious logs
where the covert nodes would appear if the covert nodes became overt. A
mathematical model is developed for the maximal likelihood estimation of the
network behind the social interactions and for the identification of the
suspicious logs. Precision, recall, and F measure characteristics are
demonstrated with the dataset generated from a real organization and the
computationally synthesized datasets. The performance is close to the
theoretical limit for any covert nodes in the networks of any topologies and
sizes if the ratio of the number of observation to the number of possible
communication patterns is large.


title: Finitistic and Representation Dimensions

abstract:
  We prove that the finitistic dimension conjecture, the Gorenstein Symmetry
Conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama
conjecture hold for artin algebras which can be realized as endomorphism
algebras of modules over representation-finite algebras. Note it is a question
whether or not all artin algebras have such realizations. It was also shown
that if every quasi-hereditary algebras has a left idealized extension which is
a monomial algebra or an algebra whose representation dimension is not more
than 3, then the finitistic dimension conjecture holds.


title: Zero loci of admissible normal functions with torsion singularities

abstract:
  We show that the zero locus of a normal function on a smooth complex
algebraic variety S is algebraic provided that the normal function extends to a
admissible normal function on a smooth compactification of S with torsion
singularity. This result generalizes our previous result for admissible normal
functions on curves [arxiv:math/0604345 [math.AG]]. It has also been obtained
by M. Saito using a different method in a recent preprint [arXiv:0803.2771v2].


title:
Core Polarization and Tensor Coupling Effects on Magnetic Moments of
  Hypernuclei

abstract:
  The effects of core polarization and tensor coupling on the magnetic moments
in $^{13}_\Lambda$C, $^{17}_\Lambda$O, and $^{41}_\Lambda$Ca
$\Lambda$-hypernuclei are studied in the Dirac equation with scalar, vector and
tensor potentials. It is found that the effect of core polarization on the
magnetic moments is suppressed by $\Lambda$ tensor coupling. The $\Lambda$
tensor potential reduces the spin-orbit splitting of $p_\Lambda$ states
considerably. However, almost the same magnetic moments are obtained using the
hyperon wave function obtained via the Dirac equation either with or without
the $\Lambda$ tensor potential in the electromagnetic current vertex. The
deviations of magnetic moments for $p_\Lambda$ states from the Schmidt values
are found to increase with nuclear mass number.


title: On de Sitter radiation via quantum tunneling

abstract:
  We discuss why the tunneling picture does not necessarily lead to Hawking
radiation from the de Sitter horizon. The experience with the condensed matter
analogs of event horizon suggests that the de Sitter vacuum is stable against
the Hawking radiation. On the other hand the detector immersed into the de
Sitter background will detect the radiation which looks as thermal with the
effective temperature twice larger than the Hawking temperature associated with
the cosmological horizon.


title:
Semiconductor to metal transition in SWNTs caused by interaction with
  gold and platinum nanoparticles

abstract:
  Single-walled carbon nanotubes (SWNTs) have been coated with gold and
platinum nanoparticles either by microwave treatment or by the click reaction
and the Raman spectra of these SWNT-metal nanoparticle composites have been
investigated. Analysis of the G bands in the Raman spectra shows an increase in
the proportion of metallic SWNTs on attachment with metal nanoparticles. This
conclusion is also supported by the changes observed in the RBM bands.
Ab-initio calculations reveal that semiconductor-metal transition occurs in
SWNTs due to Columbic charge transfer between the metal nanoparticles and the
semiconducting SWNTs.


title:
Star Formation in the Most Distant Molecular Cloud in the Extreme Outer
  Galaxy: A Laboratory of Star Formation in an Early Epoch of the Galaxy's
  Formation

abstract:
  We report the discovery of active star formation in Digel's Cloud 2, which is
one of the most distant giant molecular clouds known in the extreme outer
Galaxy (EOG). At the probable Galactic radius of ~20 kpc, Cloud 2 has a quite
different environment from that in the solar neighborhood, including lower
metallicity, much lower gas density, and small or no perturbation from spiral
arms. With new wide-field near-infrared (NIR) imaging that covers the entire
Cloud 2, we discovered two young embedded star clusters located in the two
dense cores of the cloud. Using our NIR and 12CO data as well as HI, radio
continuum, and IRAS data in the archives, we discuss the detailed star
formation processes in this unique environment. We show clear evidences of a
sequential star formation triggered by the nearby huge supernova remnant, GSH
138-01-94. The two embedded clusters show a distinct morphology difference: the
one in the northern molecular cloud core is a loose association with
isolated-mode star formation, while the other in the southern molecular cloud
core is a dense cluster with cluster-mode star formation. We propose that high
compression by the combination of the SNR shell and an adjacent shell caused
the dense cluster formation in the southern core. Along with the low
metallicity range of the EOG, we suggest that EOG could be an excellent
laboratory for the study of star formation processes, such as those triggered
by supernovae, that occured during an early epoch of the Galaxy's formation. In
particular, the study of the EOG may shed light on the origin and role of the
thick disk, whose metallicity range matches with that of the EOG well.


title:
Nonvolatile Static Random Access Memory (NV-SRAM) Using Magnetic Tunnel
  Junctions with Current-Induced Magnetization Switching Architecture

abstract:
  We propose and computationally analyze a nonvolatile static random access
memory (NV-SRAM) cell using magnetic tunnel junctions (MTJs) with
magnetic-field-free current-induced magnetization switching (CIMS)
architecture. A pair of MTJs connected to the storage nodes of a standard SRAM
cell with CIMS architecture enables fully electrical store and restore
operations for nonvolatile logic information. The proposed NV-SRAM is expected
to be a key component of next-generation power-gating logic systems with
extremely low static-power dissipation.


title: Force, quantum mechanics and approximate energy eigenstates

abstract:
  The prevalent role of force in traditional quantum mechanics is outlined,
with special reference to approximate calculations for stationary states. It
will be explored how far this force concept can be made useful in the concerned
area. The basic idea is to differentiate the Schroedinger stationary equation
once. Thus, one can eliminate the unknown energy as well, and then examine how
a force-based approach can be beneficial in providing quickly the nodal
information and in assessing the quality of an approximate function. Further,
it will be demonstrated how the minimization of a suitable quantity derived
from force may constitute a variational principle for bound states. The
strategy applies also to Siegert states where traditional energy extremization
principle ceases to work. Additionally, the utility of the force concept in
semiclassical mechanics will be investigated.


