Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio

Characterization of Gaps and Elements of a Numerical Semigroup Using Groebner Bases

This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way which enables us to prove some results and a hopefully interesting characterization of the elements of a semigroup in terms of Groebner bases

A Topology-Independent Mapping Technique for Application-Specific Networks-on-Chip

The design of Networks-on-Chip (NoCs) involves several key issues, including the topological mapping, that is, the mapping of the processing elements or Intellectual Properties (IPs) to the network nodes. Although several proposals have been focused on topological mapping last years, this topic is still an open issue. In this paper, we propose, in an extended manner, a topology-independent mapping technique for application-specific NoCs that can be used with regular or irregular topologies, and with any routing algorithm. This technique globally matches the communication pattern generated by the IPs with the available network bandwidth in the different parts of the network. The evaluation results show that the proposed technique can provide better performance than other mapping techniques not only in terms of average latency and network throughput, but also in terms of power consumption

Void Content Minimization in Vacuum Infusion (VI) via Effective Degassing

This paper addresses the major concern which component porosity represents in Vacuum Infusion (VI) manufacturing due to resin gelation at pressures close to absolute vacuum. Degassing is a fundamental step to minimize or even avoid resin outgassing and enhance dissolution of voids created during preform impregnation. The efficacy of different degassing procedures based on vacuum degassing, and assisted by adding a nucleation medium, High Speed (HS) resin stirring and/or later pressurization during different time intervals have been analyzed in terms of final void content is studied. Through a rigorous and careful design of the manufacturing process, outgassing effects on final void content were isolated from the rest of porosity causes and specimens with two clearly identifiable regions in terms of porosity were manufactured to facilitate its analysis. Maximum void content was kept under 4% and porous area size was reduced by 72% with respect to conventional vacuum degassing when resin was stirred at HS; therefore, highlighting the importance of enhancing bubble formation during degassing