Computing SL(2,C) Central Functions with Spin Networks

Let G=SL(2,C) and F_r be a rank r free group. Given an admissible weight in N^{3r-3}, there exists a class function defined on Hom(F_r,G) called a central function. We show that these functions admit a combinatorial description in terms of graphs called trace diagrams. We then describe two algorithms (implemented in Mathematica) to compute these functions.Comment: to appear in Geometriae Dedicat

The Centurion 18 telescope of the Wise Observatory

We describe the second telescope of the Wise Observatory, a 0.46-m Centurion 18 (C18) installed in 2005, which enhances significantly the observing possibilities. The telescope operates from a small dome and is equipped with a large-format CCD camera. In the last two years this telescope was intensively used in a variety of monitoring projects. The operation of the C18 is now automatic, requiring only start-up at the beginning of a night and close-down at dawn. The observations are mostly performed remotely from the Tel Aviv campus or even from the observer's home. The entire facility was erected for a component cost of about 70k$ and a labor investment of a total of one man-year. We describe three types of projects undertaken with this new facility: the measurement of asteroid light variability with the purpose of determining physical parameters and binarity, the following-up of transiting extrasolar planets, and the study of AGN variability. The successful implementation of the C18 demonstrates the viability of small telescopes in an age of huge light-collectors, provided the operation of such facilities is very efficient.Comment: 16 pages, 13 figures, some figures quality was degraded, accepted for publication in Astrophysics and Space Scienc

Can forest management based on natural disturbances maintain ecological resilience?

Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance

Nitrogen Retention in Headwater Streams: The Influence of Groundwater-Surface Water Exchange

Groundwater-surface water (GW-SW) interaction lengthens hydraulic residence times, increases contact between solutes and biologically active surfaces, and often creates a gradient of redox conditions conducive to an array of biogeochemical processes. As such, the interaction of hydraulic patterns and biogeochemical activity is suspected to be an important determinant of elemental spiraling in streams. Hydrologic interactions may be particularly important in headwater streams, where the extent of the GW-SW mixing environment (i.e., hyporheic zone) is proportionately greater than in larger streams. From our current understanding of stream ecosystem function, we discuss nitrogen (N) spiraling, present a conceptual model of N retention in streams, and use both of these issues to generate specific research questions and testable hypotheses regarding N dynamics in streams

Generalizations of Gronwall-Bihari Inequalities on Time Scales

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be applied are provided. An application to the qualitative analysis of a nonlinear dynamic equation is discussed.Comment: This is a preprint of an article accepted (16/May/2008) for publication in the "Journal of Difference Equations and Applications"; J. Difference Equ. Appl. is available online at http://www.informaworld.co

Molecular Dynamics Study of the Primary Ferrofluid Aggregate Formation

Investigations of the phase transitions and self-organization in the magnetic aggregates are of the fundamental and applied interest. The long-range ordering structures described in the Tom\'anek's systematization (M. Yoon, and D. Tom\'anek, 2010 [1]) are not yet obtained in the direct molecular dynamics simulations. The resulted structures usually are the linear chains or circles, or, else, amorphous (liquid) formations. In the present work, it was shown, that the thermodynamically equilibrium primary ferrofluid aggregate has either the long-range ordered or liquid phase. Due to the unknown steric layer force and other model idealizations, the clear experimental verification of the real equilibrium phase is still required. The predicted long-range ordered (crystallized) phase produces the faceting shape of the primary ferrofluid aggregate, which can be recognized experimentally. The medical (antiviral) application of the crystallized aggregates has been suggested. Dynamic formation of all observed ferrofluid nanostructures conforms to the Tom\'anek's systematization.Comment: Revised in the JMM

A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte

Determination of the Strange Quark Content of the Nucleon from a Next-to-Leading-Order QCD Analysis of Neutrino Charm Production

We present the first next-to-leading-order QCD analysis of neutrino charm production, using a sample of 6090 $\nu_\mu$- and $\bar\nu_\mu$-induced opposite-sign dimuon events observed in the CCFR detector at the Fermilab Tevatron. We find that the nucleon strange quark content is suppressed with respect to the non-strange sea quarks by a factor \kappa = 0.477 \: ^{+\:0.063}_{-\:0.053}, where the error includes statistical, systematic and QCD scale uncertainties. In contrast to previous leading order analyses, we find that the strange sea $x$-dependence is similar to that of the non-strange sea, and that the measured charm quark mass, $m_c = 1.70 \pm 0.19 \:{\rm GeV/c}^2$, is larger and consistent with that determined in other processes. Further analysis finds that the difference in $x$-distributions between $xs(x)$ and $x\bar s(x)$ is small. A measurement of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|=0.232 ^{+\:0.018}_{-\:0.020}$ is also presented. uufile containing compressed postscript files of five Figures is appended at the end of the LaTeX source.Comment: Nevis R#150

The chemical enrichment of the ICM from hydrodynamical simulations

The study of the metal enrichment of the intra-cluster and inter-galactic media (ICM and IGM) represents a direct means to reconstruct the past history of star formation, the role of feedback processes and the gas-dynamical processes which determine the evolution of the cosmic baryons. In this paper we review the approaches that have been followed so far to model the enrichment of the ICM in a cosmological context. While our presentation will be focused on the role played by hydrodynamical simulations, we will also discuss other approaches based on semi-analytical models of galaxy formation, also critically discussing pros and cons of the different methods. We will first review the concept of the model of chemical evolution to be implemented in any chemo-dynamical description. We will emphasise how the predictions of this model critically depend on the choice of the stellar initial mass function, on the stellar life-times and on the stellar yields. We will then overview the comparisons presented so far between X-ray observations of the ICM enrichment and model predictions. We will show how the most recent chemo-dynamical models are able to capture the basic features of the observed metal content of the ICM and its evolution. We will conclude by highlighting the open questions in this study and the direction of improvements for cosmological chemo-dynamical models of the next generation.Comment: 25 pages, 11 figures, accepted for publication in Space Science Reviews, special issue "Clusters of galaxies: beyond the thermal view", Editor J.S. Kaastra, Chapter 18; work done by an international team at the International Space Science Institute (ISSI), Bern, organised by J.S. Kaastra, A.M. Bykov, S. Schindler & J.A.M. Bleeke