title: Maximal contact and normal crossings in resolution of singularities

abstract: This paper has been withdrawn by the author


title: On monotonicity of F-blowup sequences

abstract:
  For each variety in positive characteristic, there is a series of canonically
defined blowups, called F-blowups. We are interested in the question of whether
the $e+1$-th blowup dominates the $e$-th, locally or globally. It is shown that
the answer is affirmative (globally for any $e$) when the given variety is
F-pure. As a corollary, we obtain some result on the stability of the sequence
of F-blowups. We also give a sufficient condition for local domination.


title:
Effects of hydrogen bonding on supercooled liquid dynamics and the
  implications for supercooled water

abstract:
  The supercooled state of bulk water is largely hidden by unavoidable
crystallization, which creates an experimentally inaccessible temperature
regime - a 'no man's land'. We address this and circumvent the crystallization
problem by systematically studying the supercooled dynamics of hydrogen bonded
oligomeric liquids (glycols), where water corresponds to the chain-ends alone.
This novel approach permits a 'dilution of water' by altering the hydrogen bond
concentration via variations in chain length. We observe a dynamic crossover in
the temperature dependence of the structural relaxation time for all glycols,
consistent with the common behavior of most supercooled liquids. We find that
the crossover becomes more pronounced for increasing hydrogen bond
concentrations, which leads to the prediction of a marked dynamic transition
for water within 'no man's land' at T~220 K. Interestingly, the predicted
transition thus takes place at a temperature where a so called 'strong-fragile'
transition has previously been suggested. Our results, however, imply that the
dynamic transition of supercooled water is analogous to that commonly observed
in supercooled liquids. Moreover, we find support also for the existence of a
secondary relaxation of water with behavior analogous to that of the secondary
relaxation observed for the glycols.


title:
Updated Measurement of phi_3 with a Dalitz Plot Analysis of B->D(*)K
  Decay

abstract:
  We present an updated measurement of the unitarity triangle angle phi_3 using
a Dalitz plot analysis of the K^0_S pi+ pi- decay of the neutral D meson
produced in B+- ->D(*)K+- decays. The method exploits the interference between
D^0 and Dbar^0 to extract the angle phi_3, strong phase delta and the ratio r
of suppressed and allowed amplitudes. We apply this method to a 605 fb-1 data
sample collected by the Belle experiment. The analysis uses two modes: B+- ->
DK+-, and B+- -> D*K+- with D* -> D pi0, as well as the corresponding
charge-conjugate modes. From a combined maximum likelihood fit to the two
modes, we obtain phi_3=76+12-13(stat)+-4(syst)+-9(model). The statistical
significance of CP violation (phi_3\neq 0) in our measurement is
(1-5.5*10^{-4}), or 3.5 standard deviations. These results are preliminary.


title: Magnetic Charge Lattices, Moduli Spaces and Fusion Rules

abstract:
  We analyze the set of magnetic charges carried by smooth BPS monopoles in
Yang-Mills-Higgs theory with arbitrary gauge group G spontaneously broken to a
subgroup H. The charges are restricted by a generalized Dirac quantization
condition and by an inequality due to Murray. Geometrically, the set of allowed
charges is a solid cone in the coroot lattice of G, which we call the Murray
cone. We argue that magnetic charge sectors correspond to points in the Murray
cone divided by the Weyl group of H; hence magnetic charge sectors are labelled
by dominant integral weights of the dual group H*. We define generators of the
Murray cone modulo Weyl group, and interpret the monopoles in the associated
magnetic charge sectors as basic; monopoles in sectors with decomposable
charges are interpreted as composite configurations. This interpretation is
supported by the dimensionality of the moduli spaces associated to the magnetic
charges and by classical fusion properties for smooth monopoles in particular
cases. Throughout the paper we compare our findings with corresponding results
for singular monopoles recently obtained by Kapustin and Witten.


title:
Asymptotic stability of ground states in 3D nonlinear Schroedinger
  equation including subcritical cases

abstract:
  We consider a class of nonlinear Schroedinger equation in three space
dimensions with an attractive potential. The nonlinearity is local but rather
general encompassing for the first time both subcritical and supercritical (in
$L^2$) nonlinearities. We study the asymptotic stability of the nonlinear bound
states, i.e. periodic in time localized in space solutions. Our result shows
that all solutions with small initial data, converge to a nonlinear bound
state. Therefore, the nonlinear bound states are asymptotically stable. The
proof hinges on dispersive estimates that we obtain for the time dependent,
Hamiltonian, linearized dynamics around a careful chosen one parameter family
of bound states that "shadows" the nonlinear evolution of the system. Due to
the generality of the methods we develop we expect them to extend to the case
of perturbations of large bound states and to other nonlinear dispersive wave
type equations.


title:
Electronic structure of edge and vortex states in chiral mesoscopic
  superconductor

abstract:
  We study a subgap quasiparticle spectrum in a mesoscopic disk of chiral
superconductor. We find an exact expression for the spectrum of surface states
localized at the disk edge. Considering an Abrikosov vortex placed at the
center of a superconducting disk we investigate the spectrum transformation
near the intersection points of surface and vortex anomalous energy branches .
The resulting splitting of the anomalous branches due to the hybridization of
edge and vortex states is determined by an external magnetic field and can lead
in particular to the formation of a set of minigaps in the quasiparticle
spectrum. Tuning the external magnetic field makes it possible to control the
width of minigaps and the positions of corresponding density of states
singularities at the minigaps edges.


title: Vortex solutions of the discrete Gross-Pitaevskii equation

abstract:
  In this paper, we consider the dynamical evolution of dark vortex states in
the two-dimensional defocusing discrete nonlinear Schroedinger model, a model
of interest both to atomic physics and to nonlinear optics. We find that in a
way reminiscent of their 1d analogs, i.e., of discrete dark solitons, the
discrete defocusing vortices become unstable past a critical coupling strength
and, in the infinite lattice, they apparently remain unstable up to the
continuum limit where they are restabilized. In any infinite lattice,
stabilization windows of the structures may be observed. Systematic tools are
offered for the continuation of the states both from the continuum and,
especially, from the anti-continuum limit. Although the results are mainly
geared towards the uniform case, we also consider the effect of harmonic
trapping potentials.


