2,117 research outputs found
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
We develop an elementary formula for certain non-trivial elements of upper
cluster algebras. These elements have positive coefficients. We show that when
the cluster algebra is acyclic these elements form a basis. Using this formula,
we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is
properly contained in its upper cluster algebra
Geometric description of C-vectors and real L\"osungen
We introduce real Loesungen as an analogue of real roots. For each mutation
sequence of an arbitrary skew-symmetrizable matrix, we define a family of
reflections along with associated vectors which are real Loesungen and a set of
curves on a Riemann surface. The matrix consisting of these vectors is called
L-matrix. We explain how the L-matrix naturally arises in connection with the
C-matrix. Then we conjecture that the L-matrix depends (up to signs of row
vectors) only on the seed, and that the curves can be drawn without
self-intersections, providing a new combinatorial/geometric description of
c-vectors
Maximal green sequences for arbitrary triangulations of marked surfaces (Extended Abstract)
International audienceIn 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
Relaxed plasma equilibria and entropy-related plasma self-organization principles
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed
The ingestion of a sodium loaded sports drink during simulated flat water kayaking does not improve performance.
Maximal green sequences for arbitrary triangulations of marked surfaces (Extended Abstract)
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
Journey to Burning Man
This comic book tells the story of four friends coping from personal trauma and stress as they embark on a journey of self-discovery and healing. The storyline focuses on character development and growth as they travel to the Burning Man festival in the Black Rock Desert of Nevada. This trip, and their desire to go in the first place, reflects open-mindedness and a willingness to engage in alternative forms of medicine beneficial to surviving and thriving after illness or injury
- …