On the Schiffler center

Incenter Symmetry , Euler lines , and Schiffler Points

We look at the four-fold symmetry given by the Incenter quadrangle of a triangle, and the relation with the cirumcircle, which in this case is the nine-point conic of the quadrangle. By investigating Euler lines of Incenter triangles, we show that the classical Schiffler point extends to a set of four Schiffler points, all of which lie on the Euler line. We discover also an additional quadrangl...

On a category of cluster algebras

Abstract. We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and provide combinatorial methods for constructing special classes of monomorphisms and epimorphisms. In the case of cluster algebras from surfaces, we de...

An enantioselective total synthesis of (+)-peloruside A.

M-cluster Categories and M-replicated Algebras

Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category Cm(A) of A is the m-left part Lm(A (m)) of the m-replicated algebra of A. Moreover, we obtain a one-toone correspondence between the tilting objects in Cm(A) (that is, the m-clusters) and those tilting modules in modA(m) for which all non projective-injective di...

New Tools for Decomposition of Sea Floor Pressure Data

In recent years more and more long-term broadband data sets are collected in geosciences. Therefore there is an urgent need of algorithms which semiautomatically analyse and decompose these data into separate periods which are associated with different processes. Often Fourier and Wavelet Transform is used to decompose the data into short and long period effects but these fail often because of ...