Maximizing Neumann fundamental tones of triangles

We prove sharp isoperimetric inequalities for Neumann eigenvalues of the Laplacian on triangular domains. The first nonzero Neumann eigenvalue is shown to be maximal for the equilateral triangle among all triangles of given perimeter, and hence among all triangles of given area. Similar results are proved for the harmonic and arithmetic means of the first two nonzero eigenvalues

Ab initio study of canted magnetism of finite atomic chains at surfaces

By using ab initio methods on different levels we study the magnetic ground state of (finite) atomic wires deposited on metallic surfaces. A phenomenological model based on symmetry arguments suggests that the magnetization of a ferromagnetic wire is aligned either normal to the wire and, generally, tilted with respect to the surface normal or parallel to the wire. From a first principles point of view, this simple model can be best related to the so--called magnetic force theorem calculations being often used to explore magnetic anisotropy energies of bulk and surface systems. The second theoretical approach we use to search for the canted magnetic ground state is first principles adiabatic spin dynamics extended to the case of fully relativistic electron scattering. First, for the case of two adjacent Fe atoms an a Cu(111) surface we demonstrate that the reduction of the surface symmetry can indeed lead to canted magnetism. The anisotropy constants and consequently the ground state magnetization direction are very sensitive to the position of the dimer with respect to the surface. We also performed calculations for a seven--atom Co chain placed along a step edge of a Pt(111) surface. As far as the ground state spin orientation is concerned we obtain excellent agreement with experiment. Moreover, the magnetic ground state turns out to be slightly noncollinear.Comment: 8 pages, 5 figures; presented on the International Conference on Nanospintronics Design and Realizations, Kyoto, Japan, May 2004; to appear in J. Phys.: Cond. Matte

High Resolution Mid-Infrared Imaging of Ultraluminous Infrared Galaxies

Observations of ultraluminous infrared galaxies (ULIRGs) with an achieved resolution approaching the diffraction limit in the mid-infrared from 8 - 25 $\mu$m using the Keck Telescopes are reported. We find extremely compact structures, with spatial scales of $< 0.3''$ (diameter) in six of the seven ULIRGs observed. These compact sources emit between 30% and 100% of the mid-infrared energy from these galaxies. We have utilized the compact mid-infrared structures as a diagnostic of whether an AGN or a compact (100 -- 300 pc) starburst is the primary power source in these ULIRGs. In Markarian 231, the upper limit on the diameter of the 12.5 $\mu$m source, 0.13$''$, shows that the size of the infrared source must increase with increasing wavelength, consistent with AGN models. In IRAS 05189-2524 and IRAS 08572+3915 there is strong evidence that the source size increases with increasing wavelength. This suggests heating by a central source rather than an extended luminosity source, consistent with the optical classification as an AGN. The compact mid-infrared sources seen in the other galaxies cannot be used to distinguish the ultimate luminosity source. If these ULIRGs are powered by compact starbursts, the star formation rates seen in the central few hundred parsecs far exceed the global rates seen in nearby starburst galaxies, and approach the surface brightness of individual clusters in nearby starburst galaxies.Comment: 33pages, 6 tables, 5 figures, Accepted for publication in A

Specifying computer-supported collaboration scripts

Collaboration scripts are activity programs which aim to foster collaborative learning by structuring interaction between learners. Computer-supported collaboration scripts generally suffer from the problem of being restrained to a specific learning platform and learning context. A standardization of collaboration scripts first requires a specification of collaboration scripts that integrates multiple perspectives from computer science, education and psychology. So far, only few and limited attempts at such specifications have been made. This paper aims to consolidate and expand these approaches in light of recent findings and to propose a generic framework for the specification of collaboration scripts. The framework enables a description of collaboration scripts using a small number of components (participants, activities, roles, resources and groups) and mechanisms (task distribution, group formation and sequencing)

Structural Stability and Renormalization Group for Propagating Fronts

A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection principle for propagating fronts. We give examples, using numerical and renormalization group methods.Comment: 14 pages, uiucmac.tex, no figure

Temporal Model Adaptation for Person Re-Identification

Person re-identification is an open and challenging problem in computer vision. Majority of the efforts have been spent either to design the best feature representation or to learn the optimal matching metric. Most approaches have neglected the problem of adapting the selected features or the learned model over time. To address such a problem, we propose a temporal model adaptation scheme with human in the loop. We first introduce a similarity-dissimilarity learning method which can be trained in an incremental fashion by means of a stochastic alternating directions methods of multipliers optimization procedure. Then, to achieve temporal adaptation with limited human effort, we exploit a graph-based approach to present the user only the most informative probe-gallery matches that should be used to update the model. Results on three datasets have shown that our approach performs on par or even better than state-of-the-art approaches while reducing the manual pairwise labeling effort by about 80%

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Hubble Space Telescope Images of Magellanic Cloud Planetary Nebulae: Data and Correlations across Morphological Classes

The morphology of planetary nebulae (PNe) provides an essential tool for understanding their origin and evolution, as it reflects both the dynamics of the gas ejected during the TP-AGB phase, and the central star energetics. Here we study the morphology of 27 Magellanic Cloud planetary nebulae (MCPNe) and present an analysis of their physical characteristics across morphological classes. Similar studies have been successfully carried out for galactic PNe, but were compromised by the uncertainty of individual PN distances. We present our own HST/FOC images of 15 Magellanic Cloud PNe (MCPNe) acquired through a narrow-band lambda 5007 [O III] filter. We use the Richardson-Lucy deconvolution technique on these pre-COSTAR images to achieve post-COSTAR quality. Three PNe imaged before and after COSTAR confirm the high reliability of our deconvolution procedure. We derive morphological classes, dimensions, and surface photometry for all these PNe. We have combined this sample with HST/PC1 images of 15 MCPNe, three of which are in common with the FOC set, acquired by Dopita et al. (1996), to obtain the largest MCPN sample ever examined from the morphological viewpoint. By using the whole database, supplemented with published data from the literature, we have analyzed the properties of the MCPNe and compared them to a typical, complete galactic sample. Morphology of the MCPNe is then correlated with PN density, chemistry, and evolution.Comment: text file lstanghe_mcpn.tex (LaTex); Figures 2 through 10, Figure 5 is in 3 parts (a,b,c); Figure 1 available by regular mail only; ApJ, in press, November 10, 199

Gap Formation in the Dust Layer of 3D Protoplanetary Disks

We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.Comment: 5 page, 4 figures. Accepted for publication in Astrophysics & Space Scienc