Noncommutative Residues and a Characterisation of the Noncommutative Integral

We continue the study of the relationship between Dixmier traces and noncommutative residues initiated by A. Connes. The utility of the residue approach to Dixmier traces is shown by a characterisation of the noncommutative integral in Connes' noncommutative geometry (for a wide class of Dixmier traces) as a generalised limit of vector states associated to the eigenvectors of a compact operator (or an unbounded operator with compact resolvent), i.e. as a generalised quantum limit. Using the characterisation, a criteria involving the eigenvectors of a compact operator and the projections of a von Neumann subalgebra of bounded operators is given so that the noncommutative integral associated to the compact operator is normal, i.e. satisfies a monotone convergence theorem, for the von Neumann subalgebra.Comment: 15 page

Periodic minimal surfaces of cubic symmetry

A survey of cubic minimal surfaces is presented, based on the concept of fundamental surface patches and their relation to the asymmetric units of the space groups. The software Surface Evolver has been used to test for stability and to produce graphic displays. Particular emphasis is given to those surfaces that can be generated by a finite piece bounded by straight lines. Some new varieties have been found and a systematic nomenclature is introduced, which provides a symbol (a ‘gene’) for each triply-periodic minimal surface that specifies the surface unambiguously

Ten Years of Community Profiles in New Hampshire

Through a program called Community Profiles, the University of New Hampshire Cooperative Extension has helped 57 New Hampshire communities develop a vision for their future and mobilize local residents to act on that vision. The Community Profile process is based on the premise that communities must engage members in identifying and documenting common and deeply held values from which to craft a vision for the future if they are to build and sustain community vitality. The process also helps communities find new and creative ways to pursue that vision by leveraging resources within and outside of the community. These resources include individual skills, local organizational capacity, and local, state, and regional institutional-support structures. Since creating and pursuing a vision is a challenge for communities that often rely on volunteers, the Community Profiles program was conceived to help them achieve these functions. Community Profiles is, in essence, a process that enables community residents to take stock of current conditions, build a collective set of goals for their future, and develop an action plan for realizing that vision. In the past 10 years, UNH Cooperative Extension has helped nearly a quarter of the state’s incorporated cities and towns conduct Community Profiles. This retrospective shares with our stakeholders the various successes that communities have had as a result of the process. This publication was inspired by stories emerging from Community Profiles conducted between 1996 and 2006 in 42 communities. The communities selected for this report were either particularly successful at carrying out the Community Profiles process, or they achieved positive outcomes as a result of the process. Through this report we will tell their stories and illustrate how these and other communities can work together to shape their future through persistence, creativity and teamwork

Numerical variational methods applied to cylinder buckling

We review and compare different computational variational methods applied to a system of fourth order equations that arises as a model of cylinder buckling. We describe both the discretization and implementation, in particular how to deal with a 1 dimensional null space. We show that we can construct many different solutions from a complex energy surface. We examine numerically convergence in the spatial discretization and in the domain size. Finally we give a physical interpretation of some of the solutions found.Comment: 23 pages, 12 figures, 6 table

Herschel observations in the ultracompact HII region Mon R2: Water in dense photon-dominated regions (PDRs)

Context. Monoceros R2, at a distance of 830 pc, is the only ultracompact Hii region (UC H_(II)) where the photon-dominated region (PDR) between the ionized gas and the molecular cloud can be resolved with Herschel. Therefore, it is an excellent laboratory to study the chemistry in extreme PDRs (G_0 > 10^5 in units of Habing field, n > 10^6 cm^9−3)). Aims. Our ultimate goal is to probe the physical and chemical conditions in the PDR around the UC H_(II) Mon R2. Methods. HIFI observations of the abundant compounds ^(13)CO, C^(18)O, o-H_2^(18)O, HCO^+, CS, CH, and NH have been used to derive the physical and chemical conditions in the PDR, in particular the water abundance. The modeling of the lines has been done with the Meudon PDR code and the non-local radiative transfer model described by Cernicharo et al. Results. The ^(13)CO, C^(18)O, o-H^(18)_2O, HCO^+ and CS observations are well described assuming that the emission is coming from a dense (n = 5 × 10^6 cm^(−3), N(H_2) > 10^(22) cm^(−2)) layer of molecular gas around the H_(II) region. Based on our o-H^(18)_2O observations, we estimate an o-H_2O abundance of ≈2 × 10^(−8). This is the average ortho-water abundance in the PDR. Additional H^(18)_2O and/or water lines are required to derive the water abundance profile. A lower density envelope (n ~ 10^5 cm^(−3), N(H_2) = 2−5 × 10^(22) cm^(−2)) is responsible for the absorption in the NH 1_1 → 0_2 line. The emission of the CH ground state triplet is coming from both regions with a complex and self-absorbed profile in the main component. The radiative transfer modeling shows that the ^(13)CO and HCO^+ line profiles are consistent with an expansion of the molecular gas with a velocity law, v_e = 0.5 × (r/R_(out))^(−1) km s^(−1), although the expansion velocity is poorly constrained by the observations presented here. Conclusions. We determine an ortho-water abundance of ≈2 × 10^(−8) in Mon R2. Because shocks are unimportant in this region and our estimate is based on H^(18)_2O observations that avoids opacity problems, this is probably the most accurate estimate of the water abundance in PDRs thus far

Coronavirus and long term lockdown – How HR need to be proactive and not panic

As the nationwide lockdown is extended, and uncertainty surrounding when it will end, a HR expert and digital transformation expert from the University of Salford Business School give their top tips for HR teams when supporting their staff with long term working from home

Non-diffracting Optical Beams in a Three-level Raman System

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam which couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows to propagate single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.Comment: 8 pages, 7 figure

Current developments in LC-MS for pharmaceutical analysis

The current developments in liquid chromatography-mass spectrometry (LC-MS) and its applications to the analysis of pharmaceuticals are reviewed. Various mass spectrometric techniques, including electrospray and nanospray ionization, atmospheric pressure chemical ionization and photoionization and their interface with liquid chromatographic techniques are described. These include high performance liquid chromatography, capillary electrophoresis and capillary electrochromatography and the advantages and disadvantages of each technique are discussed. The applications of LC-MS to the studies of in vitro and in vivo drug metabolism, identification and characterization of impurities in pharmaceuticals, analysis of chiral impurities in drug substances and high-throughput LC-MS-MS systems for applications in the “accelerated drug discovery” process are described

A 100 pc Elliptical and Twisted Ring of Cold and Dense Molecular Clouds Revealed by Herschel Around the Galactic Center

Thermal images of cold dust in the Central Molecular Zone of the Milky Way, obtained with the far-infrared cameras on board the Herschel satellite, reveal a ~3 × 10^7 M_☉ ring of dense and cold clouds orbiting the Galactic center. Using a simple toy model, an elliptical shape having semi-major axes of 100 and 60 pc is deduced. The major axis of this 100 pc ring is inclined by about 40° with respect to the plane of the sky and is oriented perpendicular to the major axes of the Galactic Bar. The 100 pc ring appears to trace the system of stable x_2 orbits predicted for the barred Galactic potential. Sgr A⋆ is displaced with respect to the geometrical center of symmetry of the ring. The ring is twisted and its morphology suggests a flattening ratio of 2 for the Galactic potential, which is in good agreement with the bulge flattening ratio derived from the 2MASS data