April 2003 arXiv papers — page 7

Vidar Gudmundsson, Chi-Shung Tang, Andrei Manolescu

We present a grid-free DFT model appropriate to explore the time evolution of electronic states in a semiconductor nanostructure. The model can be used to investigate both the linear and the nonlinear response of the system to an external short-time perturbation in the THz regime. We use the model to study the effects of impurities on the magneto-spectroscop

A. V. Syromyatnikov, S. V. Maleyev

We give a physical picture of the low-energy sector of the spin-$\frac12$ kagome Heisenberg antiferromagnets (KAFs). It is shown that kagome lattice can be represented as a set of blocks containing 12 spins, having form of stars and arranged in a triangular lattice. Each of these stars has two degenerate singlet ground states which can be considered in terms

Yoichi Ando, X. F. Sun, J. Takeya, Seiki Komiya

In-plane and out-of-plane thermal conductivities (κ_{ab} and κ_{c}) are measured on single crystals of pure, 1%-hole-doped, and 1%-Zn-doped La_{2}CuO_{4}. The roles of magnons and the spin stripes in the heat transport in these samples are discussed. Comparison with the heat transport in CuGeO_{3}, which shows similar κ(T) behavior as that of La_{2}CuO_{4},

Anatoli Polkovnikov, Subir Sachdev, Matthias Vojta

We present additional details of the scanning tunneling microscopy (STM) spectra predicted by the model of pinning of dynamic spin collective modes in d-wave superconductor proposed by Polkovnikov et al. (cond-mat/0203176). Along with modulations at the twice the wavevector of the spin collective mode, the local density of states (LDOS) displays features lin

Scott T. Miller, Sylvain Veilleux

The results from deep long-slit spectroscopy of nine edge-on spiral galaxies with known extraplanar line emission are reported. Emission from Halpha, [N II] lambda 6548, 6583, and [S II] lambda 6716, 6731 is detected out to heights of a few kpc in all of these galaxies. Several other fainter diagnostic lines such as [O I] lambda 6300, [O III] lambda 4959, 50

L. Pirogov, I. Zinchenko, P. Caselli, L. E. B. Johansson

We present the results of N2H+(1-0) observations of 35 dense molecular cloud cores from the northern and southern hemispheres where massive stars and star clusters are formed. Line emission has been detected in 33 sources, for 28 sources detailed maps have been obtained. The optical depth of (23-12) component toward peak intensity positions of 10 sources is

Timothy C. Beers

HE 0107-5240 is a star in more than once sense of the word. Chemically, it is the most primitive object yet discovered, and it is at the centre of debate about the origins of the first elements in the Universe.

John Dubinski, Juhan Kim, Changbom Park, Robin Humble

We describe a parallel, cosmological N-body code based on a hybrid scheme using the particle-mesh (PM) and Barnes-Hut (BH) oct-tree algorithm. We call the algorithm GOTPM for Grid-of-Oct-Trees-Particle-Mesh. The code is parallelized using the Message Passing Interface (MPI) library and is optimized to run on Beowulf clusters as well as symmetric multi-proces

Vladimir L. Kalashnikov

Numerical investigation of the static spherically symmetric vacuum solution of the Logunov equations confirms the analytical results and demonstrates a strong repulsion at sub-Planckian distance from the Schwarzschild-like singularity, which is stable against the small perturbations. We suppose that the final stage of the stellar collapse in the relativistic

Elena Jimenez-Bailon, Maria Santos-Lleo, Jose Miguel Mas-Hesse, Matteo Guainazzi

We present evidence of the co-existence of either an AGN or an ultraluminous X-ray source (ULX), together with a young super stellar cluster in the 3 central parsecs of NGC4303. The galaxy contains a low luminosity AGN and hosts a number of starburst regions in a circumnuclear spiral, as well as in the nucleus itself. A high spatial resolution Chandra image

P. Popowski, C. A. Nelson, D. P. Bennett, A. J. Drake

We describe a few recent microlensing results from the MACHO Collaboration. The aim of the MACHO Project was the identification and quantitative description of dark and luminous matter in the Milky Way using microlensing toward the Magellanic Clouds and Galactic bulge. We start with a discussion of the HST follow-up observations of the microlensing events to

