July 2006 arXiv papers — page 21

M. de Campos

We study the gravitational collapse of a dust dark matter star in a $Λ$-background. We consider two distinct cases: First we do not have a dark matter and dark energy coupling; second, we consider that $Λ$ decay in dark particles. The approach adopted assumes a modified matter expansion rate and we have formation of a black hole, since that, we have the form

A. Skopenkov

We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as explicit constructions of embeddings. Using this approach we obtain complete concrete classification results below the me

B. F. L. Ward

We present a new approach to quantum general relativity based on the idea of Feynman to treat the graviton in Einstein's theory as a point particle field subject to quantum fluctuations just as any such field is in the well-known Standard Model of the electroweak and strong interactions. We show that by using resummation techniques based on the extension

F. Soto, H. Berger, L. Cabo, C. Carballeira

The fluctuation-diamagnetism (FD) above the superconducting transition was measured in 2H-NbSe2 single crystals. The moderate uniaxial anisotropy of this compound, and some experimental improvements, allowed to measure the superconducting fluctuation effects in the two main crystallographic directions. These results reveal that the nonlocal electrodynamic ef

Rebecca Goldin, Megumi Harada

Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrangements. By developing hyperkähler analogu

Tomonori Totani

There are several lines of evidence that the super-massive black hole at the Galactic center had higher activities in the past than directly observed at present. Here I show that these lines of evidence can quantitatively and consistently be explained if the mean accretion rate during the past ~10^7 yrs has been ~10^{3-4} times higher than the current rate,

Walter Grimus, Helmut Kuhbock

We investigate a scenario in a supersymmetric SO(10) Grand Unified Theory in which the fermion mass matrices are generated by renormalizable Yukawa couplings of the $\mathbf{10} \oplus \mathbf{120} \oplus \bar{\mathbf{126}}$ representation of scalars. We reduce the number of parameters by assuming spontaneous CP violation and a $\mathbbm{Z}_2$ family symmetr

V. Sauli, J. Adam, P. Bicudo

The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermi

R. Appleby, P. Bambade, O. Dadoun, A. Ferrari

The study of beam transport is of central importance to the design and performance assessment of modern particle accelerators. In this paper, we benchmark two contemporary codes, DIMAD and BDSIM, the latter being a relatively new tracking code built within the framework of GEANT4. We consider both the 20 mrad and 2 mrad extraction lines of the 500 GeV Intern

J. T. Mendonca, M. Marklund, P. K. Shukla, G. Brodin

A new process associated with the nonlinear optical properties of the electromagnetic vacuum, as predicted by quantum electrodynamics, is described. This can be called photon acceleration in vacuum, and corresponds to the frequency shift that takes place when a given test photon interacts with an intense beam of background radiation.

Michal Sedlak, Martin Plesch

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for a short sequence of gates - efficient quantum circuit for a given operation, is an important task. We contribute to thi

Mark D. Roberts

It is argued that string theory predicts unified field theory rather than general relativity coupled to matter fields. In unified field theory all the objects are geometrical, for strings the Kalb-Ramond matter field is identical to the asymmetric part of the metric except that the fields contribute to different sides of the field equations. The dilaton is r

M. A. L. Capri, R. F. Sobreiro, S. P. Sorella, R. Thibes

A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and Maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills theories in four dimensions.

T. G Zlosnik, P. G Ferreira, G. D Starkman

There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe on the whole it has become commonplace to invoke the presence of dark matter. An alternative approach is to modify th

B. Bagchi, P. S. Gorain, C. Quesne

We provide some explicit examples wherein the Schrödinger equation for the Morse potential remains exactly solvable in a position-dependent mass background. Furthermore, we show how in such a context, the map from the full line $(- \infty, \infty)$ to the half line $(0, \infty)$ may convert an exactly solvable Morse potential into an exactly solvable Coulomb

R. Appleby, P. Bambade, O. Dadoun, A. Ferrari

The study of beam transport is of central importance to the design and performance assessment of modern particle accelerators. In this work, we benchmark two contemporary codes - DIMAD and BDSIM, the latter being a relatively new tracking code built within the framework of GEANT4. We consider both the 20 mrad and 2 mrad extraction lines of the International

Konstantin Pankrashkin

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant.

