Abstract
Despite its worldwide relevance as an invasive plant, there are few studies on Ulex europaeus (gorse) and its allelopathic activity is almost unexplored. The allelochemical profile of gorse was analysed through methanolic extract of pods and roots, and its phytotoxic effects on Lactuca sativa germination. The methanolic extract of pods had no effect in germination, while extract of roots resulted in a U-shaped dose-response curve: reducing the germination at concentration 0.5 mg mL-1. GC-MS analysis detected compounds with proven antimicrobial and antioxidant activities in the pods and cytotoxic compounds in the roots, which could explain the bioassay results. The quinolizidine alkaloids (QAs) composition was evaluated to predict possible biological functions. It showed the presence of QAs in gorse that are absent in their native range, indicating broad defense strategies against bacteria, fungi, plants, and insects in the Chilean ecosystem. This could explain the superiority of gorse in the invaded areas.

Abstract
This work discusses and analyzes a class of nonconvex homogeneous optimization problems, in which the objective function is a positively homogeneous function with a certain degree, and the constraints set is determined by a single homogeneous function with another degree, and a geometric set which is a (not necessarily convex) closed cone. Once a Lagrangian dual problem is associated, it is provided various characterizations for the validity of strong duality property: one of them is related to the convexity of a certain image of the geometric set involving both homogeneous functions, so revealing a hidden convexity. We also derive a suitable S-lemma. In the case where both functions are of the same degree of homogeneity, a copositive reformulation of the original problem is established. It is also established zero-, first-and second-order optimality conditions; KKT (local or global) optimality, giving rise to the notion of L-eigenvalues with applications to symmetric tensors eigenvalues analysis.

Abstract