title:
Effect of static and dynamic disorder on electronic transport of $RCo_2$
  compounds: a study of $Ho(Al_xCo_{1-x})_2$ alloys

abstract:
  We present experimental results on thermoelectric power ({\em S}) and
electrical resistivity ($\rho $) of pseudobinary alloys
Ho(Al$_x$Co$_{1-x}$)$_2$ ($0 \leq x \leq 0.1 $), in the temperature range 4.2 K
to 300 K. The work focuses on the effects of static (induced by alloying) and
dynamic (induced by temperature) disorder on the magnetic state and electronic
transport in a metallic system with itinerant metamagnetic instability. Spatial
fluctuations of the local magnetic susceptibility in the alloys lead to a
development of a partially ordered magnetic ground state of the itinerant 3d
electron system. This results in a strong increase of the residual resistivity
and a suppression of the temperature-dependent resistivity. Thermopower
exhibits a complex temperature variation in both the magnetically ordered and
in the paramagnetic state. This complex temperature variation is referred to
the electronic density of states features in vicinity of Fermi energy and to
the interplay of magnetic and impurity scattering. Our results indicate that
the magnetic enhancement of the Co 3d-band in RCo$_{\rm 2}$--based alloys upon
a substitution of Co by non-magnetic elements is mainly related to a
progressive localization of the Co -- 3d electrons caused by disorder. We show
that the magnitude of the resistivity jump at the Curie temperature for
RCo$_{\rm 2}$ compounds exhibiting a first order phase transition is a
non-monotonic function of the Curie temperature due to a saturation of the
3d--band spin fluctuation magnitude at high temperatures.


title:
Fibre coupled dual-mode waveguide interferometer with $\lambda $/130
  fringe spacing

abstract:
  Predictions and measurements of a multimode waveguide interferometer
operating in a fibre coupled, ``dual-mode'' regime are reported. With a 1.32
micrometer source, a complete switching cycle of the output beam is produced by
a 10.0 nanometer incremental change in the 8.0 micrometer width of the hollow
planar mirror waveguide. This equates to a fringe spacing of $\sim\lambda
/130$. This is an order of magnitude smaller than previously reported results
for this form of interferometer.


title: Repulsive and restoring Casimir forces with left-handed materials

abstract:
  We investigate repulsive Casimir force between slabs containing left-handed
materials with controllable electromagnetic properties. The sign of Casimir
force is determined by the electric and magnetic properties of the materials,
and it is shown that the formation of the repulsive force is related to the
wave impedances of two slabs. The sign change of the Casimir force as a
function of the distance is studied. Special emphasis is put on the restoring
Casimir force which may be found to exist between perfectly conducting material
and metamaterial slabs. This restoring force is a natural power for the system
oscillation in vacuum and also can be used for system stabilization.


title: Notes on uniform exponential growth and Tits alternative

abstract:
  These notes contain results concerning uniform exponential growth which were
obtained in collaborations with E. Breuillard and A. Salehi-Golsefidy, mostly
during 2005, improving Eskin-Mozes-Oh theorem \cite{EMO}, as well as a uniform
uniform version of Tits alternative improving \cite{uti}.


title:
Inflationary cosmology and the late-time accelerated expansion of the
  universe in non-minimal Yang-Mills-$F(R)$ gravity and non-minimal
  vector-$F(R)$ gravity

abstract:
  We study inflationary cosmology and the late-time accelerated expansion of
the universe in non-minimal Yang-Mills (YM) theory, in which the YM field
couples to a function of the scalar curvature. It is shown that power-law
inflation can be realized due to the non-minimal YM field-gravitational
coupling which maybe caused by quantum corrections. Moreover, it is
demonstrated that both inflation and the late-time accelerated expansion of the
universe can be realized in a modified YM-$F(R)$ gravity which is consistent
with solar system tests. Furthermore, it is shown that this result can be
realized also in a non-minimal vector-$F(R)$ gravity. In addition, we consider
the duality of the non-minimal electromagnetic theory and that of the
non-minimal YM theory, and also discuss the cosmological reconstruction of the
YM theory.


title: The Minimally Immersed 4D Supermembrane

abstract:
  In this note we summarize some of the properties found in [1], and its
relation with [2]. We comment on the construction of the action of the 11D
supermembrane with nontrivial central charges minimally immersed on a 7D
toroidal manifold is obtained (MIM2).The transverse coordinates to the
supermembrane are maps to a 4D Minkowski space-time. The action is invariant
under additional symmetries in comparison to the supermembrane on a 11D
Minkowski target space. The hamiltonian in the LCG is invariant under conformal
transformations on the Riemann surface base manifold. The spectrum of the
regularized hamiltonian is discrete with finite multiplicity. Its resolvent is
compact. Susy is spontaneously broken, due to the topological central charge
condition, to four supersymmetries in 4D, the vacuum belongs to an N=1
supermultiplet. When assuming the target-space to be an isotropic 7-tori, the
potential does not contain any flat direction, it is stable on the moduli space
of parameters. Moreover due to the discrete symmetries of the hamiltonian,
there are only 7 possible minimal holomorphic immersions of the MIM2 on the
7-torus. When these symmetries are identified on the target space, it
corresponds to compactify the MIM2 on a orbifold with G2 structure. Once the
singularities are resolved it leads to the compactification of the MIM2 on a G2
manifold as shown in [2].


title: Exact solution of mean geodesic distance for Vicsek fractals

abstract:
  The Vicsek fractals are one of the most interesting classes of fractals and
the study of their structural properties is important. In this paper, the exact
formula for the mean geodesic distance of Vicsek fractals is found. The
quantity is computed precisely through the recurrence relations derived from
the self-similar structure of the fractals considered. The obtained exact
solution exhibits that the mean geodesic distance approximately increases as an
exponential function of the number of nodes, with the exponent equal to the
reciprocal of the fractal dimension. The closed-form solution is confirmed by
extensive numerical calculations.


title: Electronic structure of negatively curved graphene

abstract:
  We study the electronic structure of graphene in the presence of either
sevenfolds or eightfolds by using a gauge field-theory model. The graphene
sheet with topological defects is considered as a negative cone surface with
infinite Gaussian curvature at the center. The density of electronic states is
calculated for a single seven- and eightfold as well as for a pair of
sevenfolds with different morphology. The density of states at the Fermi energy
is found to be zero in all cases except two sevenfolds with translational
factor $M\neq 0$.