Dubi Kelmer

We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical limit almost all eigenstates converge to the volume measure of the torus. Nevertheless, we show that for each of the inv

Moshe Kamensky

We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so that constructible sets associated with a module can be interpreted in this language. The language is expanded by additiona

Frithjof B. Anders, Ralf Bulla, Matthias Vojta

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a sing

U. Maio, K. Dolag, M. Meneghetti, L. Moscardini

We present the first hydrodynamic N-body simulations of primordial gas clouds responsible for the reionisation process in dark energy cosmologies. We compare the cosmological constant scenario with a SUGRA quintessence model with marked dynamics in order to highlight effects due to the different acceleration histories imposed by the dark energy. We show that

T. Watanabe, P. Bydžovský, K. Dobashi, S. Endo

Kaon photo-production process on $^{12}$C has been studied by measuring neutral kaons in a photon energy range of 0.8$-$1.1 GeV. Neutral kaons were identified by the invariant mass constructed from two charged pions emitted in the $K^{0}_{S}\toπ^{+}π^{-}$ decay channel. The differential cross sections as well as the integrated ones in the threshold photon en

M. Oldenburg

Measurements of azimuthal anisotropy for strange and multi-strange hadrons are presented for the first time in their centrality dependence. The high statistics results of v2(pT) allow for a more detailed comparison to hydrodynamical model calculations. Number-of-constituent-quark scaling was tested for different centrality classes separately. Higher order an

Miguel Navascues, Stefano Pironio, Antonio Acin

We introduce a hierarchy of conditions necessarily satisfied by any distribution P(ab) representing the probabilities for two separate observers to obtain outcomes a and b when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Our approach can be used to obtain upper-bounds on the q

Igor Shparlinski

We consider a generalisation of the classical Lehmer problem about the distribution of modular inverses in arithmetic progression, introduced by E. Alkan, F. Stan and A. Zaharescu. Using bounds of sums of multiplicative characters instead of traditionally applied to this kind of problem Kloosterman sums, we improve their results in several directions.

M. Heydari-Fard, M. Shirazi, S. Jalalzadeh, H. R. Sepangi

We construct the Einstein field equations on a 4-dimensional brane embedded in an $m$-dimensional bulk where the matter fields are confined to the brane by means of a confining potential. As a result, an extra term in the Friedmann equation in a $m$-dimensional bulk appears that may be interpreted as the X-matter, providing a possible phenomenological explan

Ali Mostafazadeh, Seher Ozcelik

We give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η_+, and η_+-pseudo-Hermitian operators acting in two-dimensional complex Euclidean space C^2. These operators represent the physical observables of a model whose Hamiltonian and Hilbert space are respectively H and C^2 endowed with the inner

Amaury Habrard, Francois Denis, Yann Esposito

In probabilistic grammatical inference, a usual goal is to infer a good approximation of an unknown distribution P called a stochastic language. The estimate of P stands in some class of probabilistic models such as probabilistic automata (PA). In this paper, we focus on probabilistic models based on multiplicity automata (MA). The stochastic languages gener

William Guerin, Jean-Félix Riou, John P. Gaebler, Vincent Josse

We report the first realization of a guided quasicontinuous atom laser by rf outcoupling a Bose-Einstein condensate from a hybrid optomagnetic trap into a horizontal atomic waveguide. This configuration allows us to cancel the acceleration due to gravity and keep the de Broglie wavelength constant at 0.5 $μ$m during 0.1 s of propagation. We also show that ou

