From the viewpoint of mutation, we will give a brief survey of tilting theory and cluster-tilting theory together with a motivation from cluster algebras. Then we will give an introduction to τ-tilting theory which was recently developed.

The purpose of this study is to reveal the relationship between the head position, and the neck and head muscles. At 4 head positions, the activities of masseter, anterior temporal, anterior digastric, sternocleidomastoid and trapezius muscle of ten normal subjects standing straight were investigated electromyographically with surface electrodes during voluntary maximal clenching in centric occ...

We investigate the structure of (infinite dimensional) tilting modules over hereditary artin algebras. For connected algebras of infinite representation type with Grothendieck group of rank n, we prove that for each 0 ≤ i < n− 1, there is an infinite dimensional tilting module Ti with exactly i pairwise non-isomorphic indecomposable finite dimensional direct summands. We also show that any ston...

Periodic tree are combinatorial structures which are in bijection with cluster tilting objects of affine type Ãn−1. The internal edges of the tree encode the c-vectors corresponding to the cluster tilting object. (See [8].) In this paper we assign a unipotent matrix to each tree, giving the relationship between cluster tilting objects and (pro)pictures for torsion-free (pro)nilpotent groups.

In a categorification of tensor products of fundamental representations of quantum sl(k) via highest weight categories, the indecomposable tilting modules descend to the canonical basis. Projective functors map tilting modules to tilting modules implying the coefficients of the canonical basis of tensor products of finite dimensional, irreducible representations under the action of the Chevalle...

BACKGROUND Cementless hip cups need sufficient primary tilting stability to achieve osseointegration. The aim of the study was to assess differences of the primary implant stability in osteoporotic bone and in bone with normal bone density. To assess the influence of different cup designs, two types of threaded and two types of press-fit cups were tested. METHODS The maximum tilting moment fo...

In this paper the potential of a dynamic sector tilting control scheme is assessed. By intelligent control of the tilting angle for each sectoring antenna according to the current call traffic distribution, the whole cellular network performance can be improved by down-tilting the antenna around the source of peak traffic and up-tilting antennas in adjacent cells to fill in the coverage loss. W...

Twice (Tilting device with WIde Capacity) a new amplification device able to double the tilting angle of a parallel mechanism is presented. A singularity analysis is carried out: it proves that Twice can give a huge tilting angle to Parallel Kinematic Machines (PKM). Finally, practical implementation features are discussed.