title: A VLBI Search for the Origin of Wobbling in Blazar Jets

abstract:
  An increasing number of blazars have been reported to show jet wobbling
(i.e., non-regular rotations of the structural position angle of their
innermost jets in the plane of the sky with amplitudes between 20 deg. and 50
deg., and time scales between 2 yr. and 20 yr.). The physical origin for the
observed jet wobbling is still poorly understood, but as this phenomenon is
triggered in the innermost regions of the jets, it must be tied to fundamental
properties of the inner regions of the accretion system. Thus, jet wobbling may
be an interesting potential tool for supermassive black hole, accretion and jet
launching studies. As part of a joint theoretical/numerical and observational
effort to characterize the observational properties and differences between
these three possible scenarios we have started a long-term polarimetric
phase-reference 43 GHz VLBA monitoring program to observe the jet structure and
the absolute motion of the jet core of four of the blazars which have shown
some of the clearest evidence of large amplitude jet wobbling: NRAO 150, OJ
287, 3C 273, and 3C 345 . Here we present this project and we argue about its
suitability for future VSOP-2 observations.


title:
Amplitude Analysis of High Statistics Results on
  $\gamma\gamma\to\pi^+\pi^-$ and the Two Photon Width of Isoscalar States

abstract:
  We perform an Amplitude Analysis of the world published data on
$\gamma\gamma\to\pi^+\pi^-$ and $\pi^0\pi^0$. These are dominated in statistics
by the recently published results from Belle on the charged pion channel.
Nevertheless, having only limited angular information, a range of solutions
remain possible. We present two solutions with $\Gamma(f_0(980)\to\gamma\gamma)
= 0.42$ and 0.10 keV, and $\Gamma(f_2(1270)\to\gamma\gamma) = 3.14 \pm 0.20$
and $3.82 \pm 0.30$ keV, respectively: the former being the solution favoured
by $\chi^2$, the latter at the edge of acceptability. Models of the structure
of the $f_0(980)$ predict two photon widths to be between 0.2 and 0.6 keV,
depending on its composition as mainly ${\bar K}K$, ${\bar s}s$ or
${\bar{qq}}qq$. Presently available data cannot yet distinguish unambiguously
between these predictions. However, we show how forthcoming results on
$\gamma\gamma \to\pi^0\pi^0$ can not only discriminate between, but also
refine, these classes of partial wave solutions.


title: Curvature-induced quantum behaviour on a helical nanotube

abstract:
  We investigate the effect of curvature on the behaviour of a quantum particle
bound to move on a surface shaped as a helical tube. We derive and discuss the
governing Schr\"odinger equation and the corresponding quantum effective
potential which is periodic and points to the helical configuration as more
energetically favorable as compared to the straight tube. The exhibited
periodicity also leads to energy band structure of pure geometrical origin.


title: Curvature induced quantum potential on deformed surfaces

abstract:
  We investigate the effect of curvature on the behaviour of a quantum particle
bound to move on a surface. For the Gaussian bump we derive and discuss the
quantum potential which results in the appearance of a bound state for
particles with vanishing angular momentum. The Gaussian bump provides a
characteristic length for the problem. For completeness we propose an inverse
problem in differential geometry, i.e. what deformed surfaces produce
prescribed curvature induced quantum potentials. We solve this inverse problem
in the case of rotational surfaces. We also show that there exist rotational
surfaces in the form of a circular strip around the axis of symmetry which
allow particles with generic angular momentum to bind.


title: Pionic contribution to relativistic Fermi Liquid parameters

abstract:
  We calculate pionic contribution to the relativistic Fermi Liquid parameters
(RFLPs) using Chiral Effective Lagrangian. The RFLPs so determined are then
used to calculate chemical potential, exchange and nuclear symmetry energies
due to $\pi$$N$ interaction. We also evaluate two loop ring diagrams involving
$\sigma$, $\omega$ and $\pi$ meson exchanges and compare results with what one
obtains from the relativistic Fermi Liquid theory (RFLT).


title: Secret Broadcasting of W-type state

abstract:
  In this work we describe a protocol by which one can secretly broadcast
W-type state among three distant partners. This work is interesting in the
sense that we introduce a new kind of local cloning operation to generate two
W- type states between these partners from a W-type state initially shared by
them.


title: Facing the Facts

abstract:
  Human error research on overconfidence supports the benefits of early
visibility of defects and disciplined development. If risk to the enterprise is
to be reduced, individuals need to become aware of the reality of the quality
of their work. Several cycles of inspection and defect removal are inevitable.
Software Quality Management measurements of defect density and removal
efficiency are applicable. Research of actual spreadsheet error rates shows
data consistent with other software depending on the extent to which the work
product was reviewed before inspection. The paper argues that the payback for
an investment in early review time is justified by the saving in project delay
and expensive errors in use.
  'If debugging is the process of removing bugs, then programming must be the
process of putting them in' - Anon.


title: Generalized Harish-Chandra descent and applications to Gelfand pairs

abstract:
  In the first part of the paper we generalize a descent technique due to
Harish-Chandra to the case of a reductive group acting on a smooth affine
variety both defined over arbitrary local field F of characteristic zero. Our
main tool is Luna slice theorem.
  In the second part of the paper we apply this technique to symmetric pairs.
In particular we prove that the pair (GL(n,C),GL(n,R)) is a Gelfand pair. We
also prove that any conjugation invariant distribution on GL(n,F) is invariant
with respect to transposition. For non-archimedean F the later is a classical
theorem of Gelfand and Kazhdan.
  We use the techniques developed here in our subsequent work [AG3] where we
prove an archimedean analog of the theorem on uniqueness of linear periods by
H. Jacquet and S. Rallis.


title:
NMR implementation of Factoring Large Numbers with Gau\ss{}Sums:
  Suppression of Ghost Factors

abstract:
  Finding the factors of an integer can be achieved by various experimental
techniques, based on an algorithm developed by Schleich et al., which uses
specific properties of Gau\ss{}sums. Experimental limitations usually require
truncation of these series, but if the truncation parameter is too small, it is
no longer possible to distinguish between factors and so-called "ghost"
factors. Here, we discuss two techniques for distinguishing between true
factors and ghost factors while keeping the number of terms in the sum constant
or only slowly increasing. We experimentally test these modified algorithms in
a nuclear spin system, using NMR.