Kazushi Mimura

We have applied the generating functional analysis (GFA) to the continuous Hopfield model. We have also confirmed that the GFA predictions in some typical cases exhibit good consistency with computer simulation results. When a retarded self-interaction term is omitted, the GFA result becomes identical to that obtained using the statistical neurodynamics as w

S. Blyth

We present improved measurements of the branching fractions of the color-suppressed decays $\bar{B}^0 \to D^{(*)0} h^{0}$ where $h^{0}$ represents a light neutral meson $\pi^{0}$, $\eta$ or $\omega$. The measurements are based on a data sample of 140 $fb^{-1}$, collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB energy-asymmetric $e

Junichi Shigezumi

We locate almost all the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.

P. Bozhilov, R. C. Rashkov

We investigate classical rotating membranes in two different backgrounds. First, we obtain membrane solution in $AdS_4\times S^7$ background, analogous to the solution obtained by Hofman and Maldacena in the case of string theory. We find a magnon type dispersion relation similar to that of Hofman and Maldacena and to the one found by Dorey for the two spin

Quentin Duret, Bruno Machet

We show that the Cabibbo angle theta\_c satisfies the relation tan(2 theta\_c)=-+/- 1/2 when universality for diagonal neutral currents of mass eigenstates is satisfied at the same level of accuracy as the absence of their off-diagonal counterparts. The predicted value is cos theta\_c \approx 0.9732, only 7/10000 away from experimental results. No mass ratio

Clair Poignard

Consider an ambient medium and a heterogeneous entity composed of a bidimensional material surrounded by a thin membrane. The electromagnetic constants of these materials are different. By analogy with biological cells, we call this entity a cell. We study the asymptotic behavior of the electric field in the transverse magnetic (TM) mode, when the thickness

N. N. Achasov

The ϕ\toγππamplitude is found from the e+e-\toγππamplitude suggested in Ref. hep-ph/0606266. It is shown that the found amplitude differs essentially from that studied in Refs. hep-ph/0606266 and [3]. It is noticed that the suggestion of the author of Ref. hep-ph/0606266 about the phase of the ϕ\toγππamplitude is misleading.

Yi Lin

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifold $M$ satisfies the $\bar{\partial}\partial$-lemma, we prove that the

C. A. Bertulani

Pygmy resonances in light nuclei excited in electron scattering are discussed. These collective modes will be explored in future electron-ion colliders such as ELISe/FAIR (spokesperson: Haik Simon - GSI). Response functions for direct breakup are explored with few-body and hydrodynamical models, including the dependence upon final state interactions.

Michikazu Kobayashi, Makoto Tsubota

The microscopic mechanism of thermal dissipation in quantum turbulence has been numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipa

S. J. Han

This paper presents an elementary theory of the phase-coherent collective excitations in both He II in the gravitational field and atomic Bose-Einstein condensation in a trap. The theory is based on the concept of off-diagonal long-range order by Penrose and Onsager and the quantum theory of Bohm, with emphasis on the broken symmetry in a Bose-Einstein gas w

M. Bridges, A. N. Lasenby, M. P. Hobson

We constrain the form of the primordial power spectrum using Wilkinson Microwave Anisotropy Probe (WMAP) 3-year cosmic microwave background (CMB) data (+ other high resolution CMB experiments) in addition to complementary large-scale structure (LSS) data: 2dF, SDSS, Ly-alpha forest and luminous red galaxy (LRG) data from the SDSS catalogue. We compute the co

Chad T. Kishimoto, George M. Fuller, Christel J. Smith

We solve the problem of coherent Mikheyev-Smirnov-Wolfenstein (MSW) resonant active-to-sterile neutrino flavor conversion driven by an initial lepton number in the early universe. We find incomplete destruction of lepton number in this process and a sterile neutrino energy distribution with a distinctive cusp and high energy tail. These features imply altera

Jason Fulman

Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an asymptotic description of Plancherel measure of the finite general linear groups is given, and a connection of these random w

