Model structures on modules over Ding-Chen rings

An $n$-FC ring is a left and right coherent ring whose left and right self FP-injective dimension is $n$. The work of Ding and Chen in \cite{ding and chen 93} and \cite{ding and chen 96} shows that these rings possess properties which generalize those of $n$-Gorenstein rings. In this paper we call a (left and right) coherent ring with finite (left and right) self FP-injective dimension a Ding-Chen ring. In case the ring is Noetherian these are exactly the Gorenstein rings. We look at classes of modules we call Ding projective, Ding injective and Ding flat which are meant as analogs to Enochs' Gorenstein projective, Gorenstein injective and Gorenstein flat modules. We develop basic properties of these modules. We then show that each of the standard model structures on Mod-$R$, when $R$ is a Gorenstein ring, generalizes to the Ding-Chen case. We show that when $R$ is a commutative Ding-Chen ring and $G$ is a finite group, the group ring $R[G]$ is a Ding-Chen ring.Comment: 12 page

Poisson approximations for the Ising model

A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration, provided the magnetic field $a=a(n)$ tends to $-\infty$ and the pair potential $b$ remains fixed. Using the Stein-Chen method, a bound is given for the total variation error in the ferromagnetic case.Comment: 25 pages, 1 figur

TRANSLATING THE VISUAL: CHEN CHIEH-JEN’S WORK

Nacido en Taiwán y actualmente residente en Taipei, Chen Chieh-jen (1960) es un videoartista cuya obra presenta una profunda y feroz – aunque a menudo silenciosa – meditación histórica y política. Sus obras se caracterizan por la inserción de imágenes de archivo que se relacionan y dialogan con imágenes contemporáneas. Mirando el pasado de China en relación con su presente, Chen subraya las consecuencias sociales, las expectativas frustradas, las interpretaciones erróneas y las apropiaciones de la mirada occidental. En particular, este estudio aborda un vídeo realizado en 2002, “Lingchi - Echoes of a historical photograph” y otro, “Factory”, realizado en 2003 que revelan el foco principal y la praxis visual y auditiva del artista. En la obra de Chen, de hecho, la visión y, sobre todo, sus límites, tanto en el sentido concreto como en el metafórico, juegan un papel importante en la construcción de un denso discurso artístico y conceptual relacionado con la creación de imágenes y la traducción visual.Born in Taiwan and currently living in Taipei, Chen Chieh-jen (1960) is a video-artist whose oeuvre presents a profound and fierce – although often silent – historical and political meditation. His works are characterized by the insertion of archival footage in close dialogue with actual and contemporary images. Looking at China’s past in relation to its present, Chen underlines social damages, frustrated expectations, misinterpretations and appropriations by the Western gaze. In particular, this study addresses a video made in 2002, “Lingchi - Echoes of a historical photograph”, and “Factory” realized in 2003; having as a mainfocus the artist’s visual and aural praxis. In Chen’s work in fact, vision, and most of all its limits, in both a concrete and metaphorical sense, play a major part in the construction of a dense artistic and conceptual discourse related to image-making and visual translation.

Fractal atomic-level percolation in metallic glasses

Metallic glasses are metallic alloys that exhibit exotic material properties. They may have fractal structures at the atomic level, but a physical mechanism for their organization without ordering has not been identified. We demonstrated a crossover between fractal short-range (<2 atomic diameters) and homogeneous long-range structures using in situ x-ray diffraction, tomography, and molecular dynamics simulations. A specific class of fractal, the percolation cluster, explains the structural details for several metallic-glass compositions. We postulate that atoms percolate in the liquid phase and that the percolating cluster becomes rigid at the glass transition temperature