title: An archimedean analog of Jacquet - Rallis theorem

abstract:
  In this paper we prove that the symmetric pair $(GL_{n+k}(F),GL_n(F) \times
GL_k(F))$ is a Gelfand pair for any local field F of characteristic 0. For
non-archimedean F it has been proven in [JR]. We use techniques developed in
[AG2] to generalize their proof to general local fields.


title: Measuring complete quantum states with a single observable

abstract:
  Experimental determination of an unknown quantum state usually requires
several incompatible measurements. However, it is also possible to determine
the full quantum state from a single, repeated measurement. For this purpose,
the quantum system whose state is to be determined is first coupled to a second
quantum system (the "assistant") in such a way that part of the information in
the quantum state is transferred to the assistant. The actual measurement is
then performed on the enlarged system including the original system and the
assistant. We discuss in detail the requirements of this procedure and
experimentally implement it on a simple quantum system consisting of nuclear
spins.


title: Dynamics of Nonlocal Cosmology

abstract:
  Nonlocal quantum corrections to gravity have been recently proposed as a
possible solution to the cosmological fine tuning problems. We study the
dynamics of a class of nonlocal actions defined by a function of the inverse
d'Alembertian of the Ricci scalar. Power-law and expnential functions are
considered in detail, but we also show a method to reconstruct a nonlocal
correction that generates a given background expansion. We find that even the
simplest terms can, while involving only Planck scale constants, drive the late
time acceleration without changing early cosmology. This leads to a sudden
future singularity, which however may be avoided by regularizing the
d'Alembertian. We also consider the Einstein frame versions of these models.


title:
On the Multi-Component Nonlinear Schr\"odinger Equation with Constant
  Boundary Conditions

abstract:
  The multi-component nonlinear Schrodinger equation related to C.I=Sp(2p)/U(p)
and D.III=SO(2p)/U(p)-type symmetric spaces with non-vanishing boundary
conditions is solvable with the inverse scattering method (ISM). As Lax
operator L we use the generalized Zakharov-Shabat operator. We show that the
ISM for L is a nonlinear analog of the Fourier-transform method. As appropriate
generalizations of the usual Fourier-exponential functions we use the so-called
squared solutions, which are constructed in terms of the fundamental analytic
solutions (FAS) of L and the Cartan-Weyl basis of the Lie algebra, relevant to
the symmetric space. We derive the completeness relation for the squared
solutions which turns out to provide spectral decomposition of the recursion
(generating) operators, a natural generalizations of id/dx in the case of
nonlinear evolution equations.


title: Pregalactic LiBeB Production by Supernova Cosmic Rays

abstract:
  I calculate the evolution of Be and B abundances produced by cosmic rays
generated by massive stars in the pregalactic phase of the universe. The inputs
for calculation, i.e. the star formation rate and the nuclear abundances of
cosmic rays, which I assume to be the same as those of the ISM, are taken from
the results of a detailed cosmic chemical evolution model with its parameters
best fitted from several items of observational information including an early
reionization of the IGM by $z\sim 15$. I found that when the $^6$Li plateau
abundance observed in metal-poor halo stars originated in the pregalactic
cosmological cosmic ray nucleosynthesis, Be and B simultaneously produced with
$^6$Li amount to the lowest levels ever detected in metal-poor halo stars. It
is desirable to observe Be and B abundances in metal-poor halo stars with
[Fe/H]$\leq -3$ in order to elucidate the possibility of early $^6$LiBeB
production by pregalactic supernova cosmic ray nucleosynthesis.


title: Dynamics of tuples of matrices

abstract:
  In this article we answer a question raised by N. Feldman in \cite{Feldman}
concerning the dynamics of tuples of operators on $\mathbb{R}^n$. In
particular, we prove that for every positive integer $n\geq 2$ there exist $n$
tuples $(A_1, A_2, ..., A_n)$ of $n\times n$ matrices over $\mathbb{R}$ such
that $(A_1, A_2, ..., A_n)$ is hypercyclic. We also establish related results
for tuples of $2\times 2$ matrices over $\mathbb{R}$ or $\mathbb{C}$ being in
Jordan form.


title:
Tracing the [FeII]/[NeII] ratio within star forming dwarf galaxies: a
  Spitzer IRS archival study

abstract:
  Archival Spitzer observations of 41 starburst galaxies that span a wide range
in metallicity reveal for the first time a correlation between the
[FeII]/[NeII] 26.0/12.8 micron ratio and the electron gas density as traced by
the 18.7/33.4 micron [SIII] ratio, with the [FeII]/[NeII] ratio decreasing with
increasing gas density. We also find a strong correlation between the gas
density and the PAH peak to continuum strength. Using shock and photoionization
models, we see the driver of the observed [FeII]/[NeII] ratios is metallicity.
The majority of [FeII] emission in low metallicity galaxies may be
shock-derived, whilst at high metallicity, the [FeII] emission may be instead
dominated by contributions from HII and in particular from dense PDR regions.
However, the observed [FeII]/[NeII] ratios may instead be following a
metallicity-abundance relationship, with iron being less depleted onto grains
in low metallicity galaxies - a result that would have profound implications
for the use of iron emission lines as unambiguous tracers of shocks.


title: Some results on $\mathbb{R}$-computable structures

abstract:
  This survey paper examines the effective model theory obtained with the BSS
model of real number computation. It treats the following topics: computable
ordinals, satisfaction of computable infinitary formulas, forcing as a
construction technique, effective categoricity, effective topology, and
relations with other models for the effective theory of uncountable structures.


title: Ambitable topological groups

abstract:
  A topological group is said to be ambitable if each uniformly bounded
uniformly equicontinuous set of functions on the group with its right
uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n
bounded topological group is either precompact or ambitable. In the familiar
semigroups constructed over ambitable groups, topological centres have an
effective characterization.


title: Factors in random graphs

abstract:
  Let $H$ be a fixed graph on $v$ vertices. For an $n$-vertex graph $G$ with
$n$ divisible by $v$, an $H$-{\em factor} of $G$ is a collection of $n/v$
copies of $H$ whose vertex sets partition $V(G)$.
  In this paper we consider the threshold $th_{H} (n)$ of the property that an
Erd\H{o}s-R\'enyi random graph (on $n$ points) contains an $H$-factor. Our
results determine $th_{H} (n)$ for all strictly balanced $H$.
  The method here extends with no difficulty to hypergraphs. As a corollary, we
obtain the threshold for a perfect matching in random $k$-uniform hypergraph,
solving the well-known "Shamir's problem."


