Maximal green sequences for arbitrary triangulations of marked surfaces (Extended Abstract)

International audience In general, the existence of a maximal green sequence is not mutation invariant. In this paper we show that it is in fact mutation invariant for cluster quivers associated to most marked surfaces. We develop a procedure to find maximal green sequences for cluster quivers associated to an arbitrary triangulation of closed higher genus marked surfaces with at least two punctures. As a corollary, it follows that any triangulation of a marked surface with at least one boundary component has a maximal green sequence.

Density of g-Vector Cones From Triangulated Surfaces

We study $g$-vector cones associated with clusters of cluster algebras defined from a marked surface $(S,M)$ of rank $n$. We determine the closure of the union of $g$-vector cones associated with all clusters. It is equal to $\mathbb{R}^n$ except for a closed surface with exactly one puncture, in which case it is equal to the half space of a certain explicit hyperplane in $\mathbb{R}^n$. Our main ingredients are laminations on $(S,M)$, their shear coordinates, and their asymptotic behavior under Dehn twists. As an application, if $(S,M)$ is not a closed surface with exactly one puncture, the exchange graph of cluster tilting objects in the corresponding cluster category is connected. If $(S,M)$ is a closed surface with exactly one puncture, it has precisely two connected components.

Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface

We study the Ginzburg dg algebra $\Gamma _{\mathbf {T}}$ associated with the quiver with potential arising from a triangulation $\mathbf {T}$ of a decorated marked surface ${\mathbf {S}}_\bigtriangleup$, in the sense of [22]. We show that there is a canonical way to identify all finite-dimensional derived categories $\operatorname {\mathcal {D}}_{fd}(\Gamma _{\mathbf {T}})$, denoted by $\operatorname {\mathcal {D}}_{fd}({\mathbf {S}}_\bigtriangleup )$. As an application, we show that the spherical twist group $\operatorname {ST}({\mathbf {S}}_\bigtriangleup )$ associated with $\operatorname {\mathcal {D}}_{fd}({\mathbf {S}}_\bigtriangleup )$ acts faithfully on its space of stability conditions.

LABORATORY EXERCISE TO DETERMINE CONTRAST IN LASER MARKING OF ARTICLES

The laser marking has been established in recent years as one of the modern innovative methods for marking many industrial products. The report examines a new laboratory exercise for the subject Laser Technology, studied in some technical universities. A new approach is proposed to determine the contrast of the laser marking process. Described is the purpose and the main tasks as well as the new skills and knowledge that students can exercise through this laboratory exercise. Students implement a test matrix consisting of squares of a certain size using the raster marking method. Through the new laboratory exercise, students can explore and analyze the dependencies of the contrast of laser markings on different dimensions influencing the technological process. The capabilities of the new approach allow learners to become more familiar with the factors that influence the modern process of laser marking widely used in modern industry. The results of the experiments the students summarize using a new modern digital approach to analyze the contrast against the background of the marked surface. From the experimental graphical dependencies of the variation of the power and speed contrast, they draw conclusions about the optimal process parameters.

QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP

We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov–Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra.

Pyrite Oxidation under initially neutral pH conditions and in the presence of <i>Acidithiobacillus ferrooxidans</i> and micromolar hydrogen peroxide

Hydrogen peroxide (H2O2) at a micromolar level played a role in the microbial surface oxidation of pyrite crystals under initially neutral pH. When the mineral-bacteria system was cyclically exposed to 50 μM H2O2, the colonization of \\textit{Acidithiobacillus ferrooxidans} onto the mineral surface was markedly enhanced, as compared to the control (no added H2O2). This can be attributed to the effects of H2O2 on increasing the roughness of the mineral surfaces, as well as the acidity and Fe2+ concentration at the mineral-solution interfaces. All of these effects tended to create more favourable nano- to micro-scale environments in the mineral surfaces for the cell adsorption. However, higher H2O2 levels inhibited the attachment of cells onto the mineral surfaces, possibly due to the oxidative stress in the bacteria when they approached the mineral surfaces where high levels of free radicals are present as a result of Fenton-like reactions. The more aggressive nature of H2O2 as an oxidant caused marked surface flaking of the mineral surface. The XPS results suggest that H2O2 accelerated the oxidation of pyrite-S and consequently facilitated the overall corrosion cycle of pyrite surfaces. This was accompanied by pH drop in the solution in contact with the pyrite cubes.