In this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation.

‎based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified polak-ribière-polyak conjugate‎ ‎gradient method proposed by yu et al‎. ‎is presented‎.

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions given quotients of two-dimensional cobordisms. These generalize Deligne's interpolation representations groups. In this paper, we classify indecomposable objects identify the associated graded Grothendieck rings Khovanov–Sazdanovic's through sums representation over crossed products pol...

In this paper, we present a new approach for solving absolute value equation (AVE) whichuse Levenberg-Marquardt method with conjugate subgradient structure. In conjugate subgradientmethods the new direction obtain by combining steepest descent direction and the previous di-rection which may not lead to good numerical results. Therefore, we replace the steepest descentdir...

background: in most of defecography films, the symphysis pubis is obscured, especially in obese patients, and the parameters will change in values if x-ray is interpreted by different reviewers or if the patient changes his/her position between the phases. this study was carried out to determine how to do the defecography to obtain fixed parameters. â  methods: eighty patients that had been can...

We study continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish convergence theorems for those methods which are generated by approximate solutions to evolution equations governed by regular vector fields. Since the complement of the set of regular vector fields is σ-porous, we conclude that our results apply to most vector fiel...

We present sufficient conditions under which effective descent morphisms in a quasivariety of universal algebras are the same as regular epimorphisms and examples for which they are the same as regular epimorphisms satisfying projectivity. 1. Preliminaries A variety is a full subcategory of the category of structures for a first order (one sorted) language, closed under substructures, products ...

After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois extensions) can be given geometric meaning extending their geometric interpretations in the commutative case. On the other hand, we show that some constructions...

Comodules over Hopf algebroids are of central importance in algebraic topology. It is well-known that a Hopf algebroid is the same thing as a presheaf of groupoids on Aff , the opposite category of commutative rings. We show in this paper that a comodule is the same thing as a quasi-coherent sheaf over this presheaf of groupoids. We prove the general theorem that internal equivalences of preshe...