title: Effect of conformations on charge transport in a thin elastic tube

abstract:
  We study the effect of conformations on charge transport in a thin elastic
tube. Using the Kirchhoff model for a tube with any given Poisson ratio,
cross-sectional shape and intrinsic twist, we obtain a class of exact solutions
for its conformation. The tube's torsion is found in terms of its intrinsic
twist and its Poisson ratio, while its curvature satisfies a nonlinear
differential equation which supports exact {\it periodic} solutions in the form
of Jacobi elliptic functions, which we call {\it conformon lattice} solutions.
These solutions typically describe conformations with loops. Each solution
induces a corresponding quantum effective {\it periodic} potential in the
Schr\"{o}dinger equation for an electron in the tube. The wave function
describes the delocalization of the electron along the central axis of the
tube. We discuss some possible applications of this novel mechanism of charge
transport.


title:
Multivariate analysis and Jacobi ensembles: largest eigenvalue,
  Tracy--Widom limits and rates of convergence

abstract:
  Let $A$ and $B$ be independent, central Wishart matrices in $p$ variables
with common covariance and having $m$ and $n$ degrees of freedom, respectively.
The distribution of the largest eigenvalue of $(A+B)^{-1}B$ has numerous
applications in multivariate statistics, but is difficult to calculate exactly.
Suppose that $m$ and $n$ grow in proportion to $p$. We show that after
centering and scaling, the distribution is approximated to second-order,
$O(p^{-2/3})$, by the Tracy--Widom law. The results are obtained for both
complex and then real-valued data by using methods of random matrix theory to
study the largest eigenvalue of the Jacobi unitary and orthogonal ensembles.
Asymptotic approximations of Jacobi polynomials near the largest zero play a
central role.


title: Broad-line and Multi-wave Band Emission from Blazars

abstract:
  We study the correlations of the flux of the broad-line emission ($F_{BLR}$)
with the X-ray emission flux, optical emission flux at 5500 \AA and radio
emission flux at 5 GHz, respectively, for a large sample of 50 Blazars (39
flat-spectrum radio quasars (FSRQs) and 11 BL Lac objects). Our main results
are as follows. There are very strong correlations between $F_{BLR}$ and
$F_{X}$ and between $L_{BLR}$ and $L_{X}$ in both states for 39 FSRQs and the
slopes of the linear regression equations are almost equal to 1. There are weak
correlations between $F_{BLR}$ and $F_{X}$ and between $L_{BLR}$ and $L_{X}$
for 11 BL Lac objects in both states, and the slopes of the linear regression
equations are close to 1. There are significant correlations between $F_{BLR}$
and $F_{X}$ and between $L_{BLR}$ and $L_{X}$ for 50 blazars in both states,
the slopes of both the linear regression equations are also close to 1. These
results support a close link between relativistic jets and accretion on to the
central Kerr black hole. On the other hand, we find that BL Lac objects have
low accretion efficiency $\eta$, whereas FSRQs have high accretion efficiency
$\eta$. The unified model of FSRQs and BL Lac objects is also discussed.


title:
Fast Variability of Nonthermal X-Ray Emission in Cassiopeia A: Probing
  Electron Acceleration in Reverse-Shocked Ejecta

abstract:
  Recent discovery of the year-scale variability in the synchrotron X-ray
emission of the supernova remnant (SNR) RX J1713.7-3946 has initiated our study
of multi-epoch X-ray images and spectra of the young SNR Cassiopeia A based on
the Chandra archive data taken in 2000, 2002, and 2004. We have found
year-scale time variations in the X-ray intensity for a number of X-ray
filaments or knots associated with the reverse-shocked regions. The X-ray
spectra of the variable filaments are characterized by a featureless continuum,
and described by a power law with a photon index within 1.9-2.3. The upper
limits on the iron K-line equivalent width are 110 eV, which favors a
synchrotron origin of the X-ray emission. The characteristic variability
timescale of 4 yr can be explained by the effects of fast synchrotron cooling
and diffusive shock acceleration with a plausible magnetic field of 1 mG. The
X-ray variability provides a new effective way of studying particle
acceleration at supernova shocks.


title:
The radio luminosity, black hole mass and Eddington ratio for quasars
  from the Sloan Digital Sky Survey

abstract:
  We investigate the $\mbh- \sigma_*$ relation for radio-loud quasars with
redshift $z<0.83$ in Data Release 3 of the Sloan Digital Sky Survey (SDSS). The
sample consists of 3772 quasars with better model of H$\beta$ and \oiii lines
and available radio luminosity, including 306 radio-loud quasars, 3466
radio-quiet quasars with measured radio luminosity or upper-limit of radio
luminosity (181 radio-quiet quasars with measured radio luminosity). The virial
supermassive black hole mass (\mbh) is calculated from the broad \hb line, the
host stellar velocity dispersion ($\sigma_*$) is traced by the core \oiii
gaseous velocity dispersion, and the radio luminosity and the radio loudness
are derived from the FIRST catalog. Our results are follows: (1) For
radio-quiet quasars, we confirm that there is no obvious deviation from the
$\mbh- \sigma_*$ relation defined in inactive galaxies when \mbh uncertainties
and luminosity bias are concerned. (2) We find that radio-loud quasars deviate
much from the $\mbh- \sigma_*$ relation respect to that for radio-quiet
quasars. This deviation is only partly due to the possible cosmology evolution
of the $\mbh- \sigma_*$ relation and the luminosity bias. (3) The radio
luminosity is proportional to
$\mbh^{1.28^{+0.23}_{-0.16}}(\lb/\ledd)^{1.29^{+0.31}_{-0.24}}$ for radio-quiet
quasars and $\mbh^{3.10^{+0.60}_{-0.70}}(\lb/\ledd)^{4.18^{+1.40}_{-1.10}}$ for
radio-loud quasars. The weaker correlation of the radio luminosity dependence
upon the mass and the Eddington ratio for radio-loud quasars shows that other
physical effects would account for their radio luminosities, such as the black
hole spin.