Tesla E. Jeltema, Claude R. Canizares, Mark W. Bautz, David A. Buote

Using Chandra archival data, we have begun a study to quantify the evolution of cluster morphology with redshift. To quantify cluster morphology, we use the power ratio method developed by Buote and Tsai (1995). Power ratios are constructed from moments of the two-dimensional gravitational potential and are, therefore, related to a cluster's dynamical st

Alexander Rosen, Michael D. Smith

The kinematic and radiative power of molecular jets is expected to change as a protostar undergoes permanent or episodal changes in the rate at which it accretes. We study here the consequences of evolving jet power on the spatial and velocity structure, as well as the fluxes, of molecular emission from the bipolar outflow. We consider a jet of rapidly incre

Maren Hempel, Michael Hilker, Markus Kissler-Patig, Thomas H. Puzia

In this third paper of our series on near-IR and optical photometry of globular cluster systems in early-type galaxies we concentrate on the photometric results for NGC 5846 and NGC 7192, two group ellipticals, and on a first comparison between the globular cluster systems investigated so far. In NGC 5846 the colour-colour diagram shows clear bi-modality in

A. F. Zakharov, S. V. Repin

Recent X-ray observations of Galactic Black Hole Candidates and AGNs and Seyfert galaxies reveal the broad emission lines in their spectra, which can arise in the innermost parts of accretion disks. Simulation indicates that at low inclination angle the line is registered by distant observer with characteristic two-peak profile. However, at high inclination

L. Wyrzykowski, A. Udalski, M. Kubiak, M. Szymanski

We present the catalog of 2580 eclipsing binary stars detected in 4.6 square degree area of the central parts of the Large Magellanic Cloud. The photometric data were collected during the second phase of the OGLE microlensing search from 1997 to 2000. The eclipsing objects were selected with the automatic search algorithm based on an artificial neural networ

V. I. Zhukov

The process of sunspot formation is considered with the account of heat effects. According to the Le Chatelier principle, a local overheating must precede to the cooling of solar surface in the places of sunspot formation. The sunspot dynamics is a process close to the surface nucleate-free boiling in a thin layer with formation of bubbles (or craters), so w

Man Hoi Lee, S. J. Peale

(Abridged) We investigate the dynamical evolution of coplanar hierarchical two-planet systems where the ratio of the orbital semimajor axes alpha=a_1/a_2 is small. The orbital parameters obtained from a multiple Kepler fit to the radial velocity variations of a star are best interpreted as Jacobi coordinates and Jacobi coordinates should be used in any analy

Jan Troost, Asato Tsuchiya

We discuss in detail the properties of gravity with a negative cosmological constant as viewed in Cherns-Simons theory on a line times a disc. We reanalyze the problem of computing the BTZ entropy, and show how the demand of unitarity and modular invariance of the boundary conformal field theory severely constrain proposals in this framework.

Smitha Vishveshwara

The Hanbury Brown-Twiss experiment has proved to be an effective means of probing statistics of particles. Here, in a set-up involving edge-state quasiparticles in a fractional quantum Hall system, we show that a variant of the experiment composed of two sources and two sinks can be used to unearth fractional statistics. We find a clear cut signature of the

Pia Astone, Giulio D'Agostini, Sabrina D'Antonio

Bayesian reasoning is applied to the data by the ROG Collaboration, in which gravitational wave (g.w.) signals are searched for in a coincidence experiment between Explorer and Nautilus. The use of Bayesian reasoning allows, under well defined hypotheses, even tiny pieces of evidence in favor of each model to be extracted from the data. The combination of th

David J. C. MacKay, Graeme Mitchison, Paul L. McFadden

We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error co

Andrew J. Barber, Dipak Munshi, Patrick Valageas

Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations w

C. V. Ciobanu, D. T. Tambe, V. B. Shenoy, C. Z. Wang

Recent experiments have shown that steps on Si(113) surfaces self-organize into bunches due to a competition between long-range repulsive and short-range attractive interactions. Using empirical and tight-binding interatomic potentials, we investigate the physical origin of the short-range attraction, and report the formation and interaction energies of step

G. L. Kane, P. Ko, C. Kolda, Jae-hyeon Park

The decay $B_d \to ϕK_S$ is a special probe of physics beyond the Standard Model (SM), since it has no SM tree level contribution. Motivated by recent data suggesting a deviation from the SM for its time-dependent CP asymmetry, we examine supersymmetric explanations. Chirality preserving contributions are generically small, unless gluino is relatively light.

