Minimal faithful modules over Artinian rings

Let R be a left Artinian ring, and M a faithful left R-module such that no proper submodule or homomorphic image of M is faithful. If R is local, and socle(R) is central in R, we show that length(M=J(R)M) + length(socle(M)) ≤ length(socle(R)) + 1. If R is a finite-dimensional algebra over an algebraically closed field, but not necessarily local or having central socle, we get an inequality similar to the above, with the length of socle(R) interpreted as its length as a bimodule, and the summand +1 replaced by the Euler characteristic of a graph determined by the bimodule structure of socle(R). The statement proved is slightly more general than this summary; we examine the question of whether much stronger generalizations are possible. If a faithful module M over an Artinian ring is only assumed to have one of the above minimality properties { no faithful proper submodules, or no faithful proper homomorphic images { we find that the length of M=J(R)M in the former case, and of socle(M) in the latter, is ≤ length(socle(R)). The proofs involve general lemmas on decompositions of modules

Physical properties of outflows: Comparing CO and H2O based parameters in Class 0 sources

Context. The observed physical properties of outflows from low-mass sources put constraints on possible ejection mechanisms. Historically, these quantities have been derived from CO using ground-based observations. It is thus important to investigate whether parameters such as momentum rate (thrust) and mechanical luminosity (power) are the same when different molecular tracers are used. Aims. We aim at determining the outflow momentum, dynamical time-scale, thrust, energy and power using CO and H2O as tracers of outflow activity. Methods. Within the framework of the WISH key program, three molecular outflows from Class 0 sources have been mapped using the HIFI instrument aboard Herschel. We use these observations together with previously published H2 data to infer the physical properties of the outflows. We compare the physical properties derived here with previous estimates based on CO observations. Results. Inspection of the spatial distribution of H2O and H2 confirms that these molecules are co-spatial. The most prominent emission peaks in H2 coincide with strong H2O emission peaks and the estimated widths of the flows when using the two tracers are comparable. Conclusions. For the momentum rate and the mechanical luminosity, inferred values are independent of which tracer that is used, i.e., the values agree to within a factor of 4 and 3 respectively.Comment: Accepted for publication in A&A, 5 pages, 2 figure

Theory of Optical Transmission through Elliptical Nanohole Arrays

We present a theory which explains (in the quasistatic limit) the experimentally observed [R. Gordon, {\it et al}, Phys. Rev. Lett. {\bf 92}, 037401 (2004)] squared dependence of the depolarization ratio on the aspect ratio of the holes, as well as other features of extraordinary light transition. We calculated the effective dielectric tensor of a metal film penetrated by elliptical cylindrical holes and found the extraordinarily light transmission at special frequencies related to the surface plasmon resonances of the composite film. We also propose to use the magnetic field for getting a strong polarization effect, which depends on the ratio of the cyclotron to plasmon frequencies.Comment: 4 pages, 4 figure

Easy on that trigger dad: a study of long term family photo retrieval

We examine the effects of new technologies for digital photography on people's longer term storage and access to collections of personal photos. We report an empirical study of parents' ability to retrieve photos related to salient family events from more than a year ago. Performance was relatively poor with people failing to find almost 40% of pictures. We analyze participants' organizational and access strategies to identify reasons for this poor performance. Possible reasons for retrieval failure include: storing too many pictures, rudimentary organization, use of multiple storage systems, failure to maintain collections and participants' false beliefs about their ability to access photos. We conclude by exploring the technical and theoretical implications of these findings

Systems biology of energetic and atomic costs in the yeast transcriptome, proteome, and metabolome

Proteins vary in their cost to the cell and natural selection may favour the use of proteins that are cheaper to produce. We develop a novel approach to estimate the amino acid biosynthetic cost based on genome-scale metabolic models, and directly investigate the effects of biosynthetic cost on transcriptomic, proteomic and metabolomic data in _Saccharomyces cerevisiae_. We find that our systems approach to formulating biosynthetic cost produces a novel measure that explains similar levels of variation in gene expression compared with previously reported cost measures. Regardless of the measure used, the cost of amino acid synthesis is weakly associated with transcript and protein levels, independent of codon usage bias. In contrast, energetic costs explain a large proportion of variation in levels of free amino acids. In the economy of the yeast cell, there appears to be no single currency to compute the cost of amino acid synthesis, and thus a systems approach is necessary to uncover the full effects of amino acid biosynthetic cost in complex biological systems that vary with cellular and environmental conditions

Cinematic and aesthetic cartographies of subjective mutation

This article exmaines the use of cinema as a mapping of subjective mutation in the work of Deleuze, Gauttari and Berardi. Drawing on Deleuze's distinciton between the reduction of the art-work to the symptom and the idea of art as symptomatology, the article focuses on Berardi's use of cinematic examples, posing the quesiton in each case of to what extent they function as symptomatologies or mere symptoms of cultural and subjective mutations in examples ranging from Bergman's Persona to Van Sant's Elephant to finish on speculations about Fincher's The Social Network as a cirtical engagement with subjective mutation in the 21st Century

Suppression of Spin-Orbit Scattering in Strong-Disordered Gold Nanojunctions

We discovered that spin-orbit scattering in strong-disordered gold nanojunctions is strongly suppressed relative to that in weak-disordered gold thin films. This property is unusual because in weak-disordered films, spin-orbit scattering increases with disorder. Granularity and freezing of spin-orbit scattering inside the grains explains the suppression of spin-orbit scattering. We propose a generalized Elliot-Yafet relation that applies to strong-disordered granular regime.Comment: 4 pages 4 figure

Lectures on Non-BPS Dirichlet branes

A comprehensive introduction to the boundary state approach to Dirichlet branes is given. Various examples of BPS and non-BPS Dirichlet branes are discussed. In particular, the non-BPS states in the duality of Type IIA on K3 and the heterotic string on T4 are analysed in detail.Comment: 46 pages, 5 figures, LaTeX; lectures given at the TMR network school on `Quantum aspects of gauge theories, supersymmetry and quantum gravity', Torino, 26 January - 2 February 2000, and at the `Spring workshop on Superstrings and related matters', Trieste, 27 March - 4 April 2000; references adde

Structure of the Effective Potential in Nonrelativistic Chern-Simons Field Theory

We present the scalar field effective potential for nonrelativistic self-interacting scalar and fermion fields coupled to an Abelian Chern-Simons gauge field. Fermions are non-minimally coupled to the gauge field via a Pauli interaction. Gauss's law linearly relates the magnetic field to the matter field densities; hence, we also include radiative effects from the background gauge field. However, the scalar field effective potential is transparent to the presence of the background gauge field to leading order in the perturbative expansion. We compute the scalar field effective potential in two gauge families. We perform the calculation in a gauge reminiscent of the $R_\xi$-gauge in the limit $\xi\rightarrow 0$ and in the Coulomb family gauges. The scalar field effective potential is the same in both gauge-fixings and is independent of the gauge-fixing parameter in the Coulomb family gauge. The conformal symmetry is spontaneously broken except for two values of the coupling constant, one of which is the self-dual value. To leading order in the perturbative expansion, the structure of the classical potential is deeply distorted by radiative corrections and shows a stable minimum around the origin, which could be of interest when searching for vortex solutions. We regularize the theory with operator regularization and a cutoff to demonstrate that the results are independent of the regularization scheme.Comment: 24 pages, UdeM-LPN-TH-93-185, CRM-192