S. Li, H. Wang, Y. D. Sun, X. X. Yi

We introduce a new quantum heat engine, in which the working medium is a quantum system with a discrete level and a continuum. Net work done by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and the low-temperature limits, but it operates diff

Baris I. Erkmen, Jeffrey H. Shapiro

Quantum optical coherence tomography (Q-OCT) offers a factor-of-two improvement in axial resolution and the advantage of even-order dispersion cancellation when it is compared to conventional OCT (C-OCT). These features have been ascribed to the non-classical nature of the biphoton state employed in the former, as opposed to the classical state used in the l

Roderich Tumulka

I am concerned with two views of quantum mechanics that John S. Bell called ``unromantic'': spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to

D. Seidel, J. G. Muga, G. C. Hegerfeldt

We study the scattering of two-level atoms at narrow laser fields, modeled by a $δ$-shape intensity profile. The unique properties of these potentials allow us to give simple analytic solutions for one or two field zones. Several applications are studied: a single $δ$-laser may serve as a detector model for atom detection and arrival-time measurements, eithe

Daniel Comparat

The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively valid for scaled timed hamiltonian and resonance processes as well as off resonance possible constructive Stückelberg interf

Ting Wang, Xiaoguang Wang, Zhe Sun

We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations

Xin-Wei Zha, Cun-Bing Huang

In accordance with the principle of superposition and operator rule, the state of the whole system composed of the state of the particles to be teleported and quantum channel can be expanded by Bell bases and transformation operator. Theoretically, if determinant of transformation operators is not zero, the teleportation can be realized only by performing an

F. Dimer, B. Estienne, A. S. Parkins, H. J. Carmichael

The Dicke model consisting of an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realise an effective Dicke system operating

Harold Fellermann, Ricard V. Solé

The building of minimal self-reproducing systems with a physical embodiment (generically called protocells) is a great challenge, with implications for both theory and applied sciences. Although the classical view of a living protocell assumes that it includes information-carrying molecules as an essential ingredient, a dividing cell-like structure can be bu

Alex Sanchez-Pla, Miquel Salicru, Jordi Ocanya

The increasing availability of high throughput data arising from gene expression studies leads to the necessity of methods for summarizing the available information. As annotation quality improves it is becoming common to rely on the Gene Ontology (GO) to build functional profiles that characterize a set of genes using the frequency of use of each GO term or

Yueheng Lan, Peter G. Wolynes, Garegin A. Papoian

Cellular signaling networks have evolved to cope with intrinsic fluctuations, coming from the small numbers of constituents, and the environmental noise. Stochastic chemical kinetics equations govern the way biochemical networks process noisy signals. The essential difficulty associated with the master equation approach to solving the stochastic chemical kin

C. Christensen, A. Gupta, C. D. Maranas, R. Albert

We present the methods and results of a two-stage modeling process that generates candidate gene-regulatory networks of the bacterium B. subtilis from experimentally obtained, yet mathematically underdetermined microchip array data. By employing a computational, linear correlative procedure to generate these networks, and by analyzing the networks from a gra

E. Carlon, T. Heim, J. Klein Wolterink, G. T. Barkema

In a recent paper [Phys. Rev. E 68, 011906 (2003)], Naef and Magnasco suggested that the "bright" mismatches observed in Affymetrix microarray experiments are caused by the fluorescent molecules used to label RNA target sequences, which would impede target-probe hybridization. Their conclusion is based on the observation of "unexpected" asymm

Zhaoming Zhu, Andrew M. C. Dawes, Daniel J. Gauthier, Lin Zhang

We investigate slow-light via stimulated Brillouin scattering in a room temperature optical fiber that is pumped by a spectrally broadened laser. Broadening the spectrum of the pump field increases the linewidth $Δω_p$ of the Stokes amplifying resonance, thereby increasing the slow-light bandwidth. One physical bandwidth limitation occurs when the linewidth

