Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Radiative Tau Lepton Pair Production as a Probe of Anomalous Electromagnetic Couplings of the Tau

We calculate the squared matrix element for the process e+ e- --> tau+ tau- gamma allowing for anomalous magnetic and electric dipole moments at the tau tau gamma vertex. No interferences are neglected and no approximations of light fermion masses are made. We show that anomalous moments affect not only the cross section, but also the shape of the photon energy and angular distributions. We also demonstrate that in the case of the anomalous magnetic dipole moment, the contribution from interference involving Standard Model and anomalous amplitudes is significant compared to the contribution from anomalous amplitudes alone. A program to perform the calculation is available and it may be employed as a Monte Carlo generator.Comment: 14 pages, 8 figures submitted to Nuclear Physics

A new chiral ligand: 2,6-bis 4(S)-isopropyl-1-phenyl-4,5-dihydro-1H-imidazol-2-yl pyridine

The title compound, C29H33N5, is a new chiral bis(imidazolyl) pyridine derivative with a skeleton similar to the bis(oxazolyl) pyridine derivatives, which have been extensively used as ligands in various asymmetric catalytic reactions. The most prominent feature of the present compound is the considerable sp(2) character of N atoms of the imidazoline rings. The substituents at the Nsp(2) atoms can provide a means for tuning the electronic and conformational properties of the compound

Limits on the Dipole Moments of the τ\tau-Lepton via the Process $e^{+}e^{-}\to \tau^+ \tau^- \gamma in a Left-Right Symmetric Model

Limits on the anomalous magnetic moment and the electric dipole moment of the $\tau$ lepton are calculated through the reaction $e^{+}e^{-}\to \tau^+ \tau^- \gamma$ at the $Z_1$-pole and in the framework of a left-right symmetric model. The results are based on the recent data reported by the L3 Collaboration at CERN LEP. Due to the stringent limit of the model mixing angle $\phi$, the effect of this angle on the dipole moments is quite small.Comment: 15 pages, 3 figure

Population Viability of Barren-ground Grizzly Bears in Nunavut and the Northwest Territories

We modelled probabilities of population decline as a function of annual kill for a population of barren-ground grizzly bears (Ursus arctos) inhabiting Nunavut and the Northwest Territories, Canada. Our results suggest that the population is at risk of decline, especially if annual removal rates increase from the 42-year mean of 13.4 bears per year. Adding six bears to the mean annual kill results in a greater than 40% chance of a decrease by one-quarter in population size over the next 50 years, compared to a 10% chance with the current level of human-caused mortality. Additional mortalities may result from increased problem behaviour by bears at mine sites or hunt and exploration camps, given recent increases in human activity in the region, and may already be present as unreported mortality. We believe any increase in current harvest quotas would considerably lessen conservation prospects for the population.On a simulé les probabilités de baisse de la population en fonction du prélèvement annuel dans le cadre de la chasse pour une population de grizzlis de la toundra (Ursus arctos) habitant le Nunavut et les Territoires du Nord-Ouest, au Canada. Nos résultats suggèrent que la population risque de décliner, surtout si les taux de prélèvement augmentent par rapport à la moyenne établie sur 42 ans qui est de 13,4 ours par an. Le fait d'ajouter 6 ours au prélèvement de chasse annuel augmente à plus de 40 % le risque que la population décline d'un quart au cours des prochains 50 ans, par rapport à 10 % dans le cas du niveau actuel de mortalité provoquée par les humains. Vu l'augmentation récente de l'activité anthropique dans la région, d'autres individus pourraient être abattus à cause du nombre croissant de comportements problématiques des ours résidant à des sites miniers et à des campements d'exploration, et il est possible que ce phénomène existe déjà mais que les morts ne soient pas rapportées. Notre opinion est que toute augmentation des quotas actuels de prélèvement réduirait considérablement les perspectives de conservation pour la population

Templeting of Thin Films Induced by Dewetting on Patterned Surfaces

The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that account for the inter-site hydrodynamic and surface-energetic interactions. The film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic lengthscale of the instability, the upper bound for which is close to the spinodal lengthscale. The thin film pattern replicates the substrate surface energy pattern closely only when, (a) the periodicity of substrate pattern matches closely with the characteristic lengthscale, and (b) the stripe-width is within a range bounded by a lower critical length, below which no heterogeneous rupture occurs, and an upper transition length above which complex morphological features bearing little resemblance to the substrate pattern are formed.Comment: 5 pages TeX (REVTeX 4), other comments: submitted to Phys. Rev.Let

Dewetting of thin films on heterogeneous substrates: Pinning vs. coarsening

We study a model for a thin liquid film dewetting from a periodic heterogeneous substrate (template). The amplitude and periodicity of a striped template heterogeneity necessary to obtain a stable periodic stripe pattern, i.e. pinning, are computed. This requires a stabilization of the longitudinal and transversal modes driving the typical coarsening dynamics during dewetting of a thin film on a homogeneous substrate. If the heterogeneity has a larger spatial period than the critical dewetting mode, weak heterogeneities are sufficient for pinning. A large region of coexistence between coarsening dynamics and pinning is found.Comment: 4 pages, 4 figure

Toward a Sustainable Marketplace: Expanding Options and Benefits for Consumers

While popular interest in sustainable consumption continues to grow, there is a persistent gap between consumers’ typically positive explicit attitudes towards sustainability and their actual consumption behaviours. This gap can be explained, in part, by the belief that choosing to consume sustainably is both constraining and reduces individual-level benefits. While the belief that sustainable consumption depends on making trade-offs is true in some contexts, increasingly consumers are finding that more sustainable forms of consumption can provide both an expanded set of options and additional, individual-level benefits. In this essay, we discuss and illustrate an expanded set of options and benefits across the consumption cycle: from acquisition to usage and disposition. An underlying theme is the separation of material ownership from the extraction of consumer benefits across the consumption cycle. We believe that this ongoing evolution of products - and even business models - has the potential to simultaneously increase value to consumers as well as speed progress towards a more sustainable marketplace

Sibling relationships and family functioning in siblings of early adolescents, adolescents and young adults with autism spectrum disorder

The purpose of the study was to investigate how family functioning (defined as the ability that family members hold to manage stressful events, and intimate and social relationships), the degree to which family members feel happy and fulfilled with each other (called family satisfaction), and the demographical characteristics of siblings (age and gender) impacted on sibling relationships. The Circumplex Model of Marital and Family Systems and Behavioral Systems constituted the theoretical frameworks that guided our study. Eighty-six typically developing adolescents and young adults having a sister or a brother with autism spectrum disorder were enrolled. Results indicated that the youngest age group (early adolescents) reported to engage more frequently in negative behaviors with their siblings with ASD than the two older age groups (middle adolescents and young adults). No significant differences were found among the three age groups regarding behaviors derived from attachment, caregiving and affiliative systems. Family satisfaction and age significantly predicted behaviors during sibling interactions. Suggestions on prevention and intervention programs were discussed in order to prevent parentification among typically developing siblings and decrease episodes of quarrels and overt conflicts between brothers and sisters with and without AS