Anne M Green

The orbit of the Earth about the Sun produces an annual modulation in the WIMP direct detection rate. If the local WIMP velocity distribution is isotropic then the modulation is roughly sinusoidal with maximum in June, however if the velocity distribution is anisotropic the phase and shape of the signal can change. Motivated by conflicting claims about the e

M. B. Magro, F. de Campos, O. J. P. Eboli, W. Porod

We analyze the production of multileptons in the simplest supergravity model with bilinear violation of R parity at the Fermilab Tevatron. Despite the small R-parity violating couplings needed to generate the neutrino masses indicated by current atmospheric neutrino data, the lightest supersymmetric particle is unstable and can decay inside the detector. Thi

Ahmed Jellal, Michael Schreiber

We develop a matrix model to describe bilayered quantum Hall fluids for a series of filling factors. Considering two coupling layers, and starting from a corresponding action, we construct its vacuum configuration at ν=q_iK_{ij}^{-1}q_j, where K_{ij} is a 2\times 2 matrix and q_i is a vector. Our model allows us to reproduce several well-known wave functions

Alec Maassen van den Brink

The quasinormal-mode spectrum of the Schwarzschild-de Sitter black hole is studied in the limit of near-equal black-hole and cosmological radii. It is found that the mode_frequencies_ agree with the P"oschl-Teller approximation to one more order than previously realized, even though the effective_potential_ does not. Whether the spectrum approaches the l

M. C. Smith

We present a new long-duration parallax event from the OGLE-II database, sc5_2859, which has the second longest time-scale ever identified (tE = 547.6{+22.6}{-7.8} days). We argue that both the lens and source reside in the Galactic disk, making event sc5_2859 one of the first confirmed examples of so-called disk-disk microlensing. We find that the source st

The MACRO Collaboration

The energy of atmospheric neutrinos detected by MACRO was estimated using multiple coulomb scattering of upward throughgoing muons. This analysis allows a test of atmospheric neutrino oscillations, relying on the distortion of the muon energy distribution. These results have been combined with those coming from the upward throughgoing muon angular distributi

A. Z. Bonanos, K. Z. Stanek

We apply the image subtraction method to re-analyze the ESO Very Large Telescope data on M83 (NGC 5236), obtained and analyzed by Thim et al. Whereas Thim et al. found 12 Cepheids with periods between 12-55 days, we find 112 Cepheids with periods ranging from 7-91 days, as well as ~60 other variables. These include 2 candidate eclipsing binaries, which, if c

Ling-Fong Li, Feng Wu

Unification of electromagnetic, weak, and strong coupling constants is studied in the extension of standard model with additional fermions and scalars. It is remarkable that this unification in the supersymmetric extension of standard model yields a value of Weinberg angle which agrees very well with experiments. We discuss the other possibilities which can

F. Englert, L. Houart, A. Taormina, P. West

We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra, we find that for all very extensions G+++ of simple Lie algebras there are theories of gravity and matter, which admit cl

B. I. Eisenstein

We report on a search for a CP-violating asymmetry in the charmless hadronic decay B -> K*(892)+- pi-+, using 9.12 fb^-1 of integrated luminosity produced at \sqrt{s}=10.58 GeV and collected with the CLEO detector. We find A_{CP}(B -> K*(892)+- pi-+) = 0.26+0.33-0.34(stat.)+0.10-0.08(syst.), giving an allowed interval of [-0.31,0.78] at the 90% confidence le

A. Stocchi

In the last decade, the LEP and SLD experiments played a central role in the study of B hadrons (hadrons containing a b quark). New B hadrons have been observed ($B^0_s$, Λ_b$, $Ξ_b$ and $B^{**}$) and their production and decay properties have been measured. In this paper we will focus on measurements of the CKM matrix elements: $|V_{cb}|$, $|V_{ub}|$, $|V_{

Dietmar A. Salamon, Joa Weber

We study the heat flow in the loop space of a closed Riemannian manifold $M$ as an adiabatic limit of the Floer equations in the cotangent bundle. Our main application is a proof that the Floer homology of the cotangent bundle, for the Hamiltonian function kinetic plus potential energy, is naturally isomorphic to the homology of the loop space.