Teck-Ghee Lee, N. Balakrishnan, R. C. Forrey, P. C. Stancil

We present quantum mechanical close-coupling calculations of collisions between two hydrogen molecules over a wide range of energies, extending from the ultracold limit to the super-thermal region. The two most recently published potential energy surfaces for the H$_2$-H$_2$ complex, the so-called DJ (Diep and Johnson, 2000) and BMKP (Boothroyd et al., 2002)

A. A. G. Cortines, R. Riera

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well fitted by q-Gaussians with exponential d

Edward W. Piotrowski, Malgorzata Schroeder

Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows for an interesting financial interpretation of the Boltzmann/Shannon entropy. A "no-go" hypothesis for big

Antonio Siber

A simple tight-binding model is used to illustrate how the time dependence of a state vector can be obtained from all the eigenvalues and eigenvectors of the Hamiltonian. The behavior of the eigenvalues and eigenvectors is studied for various parameters and allows us to study scattering-like events, impurity states, and localization in disordered systems.

Sergey Leble, Maxim Solovchuk

The system of hydrodynamic-type equations, derived by two-side distribution function for a stratified gas in gravity field is applied to a problem of ultrasound. The theory is based on Gross-Jackson kinetic equation, which solution is built by means of locally equilibrium distribution function with different local parameters for molecules moving "up"

Sébastien Poncet, Anthony Randriamampianina

A three-dimensional direct numerical simulation (3D DNS) is performed to describe the turbulent flow in an enclosed rotor-stator cavity characterized by a large aspect ratio $G=(b-a)/h=18.32$ and a small radius ratio $a/b=0.15$ ($a$ and $b$ the inner and outer radii of the rotating disk and $h$ the interdisk spacing). Recent comparisons with velocity measure

V. Gol'dshtein, G. A. Koganov

An indicator for presence of community structure in networks is suggested. It allows one to check whether such structures can exist, in principle, in any particular network, without a need to apply computationally cost algorithms. In this way we exclude a large class of networks that do not possess any community structure.

Quentin Guegan, J. -N. Foulc, F. Ayela, O. Tillement

The properties of suspensions of fine particles in dielectric liquid (electrorheological fluids) subjected to an electric field lead to a drastic change of the apparent viscosity of the fluid. For high applied fields (~ 3-5 kV/mm) the suspension congeals to a solid gel (particles fibrillate span the electrode gap) having a finite yield stress. For moderate f

Anthony Randriamampianina, Wolf-Gerrit Fruh, Peter L. Read, Pierre Maubert

Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a

Andrew W. Steiner

The symmetry energy of nucleonic matter is usually assumed to be quadratic in the isospin density. While this may be justified at sub-saturation densities, there is no need to enforce this restriction at super-saturation densities. The presence of a quartic term can strongly modify the critical density for the direct Urca process which leads to faster coolin

J. Piekarewicz

The nucleus of 208Pb -- a system that is 18 order of magnitudes smaller and 55 orders of magnitude lighter than a neutron star -- may be used as a miniature surrogate to establish important correlations between its neutron skin and several neutron-star properties. Indeed, a nearly model-independent correlation develops between the neutron skin of 208Pb and t

Barry R. Holstein

Using a recent reformulation of the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT), we show how predictions for parity-violating observables in low-energy light hadronic systems can be understood in an analytic fashion. It is hoped that such an analytic approach may encourage additional experimental work as wel

C. Giusti, A. Meucci, F. D. Pacati

A relativistic distorted-wave impulse-approximation model is applied to neutral-current and charged-current quasi-elastic neutrino-nucleus scattering. The effects of final state interactions are investigated and the sensitivity of the results to the strange nucleon form factors is discussed in view of their possible experimental determination