title: Study of isospin violating $\phi$ excitation in $e^+e^- \to \omega\pi^0$

abstract:
  We study the reaction $e^+ e^-\to \omega\pi^0$ in the vicinity of $\phi$ mass
region. The isospin-violating $\phi$ excitation is accounted for by two major
mechanisms. One is electromagnetic (EM) transition and the other is strong
isospin violations. For the latter, we consider contributions from the
intermediate hadronic meson loops and $\phi$-$\rho^0$ mixing as the major
mechanisms via the $t$ and s-channel transitions, respectively. By fitting the
recent KLOE data, we succeed in constraining the model parameters and
extracting the $\phi\to\omega\pi^0$ branching ratio. It shows that the
branching ratio is sensitive to the $\phi$ excitation line shape and background
contributions. Some crucial insights into the correlation between isospin
violation and Okubo-Zweig-Iizuka (OZI) rule evading transitions are also
learned.


title: The strength of the Weak Lefschetz Property

abstract:
  We study a number of conditions on the Hilbert function of a level artinian
algebra which imply the Weak Lefschetz Property (WLP). Possibly the most
important open case is whether a codimension 3 SI-sequence forces the WLP for
level algebras. In other words, does every codimension 3 Gorenstein algebra
have the WLP? We give some new partial answers to this old question: we prove
an affirmative answer when the initial degree is 2, or when the Hilbert
function is relatively small. Then we give a complete answer to the question of
what is the largest socle degree forcing the WLP.


title: Separable d-permutations and guillotine partitions

abstract:
  We characterize separable multidimensional permutations in terms of forbidden
patterns and enumerate them by means of generating function, recursive formula
and explicit formula. We find a connection between multidimensional
permutations and guillotine partitions of a box. In particular, a bijection
between $d$-dimensional permutations and guillotine partitions of a
$2^{d-1}$-dimensional box is constructed. We also study enumerating problems
related to guillotine partitions under certain restrictions revealing
connections to other combinatorial structures. This allows us to obtain results
on avoided patterns in permutations.


title:
Development of a Turbulent Outflow During Electron-Positron Magnetic
  Reconnection

abstract:
  The mass symmetry between the two species in electron-positron (pair) plasmas
has interesting consequences for collisionless magnetic reconnection because
the Hall term, which plays a crucial role in supporting fast reconnection in
electron-proton plasmas, vanishes. We perform kinetic simulations of pair
reconnection in systems of various sizes, show that it remains fast, and
identify the reason why this occurs. For sufficiently large systems a
Weibel-like temperature anisotropy instability develops in the outflow from the
X-point that causes the current layer to broaden and form a Petschek-like open
outflow. We discuss the parameter regimes in which pair reconnection should be
fast and the implications for astrophysical pair plasmas.


title:
Huge tunnelling anisotropic magnetoresistance in (Ga,Mn)As
  nanoconstrictions

abstract:
  We report large anisotropic magnetoresistance (AMR) behaviours in single
lateral (Ga,Mn)As nanoconstriction of up to 1300%, along with large multistable
telegraphic switching. The nanoconstriction devices are fabricated using
high-resolution electron beam lithography of a 5 nm thick (Ga,Mn)As epilayer.
The unusual behaviour exhibited by these devices is discussed in the context of
existing theories for enhanced AMR ferromagnetic semiconductor nanoscale
devices, particularly with regard to the dependence on the magnetotransport of
the bulk material. We conclude that our results are most consistent with the
Coulomb blockade AMR mechanism.


title: New Insights from One-Dimensional Spin Glasses

abstract:
  The concept of replica symmetry breaking found in the solution of the
mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a
variety of problems in science ranging from biological to computational and
even financial analysis. Thus it is of paramount importance to understand which
predictions of the mean-field solution apply to non-mean-field systems, such as
realistic short-range spin-glass models. The one-dimensional spin glass with
random power-law interactions promises to be an ideal test-bed to answer this
question: Not only can large system sizes-which are usually a shortcoming in
simulations of high-dimensional short-range system-be studied, by tuning the
power-law exponent of the interactions the universality class of the model can
be continuously tuned from the mean-field to the short-range universality
class. We present details of the model, as well as recent applications to some
questions of the physics of spin glasses. First, we study the existence of a
spin-glass state in an external field. In addition, we discuss the existence of
ultrametricity in short-range spin glasses. Finally, because the range of
interactions can be changed, the model is a formidable test-bed for
optimization algorithms.


title: Restoring the Suzaku Source Position Accuracy and Point-Spread Function

abstract:
  We present an empirical correction of sky coordinates of X-ray photons
obtained with the XIS aboard the Suzaku satellite to improve the source
position accuracy and restore the point-spread function (PSF). The XIS images
are known to have an uncertainty in position of up to 1 arcmin, and to show
considerable degradations of the PSF. These problems are caused by a drifting
of the satellite attitude due to thermal distortion of the side panel 7, where
the attitude control system is mounted. We found that the position error
averaged over a pointing observation can be largely reduced by using the
relation between the deviation of the source position in the DETX direction and
the ecliptic latitude of the pointing target. We parameterized the wobbling of
the source position synchronized with the satellite orbital period with
temperatures of onboard radiators and elapsed time since the night-day
transition of the spacecraft. We developed software, aeattcor, to correct the
image drift using these parameters, and applied it to 27 point-source images.
We show that the radius of the 90% error circle of the source position was
reduced to 19 arcsec and the PSF was sharpened. These improvements have
enhanced the scientific capability of the Suzaku XIS.


title: Decomposing replicable functions

abstract:
  We describe an algorithm to decompose rational functions from which we
determine the poset of groups fixing these functions.


title: Triangle UD integrals in the position space

abstract:
  We investigate triangle UD ladder integrals in the position space. The
investigation is necessary to find an all-order in loop solution for an
auxiliary Lcc correlator in Wess-Zumino-Landau gauge of the maximally
supersymmetric Yang-Mills theory and to present correlators of dressed mean
gluons in terms of it in all loops. We show that triangle UD ladder diagrams in
the position space can be expressed in terms of the same UD functions Phi^(L)
in terms of which they were represented in the momentum space, for an arbitrary
number of rungs.