Avinash Singh, Animesh Datta, Subrat K. Das, Vijay A. Singh

Carrier-mediated ferromagnetism in a dilute magnetic semiconductor has been studied using i) a single-impurity based generalized RKKY approach which goes beyond linear response theory, and ii) a mean-field-plus-spin-fluctuation (MF+SF) approach within a (purely fermionic) Hubbard-model representation of the magnetic impurities, which incorporates dynamical e

Guang-Ping He, Shi-Liang Zhu, Z. D. Wang, Hua-Zhong Li

An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated in a sufficient long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junct

Qing Guo Huang, Miao Li

Very recent CMB data of WMAP offers an opportunity to test inflation models, in particular, the running of spectral index is quite new and can be used to rule out some models. We show that an noncommutative spacetime inflation model gives a good explanation of these new results. In fitting the data, we also obtain a relationship between the noncommutative pa

Zong-Kuan Guo, Yun-Song Piao, Rong-Gen Cai, Yuan-Zhong Zhang

We study the complete evolution of a flat and homogeneous universe dominated by tachyonic matter. We demonstrate the attractor behaviour of the tachyonic inflation using the Hamilton-Jacobi formalism. We else obtain analytical approximations to the trajectories of the tachyon field in different regions. The numerical calculation shows that an initial non-van

Sijie Gao

The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.

de-Hone Lin

Partial wave theory of a two dimensional scattering problem for an arbitray short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a ``hard disk'' like potential and the magnetic flux is examined. Since the nonlocal influence of magnetic flux on the charged particles is universal, the nonlocal effec

Lan Yin, Zhen-Hua Ning

In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $πna^3$. There are two types of excitations, molecular excitations and atomic excitations. Atomic excit

Masashige Matsumoto

A simple model consisting of three distinct dimer sublattices is proposed to describe the magnetism of NH4CuCl3. It explains the occurrence of magnetization plateaus only at 1/4 and 3/4 of the saturation magnetization. The field dependence of the excitation modes observed by ESR measurements is also explained by the model. The model predicts that the magneti

Namit Mahajan

We study the top quark decay to b quark and W boson in the NonCommutative Standard Model (NCSM). The lowest contribution to the decay comes from the terms quadratic in the matrix describing the noncommutative (NC) effects while the linear term is seen to identically vanish because of symmetry. The NC effects are found to be significant only for low values of

Arbab I. Arbab

We have found an empirical law for the variation of the length of the Earth's day with geologic time employing Wells's data. We attribute the lengthening of the Earth's day to the present cosmic expansion of the Universe. The prediction of law has been found to be in agreement with the astronomical and geological data. The day increases at a pres

A. Pinter, M. Lücke, Ch. Hoffmann

The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through-flow strengths Re and d

Satchidananda Naik

The anomalous Ward identity is derived for $N = 2$ SUSY Yang-Mills theories, which is resulted out of Wrapping of $D_5$ branes on Supersymmetric two cycles. From the Ward identity One obtains the Witten-Dijkgraaf-Verlinde-Verlinde equation and hence can solve for the pre-potential. This way one avoids the problem of enhancon which maligns the non-perturbativ

Beili Wang, Hongya Liu, Lixin Xu

Recent observations of Type Ia supernovae provide evidence for the acceleration of our universe, which leads to the possibility that the universe is entering an inflationary epoch. We simulate it under a ``big bounce'' model, which contains a time variable cosmological ``constant'' that is derived from a higher dimension and manifests itself

A. Lamacraft

The shot noise of spin polarized electrons is shown to be generically dependent upon spin-flip processes. Such a situation represents perhaps the simplest instance where the two-particle character of current fluctuations out of equilibrium is explicit, leading to trinomial statistics of charge transfer in a single channel model. We calculate the effect of sp

Mikhail Khovanov

We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.

Tetsutaro Higaki, Tatsuo Kobayashi

We consider the model with the dilaton and twisted moduli fields, which is inspired by type I string models. Stabilization of their vacuum expectation values is studied. We find the stabilization of the twisted moduli field has different aspects from the dilaton stabilization.

Zhi-zhong Xing, He Zhang

We propose two ans$\rm\ddot{a}$tze of lepton mass matrices with four texture zeros, and confront them with current experimental data on neutrino oscillations. The parameter space of each ansatz is carefully explored. We find that both ans$\rm\ddot{a}$tze can accommodate the normal hierarchy of neutrino masses and the bi-large pattern of lepton flavor mixing.

