Preduals of semigroup algebras

For a locally compact group $G$, the measure convolution algebra $M(G)$ carries a natural coproduct. In previous work, we showed that the canonical predual $C_0(G)$ of $M(G)$ is the unique predual which makes both the product and the coproduct on $M(G)$ weak$^*$-continuous. Given a discrete semigroup $S$, the convolution algebra $\ell^1(S)$ also carries a coproduct. In this paper we examine preduals for $\ell^1(S)$ making both the product and the coproduct weak$^*$-continuous. Under certain conditions on $S$, we show that $\ell^1(S)$ has a unique such predual. Such $S$ include the free semigroup on finitely many generators. In general, however, this need not be the case even for quite simple semigroups and we construct uncountably many such preduals on $\ell^1(S)$ when $S$ is either $\mathbb Z_+\times\mathbb Z$ or $(\mathbb N,\cdot)$.Comment: 17 pages, LaTe

Observing the sky at extremely high energies with the Cherenkov Telescope Array: Status of the GCT project

The Cherenkov Telescope Array is the main global project of ground-based gamma-ray astronomy for the coming decades. Performance will be significantly improved relative to present instruments, allowing a new insight into the high-energy Universe [1]. The nominal CTA southern array will include a sub-array of seventy 4 m telescopes spread over a few square kilometers to study the sky at extremely high energies, with the opening of a new window in the multi-TeV energy range. The Gamma-ray Cherenkov Telescope (GCT) is one of the proposed telescope designs for that sub-array. The GCT prototype recorded its first Cherenkov light on sky in 2015. After an assessment phase in 2016, new observations have been performed successfully in 2017. The GCT collaboration plans to install its first telescopes and cameras on the CTA site in Chile in 2018-2019 and to contribute a number of telescopes to the subsequent CTA production phase.Comment: 8 pages, 7 figures, ICRC201

The mean curvature at the first singular time of the mean curvature flow

Consider a family of smooth immersions $F(\cdot,t): M^n\to \mathbb{R}^{n+1}$ of closed hypersurfaces in $\mathbb{R}^{n+1}$ moving by the mean curvature flow $\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)$, for $t\in [0,T)$. We prove that the mean curvature blows up at the first singular time $T$ if all singularities are of type I. In the case $n = 2$, regardless of the type of a possibly forming singularity, we show that at the first singular time the mean curvature necessarily blows up provided that either the Multiplicity One Conjecture holds or the Gaussian density is less than two. We also establish and give several applications of a local regularity theorem which is a parabolic analogue of Choi-Schoen estimate for minimal submanifolds

Langmuir-Maxwell and Langmuir-Smoluchowski boundary conditions for thermal gas flow simulations in hypersonic aerodynamics

The simulation of nonequilibrium thermal gas flow is important for the aerothermodynamic design of re-entry and other high-altitude vehicles. In computational fluid dynamics, the accuracy of the solution to the Navier–Stokes–Fourier (N–S–F) equations depends on the accuracy of the surface boundary conditions. We propose new boundary conditions (called the Langmuir–Maxwell and the Langmuir–Smoluchowski conditions), for use with the N–S–F equations, which combine the Langmuir surface adsorption isotherm with the Maxwell/Smoluchowski slip/jump conditions in order to capture some of the physical processes involved in gas flow over a surface. These new conditions are validated for flat plate flow, circular cylinder in cross-flow, and the flow over a sharp wedge for Mach numbers ranging from 6 to 24, and for argon and nitrogen as the working gases. Our simulation results show that the new boundary conditions give better predictions for the surface pressures, compared with published experimental and DSMC data

Huon de Bordeaux peut-il être considéré comme héroï-comique?

J'examine Huon de Bordeaux pour une journée d'étude portant sur l'héroï-comique. Cet angle d'approche est bien sûr anachronique mais il permet de souligner la plasticité du texte médiéval. L'insertion d'éléments folkloriques et du merveilleux font du texte une oeuvre expérimentale

Using Metrics to Make Repository Decisions

This program will describe methods repository managers can use to help understand repository activity by emphasizing metadata and metrics. The program will repository embedded tools as well as Google Analytics to create data sets that help individuals analyze: Processes for monitoring yearly, seasonal, and monthly download and visit patterns -How to systematically evaluate download spikes and identify their sources Methods for collecting and analyzing repository data to enhance basic download counts Using comparative data to communicate with faculty about the impact of their scholarship Check out Avery Le\u27s research guide on this topic: Bring Your Stats to Life: Data Visualizations to Address and Interpret Repository Statistics

Interactions between groundwater and surface water at river banks and the confluence of rivers

Riparian vegetation depends on hydrological resources and has to adapt to changes in water levels and soil moisture conditions. The origin and mixing of water in the streamside corridor were studied in detail. The development of riparian woodland often reflects the evolution of hydrological events. River water levels and topography are certainly the main causes of the exchange between groundwater and river water through the riverbank. Stable isotopes, such as 18O, are useful tools that allow water movement to be traced. Two main water sources are typically present: (i) river water, depleted of heavy isotopes, originating upstream, and (ii) groundwater, which comes mainly from the local rainfall. On the Garonne River bank field site downstream of Toulouse, the mixing of these two waters is variable, and depends mainly on the river level and the geographical position. The output of the groundwater into the river water is not diffuse on a large scale, but localised at few places. At the confluence of two rivers, the water-mixing area is more complex because of the presence of a third source of water. In this situation, groundwater supports the hydrologic pressure of both rivers until they merge, this pressure could influence its outflow. Two cases will be presented. The first is the confluence of the Garonne and the Ariège Rivers in the south-west of France, both rivers coming from the slopes of the Pyrénées mountains. Localised groundwater outputs have been detected about 200 m before the confluence. The second case presented is the confluence of the Ganges and the Yamuna Rivers in the north of India, downstream of the city of Allahabad. These rivers are the two main tributaries of the Ganges, and both originate in the Himalayas. A strong stream of groundwater output was measured at the point of confluence