The NIEP

The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix. The NIEP has a long history and is a known hard (perhaps the hardest in matrix analysis?) and sought after problem. Thus, there are many subproblems and relevant results in a variety of directions. We survey most work on the problem and its several variants, with an emphasis on recent results, and include 130 references. The survey is divided into: a) the single eigenvalue problems; b) necessary conditions; c) low dimensional results; d) sufficient conditions; e) appending 0's to achieve realizability; f) the graph NIEP's; g) Perron similarities; and h) the relevance of Jordan structure

Singular dynamics under a weak potential on a sphere

We give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. We perform a McGehee-type blow-up in order to cope with the singularity of the potential when the point mass goes through the singularity. In addition we investigate the rest-points of the flow, the invariant (stable and unstable) manifolds and we give a complete dynamical description of the motion

Measuring consumer effort in circular economy initiatives in the food domain: An exploratory analysis

: The transition towards a Circular Economy (CE) system requires a change in consumers' behavioural pattern that implies a certain level of effort which, in turn, could affect initiatives' success. Although consumers' role in CE is increasingly drawing the attention of scholars, limited knowledge is available on the evaluation of consumer's effort in CE initiatives. The current research provides an identification and measurement of the core parameters affecting consumer effort, offering a comprehensive Effort Index applied to 20 CE companies operating in food domain. Companies were classified in 5 categories (Quantity of food, Appearance of food, Edibility of food, Living with food and Local and sustainable food); the analysis of the companies revealed 14 parameters building the Effort Index. Results showed that initiatives ascribable to the category "Local and sustainable food" require higher levels of consumer effort; in contrast, case studies belonging to "Edibility of food" group are less effort-requiring