Gideon Simpson, Marc Spiegelman, Michael I. Weinstein

An outstanding problem in Earth science is understanding the method of transport of magma in the Earth's mantle. Models for this process, transport in a viscously deformable porous media, give rise to scalar degenerate, dispersive, nonlinear wave equations. We establish a general local well-posedness for a physical class of data (roughly $H^1$) via fixed

M. Marder

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where

Arseni Goussev, J. R. Dorfman

We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave pac

Sibel Baskal, Elena Georgieva, Y. S. Kim

The two-by-two scattering matrix for one-dimensional scattering processes is a three-parameter Sp(2) matrix or its unitary equivalent. For one-dimensional crystals, it would be repeated applications of this matrix. The problem is how to calculate N repeated multiplications of this matrix. It is shown that the original Sp(2) matrix can be written as a similar

Y. Charles Li

In this article, we prove the existence of Arnold diffusion for an interesting specific system -- discrete nonlinear Schrödinger equation. The proof is for the 5-dimensional case with or without resonance. In higher dimensions, the problem is open. Progresses are made by establishing a complete set of Melnikov-Arnold integrals in higher and infinite dimensio

Ehud Hrushovski, Ya'acov Peterzil, Anand Pillay

We discuss measures, invariant measures on definable groups, and genericity, often in an NIP (failure of the independence property) environment. We complete the proof of the third author's conjectures relating definably compact groups $G$ in saturated $o$-minimal structures to compact Lie groups. We also prove some other structural results about such $G$

G. David, T. DePauw, T. Toro

In 1960 Reifenberg proved the topological disc property. He showed that a subset of $R^n$ which is well approximated by $m$-dimensional affine spaces at each point and at each (small) scale is locally a bi-Hölder image of the unit ball in $R^m$. In this paper we prove that a subset of $R^3$ which is well approximated by a minimal cone at each point and at ea

Eduard Kontorovich, Michael Megrelishvili

It is well known that for a transitive dynamical system (X,f) sensitivity to initial conditions follows from the assumption that the periodic points are dense. This was done by several authors: Banks, Brooks, Cairns, Davis and Stacey, Silverman, and also by Glasner and Weiss. In the latter article Glasner and Weiss established a stronger result (for compact

Guillaume Lecué

We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The idea is to develop the Bayes rule in a fundamental system of $L^2([0,1]^d)$ made of indicator of dyadic sets and to assume

Aleksei Beltukov, David Feldman

We establish new relations which connect Euclidean sonar transforms (integrals taken over spheres with centers in a hyperplane) with classical Radon transforms. The relations, stated as operator identities, allow us to reduce the inversion of sonar transforms to classical Radon inversion.

Jose F Alves, Vitor Araujo

We consider dynamical systems on compact manifolds, which are local diffeomorphisms outside an exceptional set (a compact submanifold). We are interested in analyzing the relation between the integrability (with respect to Lebesgue measure) of the first hyperbolic time map and the existence of positive frequency of hyperbolic times. We show that some (strong

Vitor Araujo

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost a

Vitor Araujo

Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show the existence of time averages for almost every orbit of each point of M, imposing mild conditions on the families. Moreover these averages are given by a finite number of physical absolutely continuous sta

Jinqiao Duan, Andrei V. Fursikov

The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable fluctuations in numerical realization of stabilization procedures are taken into account and they are supposed to be ind

Michael Mihalik, John Ratcliffe, Steven Tschantz

In this paper we describe a family of isomorphism invariants of a finitely generated Coxeter group W. Each of these invariants is the isomorphism type of a quotient group W/N of W by a characteristic subgroup N. The virtue of these invariants is that W/N is also a Coxeter group. For some of these invariants, the isomorphism problem of W/N is solved and so we

Bernard Bonnard, Emmanuel Trélat

Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^ω)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.

