The concept of linear sets in projective spaces was introduced by Lunardon in 1999 and it plays central roles in the study of blocking sets, semifields, rank-metric codes and etc. A linear set with the largest possible cardinality is called scattered. Despite of two decades of study, there are only three known families of maximum scattered linear sets defined over PG(1,q^n) for infinitely many n. The first family is called pseudo-regulus type by Blokhuis and Lavrauw in 1999. The second family was found by Lunardon and Polverino in 2001 and later generalized by Sheekey in 2016. The third family was constructed by Longobardi, Marino, Trombetti and the speaker recently. In this talk, we consider the equivalence problem of maximum scattered linear sets and we show some restrictions on their automorphism groups.

Quadratically-constrained quadratic programming (QCQP) is an optimization problem that has many practical applications, for example, network localization problems, max-cut problems, and polynomial optimization problems. Since QCQP is NP-hard, semidefinite programming (SDP) relaxation is often employed to obtain a good approximate solution, and many researchers have discussed the condition for the SDP relaxation to give an exact optimal solution of the original QCQP.

智能运维是保障航空、航天、能源、化工等领域众多关键装备安全稳定运行的基础。当前智能运维技术大多建立在恒定转速、恒定负载的基本假设之上。然而，在工业4.0时代，大量重要装备运行于变速-变载的复杂服役环境。工况的无规律变化使得传统的运维理论与预测技术不再有效，很多潜在故障源无法被准确识别与预测，给工业生产带来了巨大的经济损失。汇报人结合课题组多年的研究成果和工程实践，从机理层面剖析了变工况对当前机电装备智能运维带来的挑战；探讨了若干变工况动态信息的前沿处理技术；以及如何化害为利，主动利用机电装备的多源信息开展早期和定量化诊断。相关方法可为风电、高铁、工业机器人、精密机床、自动化产线等重要装备的健康监测和智能运维提供新思路。