title:
On SUGRA description of boost-invariant conformal plasma at strong
  coupling

abstract:
  We study string theory duals of the expanding boost invariant conformal gauge
theory plasmas at strong coupling. The dual supergravity background is
constructed as an asymptotic late-time expansion, corresponding to
equilibration of the gauge theory plasma. The absence of curvature
singularities in the first few orders of the late-time expansion of the dual
gravitational background unambiguously determines the equilibrium equation of
the state, and the shear viscosity of the gauge theory plasma. While the
absence of the leading pole singularities in the gravitational curvature
invariants at the third order in late-time expansion determines the relaxation
time of the plasma, the subleading logarithmic singularity can not be canceled
within a supergravity approximation. We comment on the possible interpretations
of this singularity.


title: Organization of modular networks

abstract:
  We examine the global organization of heterogeneous equilibrium networks
consisting of a number of well distinguished interconnected
parts--``communities'' or modules. We develop an analytical approach allowing
us to obtain the statistics of connected components and an intervertex distance
distribution in these modular networks, and to describe their global
organization and structure. In particular, we study the evolution of the
intervertex distance distribution with an increasing number of interlinks
connecting two infinitely large uncorrelated networks. We demonstrate that even
a relatively small number of shortcuts unite the networks into one. In more
precise terms, if the number of the interlinks is any finite fraction of the
total number of connections, then the intervertex distance distribution
approaches a delta-function peaked form, and so the network is united.

categories: cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph


title:
First Observation of Coherent $\pi^0$ Production in Neutrino Nucleus
  Interactions with $E_{\nu}<$ 2 GeV

abstract:
  The MiniBooNE experiment at Fermilab has amassed the largest sample to date
of $\pi^0$s produced in neutral current (NC) neutrino-nucleus interactions at
low energy. This paper reports a measurement of the momentum distribution of
$\pi^0$s produced in mineral oil (CH$_2$) and the first observation of coherent
$\pi^0$ production below 2 GeV. In the forward direction, the yield of events
observed above the expectation for resonant production is attributed primarily
to coherent production off carbon, but may also include a small contribution
from diffractive production on hydrogen. Integrated over the MiniBooNE neutrino
flux, the sum of the NC coherent and diffractive modes is found to be (19.5
$\pm$1.1 (stat) $\pm$2.5 (sys))% of all exclusive NC $\pi^0$ production at
MiniBooNE. These measurements are of immediate utility because they quantify an
important background to MiniBooNE's search for $\nu_{\mu} \to \nu_e$
oscillations.


title: Cohomology of Flag Varieties and the Brylinski-Kostant Filtration

abstract:
  Let G be a semisimple complex algebraic group with Borel subgroup B and let P
be a parabolic subgroup of G. Let T*(G/P) denote the cotangent bundle of G/P.
Ranee Brylinski discovered a connection between cohomology of G-equivariant
line bundles on T*(G/B) and the so-called Brylinski-Kostant filtration, which
describes the action of principal sl_2 triples on G-representations. In this
paper we generalize these results to a larger class of sl_2 triples. Along the
way we also obtain generalizations of results due to Broer on cohomology of
G-equivariant bundles on T*(G/P) for various parabolics P.


title: Solution of the Holstein polaron anisotropy problem

abstract:
  We study Holstein polarons in three-dimensional anisotropic materials. Using
a variational exact diagonalization technique we provide highly accurate
results for the polaron mass and polaron radius. With these data we discuss the
differences between polaron formation in dimension one and three, and at small
and large phonon frequency. Varying the anisotropy we demonstrate how a polaron
evolves from a one-dimensional to a three-dimensional quasiparticle. We thereby
resolve the issue of polaron stability in quasi-one-dimensional substances and
clarify to what extent such polarons can be described as one-dimensional
objects. We finally show that even the local Holstein interaction leads to an
enhancement of anisotropy in charge carrier motion.


title:
Competing Orders and Spin-Density-Wave Instability in
  La(O$_{1-x}$F$_x$)FeAs

abstract:
  The interplay between different ordered phases, such as superconducting,
charge or spin ordered phases, is of central interest in condensed matter
physics. The very recent discovery of superconductivity with a remarkable
T$_c$= 26 K in Fe-based oxypnictide La(O$_{1-x}$F$_x$)FeAs is a surprise to the
scientific community\cite{Kamihara08}. The pure LaOFeAs itself is not
superconducting but shows an anomaly near 150 K in both resistivity and dc
magnetic susceptibility. Here we provide combined experimental and theoretical
evidences showing that the anomaly is caused by the spin-density-wave (SDW)
instability, and electron-doping by F suppresses the SDW instability and
recovers the superconductivity. Therefore, the La(O$_{1-x}$F$_x$)FeAs offers an
exciting new system showing competing orders in layered compounds.


title:
Spin-polarized tunneling through randomly transparent magnetic
  junctions: Reentrant magnetoresistance approaching the Julliere limit

abstract:
  Electron conductance in planar magnetic tunnel junctions with long-range
barrier disorder is studied within Glauber-eikonal approximation enabling exact
disorder ensemble averaging by means of the Holtsmark-Markov method. This
allows us to address a hitherto unexplored regime of the tunneling
magnetoresistance effect characterized by the crossover from
momentum-conserving to random tunneling as a function of the defect
concentration. We demonstrate that such a crossover results in a reentrant
magnetoresistance: It goes through a pronounced minimum before reaching
disorder- and geometry-independent Julliere's value at high defect
concentrations.


title:
Geometric Phase for Neutral Particle in the Presence of a Topological
  Defect

abstract:
  In this paper we study the quantum dynamics of a neutral particle in the
presence of a topological defect. We investigate the appearance of a geometric
phase in the relativistic quantum dynamics of neutral particle which possesses
permanent magnetic and electric dipole moments in the presence of an
electromagnetic fields in this curved background. The nonrelativistic quantum
dynamics are investigated using the Foldy-Wouthuysen expansion. The
gravitational Aharonov-Casher and He-Mckellar-Wilkens effects are investigated
for a series of electric and magnetic fields configurations.


title: Polarity-dependent dielectric torque in nematic liquid crystals

abstract:
  The dielectric dispersion in the uniaxial nematic liquid crystals affects the
switching dynamics of the director, as the dielectric torque is determined by
not only the present values of the electric field and director but also by
their past values. We demonstrate that this dielectric memory leads to an
unusual contribution to the dielectric torque that is linear in the present
field and thus polarity-sensitive. This torque can be used to accelerate the
switch-off phase of director dynamics.