Emmanuel Trélat

We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere ne

Emmanuel Trélat

Let $T>0$ fixed. We consider the optimal control problem for analytic affine systems: $\ds{\dot{x}=f\_0(x)+\sum\_{i=1}^m u\_if\_i(x)}$, with a cost of the form: $\ds{C(u)=\int\_0^T \sum\_{i=1}^m u\_i^2(t)dt}$. For this kind of systems we prove that if there are no minimizing abnormal extremals then the value function $S$ is subanalytic. Secondly we prove tha

Miles Gould

It has long been known that every weak monoidal category A is equivalent via monoidal functors and monoidal natural transformations to a strict monoidal category st(A). We generalise the definition of weak monoidal category to give a definition of weak P-category for any strongly regular (operadic) theory P, and show that every weak P-category is equivalent

Jean-Gabriel Luque, Gérard Henry Edmond Duchamp

Let $\M(A,θ)$ be a free partially commutative monoid. We give here a necessary and sufficient condition on a subalphabet $B\subset A$ such that the right factor of a bisection $\M(A,θ)=\M(B,θ\_B).T$ be also partially commutative free. This extends strictly the (classical) elimination theory on partial commutations and allows to construct new factorizations o

Gérard Henry Edmond Duchamp, Jean-Gabriel Luque

This article is devoted to the study of monoids which can be endowed with a shuffle product with coefficients in a semiring. We show that, when the multiplicities do not belong to a ring with prime characteristic, such a monoid is a monoid of traces. When the characteristic is prime, we give a decomposition of the congruences $\equiv$ (or relators $R$) such

Shiro Goto, Ken-ichi Yoshida

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous $k$-algebras $A$ in terms of the dimension $d$, the codimension $c$, the initial degree $q$, and the length of the local cohomology modules of $A$. Next, we introduce the notion of Buchsbaum $k$-algebras with minimal multiplicity of degree $q$, and give several characteriza

Roland Bacher

We present a few factorizations of polynomials over finite fields. These factorizations are related to traces, compositions of polynomials and binomial coefficients. As a corollary we obtain a description of all irreducible polynomials $Q\in {\mathbb F}\_2[x]$ such that $Q(1+x+x^2)$ (or $Q(x+x^2)$) remain irreducible.

Gérard Duchamp, Marianne Flouret, Eric Laugerotte, Jean-Gabriel Luque

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws.

Gérard Duchamp, Eric Laugerotte, Jean-Gabriel Luque

In the classical theory of formal languages, finite state automata allow to recognize the words of a rational subset of $Σ^*$ where $Σ$ is a set of symbols (or the alphabet). Now, given a semiring $(\K,+,.)$, one can construct $\K$-subsets of $Σ^*$ in the sense of Eilenberg, that are alternatively called noncommutative formal power series for which a framewo

Jean-Gabriel Luque, J. -Y. Thibon

The hyperdeteminants considered here are the simplest analogues of determinants for higher rank tensors which have been defined by Cayley, and apply only to tensors with an even number of indices. We have shown in a previous article that the calculation of certain multidimensional integrals could be reduced to the evaluation of hyperdeterminants of Hankel ty

Tsuyoshi Miezaki, Hiroshi Nozaki, Junichi Shigezumi

We locate all of the zeros of the Eisenstein series associated with the Fricke groups $Γ_0^{*}(2)$ and $Γ_0^{*}(3)$ in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (``{\it On the zeros of Eisenstein series}'', 1970).

Claire David, Pierre Sagaut, Tapan Sengupta

A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular

Glenn Merlet

We analyze the asymptotic behavior of random variables $x(n,x\_0)$ defined by $x(0,x\_0)=x\_0$ and $x(n+1,x\_0)=A(n)x(n,x\_0)$, where $\sAn$ is a stationary and ergodic sequence of random matrices with entries in the semi-ring \mbox{$\R\cup\{-\infty\}$} whose addition is the $\max$ and whose multiplication is $+$. Such sequences modelize a large class of dis

Jean-Francois Dat

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a question left open since Bernstein's fundamental work for R=C. In a first step, we prove that this noetherian proper