Greg Smith, Souma Chaudhury, Poul S. Jessen

The linear Faraday effect is used to implement a continuous measurement of the spin of a sample of laser cooled atoms trapped in an optical lattice. One of the optical lattice beams serves also as a probe beam, thereby allowing one to monitor the atomic dynamics in real time and with minimal perturbation. A simple theory is developed to predict the measureme

Samuel Kutin

We extend Shi's 2002 quantum lower bound for collision in $r$-to-one functions with $n$ inputs. Shi's bound of $Ω((n/r)^{1/3})$ is tight, but his proof applies only in the case where the range has size at least $3n/2$. We give a modified version of Shi's argument which removes this restriction.

Magued B. Nasr, Bahaa E. A. Saleh, Alexander V. Sergienko, Malvin C. Teich

We present an experimental demonstration of quantum optical coherence tomography (QOCT). The technique makes use of an entangled twin-photon light source to carry out axial optical sectioning. QOCT is compared to conventional optical co1herence tomography (OCT). The immunity of QOCT to dispersion, as well as a factor of two enhancement in resolution, are exp

Howard Barnum

Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes of possible operations we may perform a system: ``operational states.'' I discuss general frameworks for ``oper

Asher Peres

There are no ``unknown quantum states.'' It's a contradiction in terms. Moreover, Alice and Bob are only inanimate objects. They know nothing. What is teleported instantaneously from one system (Alice) to another system (Bob) is the applicability of the preparer's knowledge to the state of a particular qubit in these systems. The operation ne

J. M. Vargas-Martinez, H. Moya-Cessa

We present a phase formalism that passes the Barnett-Pegg acid test, i.e. phase fluctuations for a number state are the expected value $π^2/3$ which are the fluctuations for a classical random phase distribution. The formalism is shown to have consistency subjected to different approaches.

A. Adelswaerd, S. Wallentowitz, W. Vogel

The equations of motion for the molecular rotation are derived for vibrationally cold dimers that are polarized by off-resonant laser light. It is shown that, by eliminating electronic and vibrational degrees of freedom, a quantum master equation for the reduced rotational density operator can be obtained. The coherent rotational dynamics is caused by stimul

W. D. Heiss

Exceptional points associated with non-hermitian operators, i.e. operators being non-hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values.

Paul Benioff

This work is based on the idea that extension of physical and mathematical theories to include the amount of space, time, momentum, and energy resources required to determine properties of systems may influence what is true in physics and mathematics at a foundational level. Background material, on the dependence of region or system sizes on both the resourc

Giovanni Andrea Fantasia

In the present work we investigate the possibility of superluminal information transmission in quantum theory. We give simple and general arguments to prove that the general structure (Hilbert's space plus instantaneous state reduction) of the theory allows the existence of superluminal communication. We discuss how this relates with existing no-signalli

S. Krishnamurthy, P. V. Santos

Numerical Calculations are employed to study the modulation of light by surface acoustic waves (SAWs) in photonic band gap (PBG) structures. The on/off contrast ratio in PBG switch based on optical cavity is determined as a function of the SAW induced dielectric modulation. We show that these structures exhibit high contrast ratios even for moderate acousto-

Roberto Benzi, Elisabetta De Angelis, Rama Govindarajan, Itamar Procaccia

Recent direct numerical simulations of the FENE-P model of non-Newtonian hydrodynamics revealed that the phenomenon of drag reduction by polymer additives exists (albeit in reduced form) also in homogeneous turbulence. We introduce here a simple shell model for homogeneous viscoelastic flows that recaptures the essential observations of the full simulations.

Masato Ida

It is known that in a certain case, the secondary Bjerknes force, which is a radiation force acting between pulsating bubbles, changes, e.g., from attraction to repulsion as the bubbles approach each other. In this paper, a theoretical discussion of this phenomenon for two spherical bubbles is described. The present theory based on analysis of the transition

Jerome Margueron, Philippe Chomaz

The phase diagram of nuclear matter is quite rich - it shows such phenomena as phase-transitions, formation of condensates, clustering, etc. From the analysis of the spinodal instability, one can learn about the region of liquid-gas coexistence in nuclear matter at low densities and finite isospin asymmetries. In a recent paper, we have shown that asymmetric

C. A. Bertulani

I discuss a few of the recent developments in nuclear reactions at very low energies with emphasis on the role of radioactive beam facilities.

