Uniformization of metric surfaces using isothermal coordinates

We establish a uniformization result for metric surfaces – metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be covered by quasiconformal images of Euclidean domains is quasiconformally equivalent to a Riemannian surface. To prove this, we construct an atlas of suitable isothermal coordinates.

The braid group and its presentation

In this paper, we recall the geometric definition of the braid group by Emil Artin and we give a complete, elementary geometric/topological proof of the standard presentation of the braid group on [Formula: see text] strings.

Anomaly inflow methods for SCFT constructions in type IIB

We extend the anomaly inflow methods developed in M-theory to SCFTs engineered via D3-branes in type IIB. We show that the ’t Hooft anomalies of such SCFTs can be computed systematically from their geometric definition. Our procedure is tested in several 4d examples and applied to 2d theories obtained by wrapping D3-branes on a Riemann surface. In particular, we show how to analyze half-BPS regular punctures for 4d $$ \mathcal{N} $$ N = 4 SYM on a Riemann surface. We discuss generalizations of this formalism to type IIB configurations with F3, H3 fluxes, as well as to F-theory setups.

Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction

A geometric definition of entanglements in athermal random networks is proposed and is linked to the network stiffness. Entanglements produce a self-equilibrated stress which increases the stiffness.

STUDENTS' POSITIONING AND EMOTIONS IN LEARNING GEOMETRIC DEFINITION

The purpose of the present paper is to study the positions and emotions of grade 7 students who work with technology to learn geometry. This consideration of students’ emotions is socially based, which makes it necessary to use a socially-based theoretical framework in order to study them. One such theory is the discursive analysis framework suggested by Evans, Morgan, and Tsatsarony, which is utilized in the present paper to analyze the positioning and emotions of fifteen groups of grade seven students who utilized technology to investigate the circle topic. The findings show that the group leaders took their positions through knowledge, action, initiation, persistence and meta-processes, while the followers of directions took their positions by accepting the group leader's requests. What most distinguished the collaborator was the communication with the other members of the group. Furthermore, the insiders used pronouns that indicated their inclusion. The results show that technology nurtured students' positive emotions as a result of nurturing their positioning throughout the investigation of the circle topic.

Modelling the fire propagation from the fuel bed to the lower canopy of ornamental species used in wildland–urban interfaces

South-eastern France is strongly affected by wildfires mostly occurring in the wildland–urban interfaces (WUIs). A WUI fire is often initiated in dead surface fuel, then can propagate to shrubs and trees when the lower canopy is close to (or touches) the ground. Whereas a previous study assessed the fire propagation from the fuel bed to the lower canopy of different species used as ornamental vegetation in this region, the objectives of the current work consisted of checking if the modelling of this fire propagation was possible using WFDS (Wildland–Urban Interface Fire Dynamical Simulator) in comparing experimental and modelling results. Experimental and modelling constraints (i.e. branch geometric definition, branch motion due to convection) showed differences in some of the recorded data (such as time to ignition, ignition temperature, mass loss and maximum temperature), but comparisons of variation in mass loss and temperature over time showed that modelling the fire propagation at the scale of a branch was possible if the branch fuel-moisture content remained lower than 25%. For both experiments and modelling, the ranking of species according to their branch flammability highlighted identical groups of species.