scholarly journals On the cluster category of a marked surface without punctures

2011 ◽  
Vol 5 (4) ◽  
pp. 529-566 ◽  
Author(s):  
Thomas Brüstle ◽  
Jie Zhang
Keyword(s):  
Cluster Category ◽  
Marked Surface

scholarly journals Cotorsion pairs in the cluster category of a marked surface

2013 ◽  
Vol 391 ◽  
pp. 209-226 ◽  
Author(s):  
Jie Zhang ◽  
Yu Zhou ◽  
Bin Zhu
Keyword(s):  
Cluster Category ◽  
Cotorsion Pairs ◽  
Marked Surface

scholarly journals Density of g-Vector Cones From Triangulated Surfaces

2020 ◽  
Vol 2020 (21) ◽  
pp. 8081-8119
Author(s):  
Toshiya Yurikusa
Keyword(s):  
Asymptotic Behavior ◽  
Half Space ◽  
Closed Surface ◽  
Cluster Algebras ◽  
Connected Components ◽  
Cluster Category ◽  
Triangulated Surfaces ◽  
Cluster Tilting ◽  
Tilting Objects ◽  
Marked Surface

Abstract 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.

scholarly journals The cluster category of a surface with punctures via group actions

2021 ◽  
Vol 389 ◽  
pp. 107884
Author(s):  
Claire Amiot ◽  
Pierre-Guy Plamondon
Keyword(s):  
Group Actions ◽  
Cluster Category

scholarly journals The cluster category of a canonical algebra

2010 ◽  
Vol 362 (08) ◽  
pp. 4313-4330 ◽  
Author(s):  
M. Barot ◽  
D. Kussin ◽  
H. Lenzing
Keyword(s):  
Cluster Category ◽  
Canonical Algebra

scholarly journals Lifting to Cluster-tilting Objects in Higher Cluster Categories

2012 ◽  
Vol 19 (04) ◽  
pp. 707-712
Author(s):  
Pin Liu
Keyword(s):  
Positive Integer ◽  
Cluster Category ◽  
Tilting Modules ◽  
Endomorphism Rings ◽  
Tilted Algebras ◽  
Cluster Categories ◽  
Cluster Tilting ◽  
Tilting Objects

Let d > 1 be a positive integer. In this note, we consider the d-cluster-tilted algebras, i.e., algebras which appear as endomorphism rings of d-cluster-tilting objects in higher cluster categories (d-cluster categories). We show that tilting modules over such algebras lift to d-cluster-tilting objects in the corresponding higher cluster category.

LABORATORY EXERCISE TO DETERMINE CONTRAST IN LASER MARKING OF ARTICLES

2019 ◽  
Vol 1 ◽  
pp. 331
Author(s):  
Lyubomir Lazov ◽  
Edmunds Teirumnieks ◽  
Erika Teirumnieka ◽  
Pavel Cacivkin ◽  
Nikolay Angelov ◽  
...  
Keyword(s):  
Optimal Process ◽  
Laser Marking ◽  
New Approach ◽  
Laser Technology ◽  
Laboratory Exercise ◽  
Innovative Methods ◽  
Modern Process ◽  
The Subject ◽  
Different Dimensions ◽  
Marked Surface

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. 

scholarly journals Algebras of acyclic cluster type: Tree type and type Ã

2013 ◽  
Vol 211 ◽  
pp. 1-50 ◽  
Author(s):  
Claire Amiot ◽  
Steffen Oppermann
Keyword(s):  
Equivalence Class ◽  
Complete Classification ◽  
Global Dimension ◽  
Path Algebra ◽  
Derived Category ◽  
Derived Equivalence ◽  
Cluster Category ◽  
Cluster Type ◽  
Tree Type

AbstractIn this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of typeÃ.We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster typeÃnfor each possible orientation ofÃn.We give an explicit way to read off the derived equivalence class in which such an algebra lies, and we describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.

On Some Geometric Invariants Associated to the Space of Flat Connections on an Open Space

1996 ◽  
Vol 39 (2) ◽  
pp. 169-177
Author(s):  
I. Biswas ◽  
K. Guruprasad
Keyword(s):  
Moduli Space ◽  
Symplectic Structure ◽  
Open Space ◽  
Geometric Invariant ◽  
Flat Connections ◽  
Geometric Invariants ◽  
Marked Surface

AbstractA geometric invariant is associated to the parabolic moduli space on a marked surface and is related to the symplectic structure of the moduli space.

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

2012 ◽  
Vol 9 (1) ◽  
pp. 557-579 ◽  
Author(s):  
Y. Ma ◽  
C. Lin
Keyword(s):  
Hydrogen Peroxide ◽  
Acidithiobacillus Ferrooxidans ◽  
Pyrite Oxidation ◽  
Surface Oxidation ◽  
Mineral Surfaces ◽  
Mineral Surface ◽  
Neutral Ph ◽  
Cell Adsorption ◽  
Ph Conditions ◽  
Marked Surface

Abstract. 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.

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