J. C. Brunelli, Ashok Das, Ziemowit Popowicz

We study the supersymmetric extensions of the Harry Dym hierarchy of equations. We obtain the susy-B extension, the doubly susy-B extension as well as the N=1 and the N=2 supersymmetric extensions for this system. The N=2 supersymmetric extension is particularly interesting, since it leads to new classical integrable systems in the bosonic limit. We prove th

Jens Bolte, Jonathan Harrison

Following the quantisation of a graph with the Dirac operator (spin-1/2) we explain how additional weights in the spectral form factor K(τ) due to spin propagation around orbits produce higher order terms in the small-τasymptotics in agreement with symplectic random matrix ensembles. We determine conditions on the group of spin rotations sufficient to genera

Andreea Munteanu, Enrique Garcia-Berro, Jordi Jose, Emilia Petrisor

In the present paper, we study the Poincare map associated to a periodic perturbation, both in space and time, of a linear Hamiltonian system. The dynamical system embodies the essential physics of stellar pulsations and provides a global and qualitative explanation of the chaotic oscillations observed in some stars. We show that this map is an area preservi

Carlos R. Fadragas, Rubén Orozco Morales

The quantitative determination of the order-chaos transition in a nonlinear dynamical system described by Hénon mapping defined as $x[n+1]=1.0-A*x[n]^2+B*y[n], y[n+1]=B*x[n]$, where $B=0.3$, and $A$ is an adjustable control parameter, was made. This was achieved by applying the Inverse Average Magnitude-Squared Coherence Index (IAMSCI). This method is based

Carlos R. Fadragas, Rubén Orozco Morales

This paper is devoted to show the results obtained by using the magnitude-squared coherence for determining order-chaos transition in a system described by the logistic equation dynamics. For determining the power spectral density of a chaotic finite-duration discrete-time sequence the Welch average periodogram method was used. This method has the advantage

G. A. T. F. da Costa, A. L. Maciel

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's formula for the free energy per site in the thermodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward id

Maciej Zworski

Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description emphasizes the quantum mechanical aspects of this concept but similar models appear in many branches of physics, chemistry

Sijue Wu

We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant densities that are equal, are inviscid, incompressible and irrotational, and that the surface tension is zero. We discuss resul

Xu-Jia Wang

This is a brief survey of recent works by Neil Trudinger and myself on the Bernstein problem and Plateau problem for affine maximal hypersurfaces.

Daniel Tataru

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions, useful in the analysis of semilinear equations, and next to the study of nonlinear wave interactions, arising in fully no

Tristan Rivière

Numerous elliptic and parabolic variational problems arising in physics and geometry (Ginzburg-Landau equations, harmonic maps, Yang-Mills fields, Omega-instantons, Yamabe equations, geometric flows in general...) possess a critical dimension in which an invariance group (similitudes, conformal groups) acts. This common feature generates, in all these differ

Vladimir Maz'ya

Wiener's criterion for the regularity of a boundary point with respect to the Dirichlet problem for the Laplace equation has been extended to various classes of elliptic and parabolic partial differential equations. They include linear divergence and nondivergence equations with discontinuous coefficients, equations with degenerate quadratic form, quasil

Tai-Ping Liu

Shock wave theory was first studied for gas dynamics, for which shocks appear as compression waves. A shock wave is characterized as a sharp transition, even discontinuity in the flow. In fact, shocks appear in many different physical situation and represent strong nonlinearity of the physical processes. Important progresses have been made on shock wave theo

YanYan Li

We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry. We will also present these results which include some Liouville type theorems, Harnack type inequalities, existence and

Tero Kilpeläinen

This is a survey on problems involving equations $-\operatorname{div}{\Cal A}(x,\nabla u)=μ$, where $μ$ is a Radon measure and ${\Cal A}:\bold {R}^n\times\bold R^n\to \bold R^n$ verifies Leray-Lions type conditions. We shall discuss a potential theoretic approach when the measure is nonnegative. Existence and uniqueness, and different concepts of solutions a

Jiaxing Hong

This paper intends to give a brief survey of the developments on realization of surfaces into $ R^3$ in the last decade. As far as the local isometric embedding is concerned, some results related to the Schlaffli-Yau conjecture are reviewed. As for the realization of surfaces in the large, some developments on Weyl problem for positive curvature and an exist

Hajer Bahouri, Jean-Yves Chemin

In this text, we shall give an outline of some recent results (see \ccite{bahourichemin2} \ccite{bahourichemin3} and \ccite{bahourichemin4}) of local wellposedness for two types of quasilinear wave equations for initial data less regular than what is required by the energy method. To go below the regularity prescribed by the classical theory of strictly hype

Luigi Ambrosio

In the first part of the paper we briefly decribe the classical problem, raised by Monge in 1781, of optimal transportation of mass. We discuss also Kantorovich's weak solution of the problem, which leads to general existence results, to a dual formulation, and to necessary and sufficient optimality conditions. In the second part we describe some recent

Ken Dykema, Dan Freeman, Keri Kornelson, David Larson

We prove the existence of tight frames whose elements lie on an arbitrary ellipsoidal surface within a real or complex separable Hilbert space H, and we analyze the set of attainable frame bounds. In the case where H is real and has finite dimension, we give an algorithmic proof. Our main tool in the infinite-dimensional case is a result we have proven which

Christopher J. Pappacena

In this paper we study Frobenius bimodules between noncommutative spaces (quasi-schemes), developing some of their basic properties. If X and Y are spaces, we study those Frobenius X,Y-bimodules M satisfying properties that are natural in the context of noncommutative algebraic geometry, focusing in particular on cartain "local" conditions on M. As a

Salih Çelik, Sultan A. Çelik

We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator $x$ is invertible and furthermore working polynomials in $\ln x$ instead of polynomials in $x$. We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual Hopf algebra. Differential geometry of th

John Rognes

Let p be an odd regular prime, and assume that the Lichtenbaum-Quillen conjecture holds for K(Z[1/p]) at p. Then the p-primary homotopy type of the smooth Whitehead spectrum Wh(*) is described. A suspended copy of the cokernel-of-J spectrum splits off, and the torsion homotopy of the remainder equals the torsion homotopy of the fiber of the restricted S^1-tr

Gert Almkvist

Starting with a rational solution to Painleve' VI, coming from a Riccati equation, using Okamoto's theory a four-parametric rational solution is obtained.

Gert Almkvist

Starting with a Riccati equation solved by hypergeometric functions, some sequences of rational solutions to Painleve' VI are obtained.

Dmitri I. Panyushev

Let $\be$ be a Borel subalgebra of a complex simple Lie algebra $\g$. An ideal of $\be$ is called ad-nilpotent, if it is contained in $[\be,\be]$. The generators of an ad-nilpotent ideal give rise to an antichain in the poset of positive roots, and the whole theory can be expressed in a combinatorial fashion, in terms of antichains. The aim of this paper is

K. Magaard, S. Shpectorov, Helmut Voelklein

Let G be a finite group. By Riemann's Existence Theorem, braid orbits of generating systems of G with product 1 correspond to irreducible families of covers of the Riemann sphere with monodromy group G. Thus many problems on algebraic curves require the computation of braid orbits. In this paper we describe an implementation of this computation. We discu

Ofer Zeitouni

Random walks in random environments (RWRE's) have been a source of surprising phenomena and challenging problems since they began to be studied in the 70's. Hitting times and, more recently, certain regeneration structures, have played a major role in our understanding of RWRE's. We review these and provide some hints on current research directio

A. Yu. Zaitsev

In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known results of Komlós--Major--Tusnády and Sakhanenko. The dependence of constants on the dimension $d$ and on distributions o

T. P. Speed

This talk will review a little over a decade's research on applying certain stochastic models to biological sequence analysis. The models themselves have a longer history, going back over 30 years, although many novel variants have arisen since that time. The function of the models in biological sequence analysis is to summarize the information concernin

Ágoston Pisztora

Phase separation is a fairly common physical phenomenon with examples including the formation of water droplets from humid air (fog, rain), the separation of a crystalline structure from an isotropic material such as a liquid or even the formation of the sizzling gas bubbles when a soda can is opened. It was recognized long ago (at least on a phenomenologica

Yuval Peres

There is a close connection between intersections of Brownian motion paths and percolation on trees. Recently, ideas from probability on trees were an important component of the multifractal analysis of Brownian occupation measure, in joint work with A. Dembo, J. Rosen and O. Zeitouni. As a consequence, we proved two conjectures about simple random walk in t