In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ...

We relate the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting (7. Towards this end, we introduce node-searching, a slight variant of searching, in which an edge is cleared by placing searchers on both of its endpoints. We also show that the minimum number of searchers necessary to node-sea...

Let be a simple and connected graph. A k-vertex separator [k-edge separator] is a subset of vertices [edges] whose deletion separates the vertex [edge] set of into two parts of equal cardinality, that are at distance greater than k in . Here we investigate the relation between the cardinality of these cutsets and the laplacian spectrum of . As a consequence of the study, we obtain the well-know...

This study aims to investigate and optimize the effects of the main parameters including the particle size, gravity and magnetic separation combination, high gradient magnetic separation, magnetic field intensity, shaking table slope, washing water flow, and electrostatic separation upon the rare earth element (REE) recoveries from iron mine waste. The electron microprobe showed that high amoun...

Latin squares can be classified as odd or even according to the signs of the permutations given by their rows and columns. In this paper, the behaviour of the parities of a latin square under the action of the isotopy group (permuting rows, columns, and symbols) and the transformation group (interchanging rows, columns, and symbols) is analyzed. A rule is given that shows that the behaviour of ...

Incisional hernia is the most common postoperative complication, affecting up to 20% of patients after abdominal surgery. Insertion of a synthetic surgical mesh has become the standard of care in ventral hernia repair. However, the implementation of a mesh does not reduce the risk of recurrence and the onset of hernia recurrence is only delayed by 2-3 years. Nowadays, more than 100 surgical mes...

This paper deals with the well known classes of threshold and difference graphs, both characterized by separators, i.e. node weight functions and thresholds. We show how to maintain minimum the value of the separator when the input (threshold or difference) graph is fully dynamic, i.e. edges/nodes are inserted/removed. Moreover, exploiting the data structure used for maintaining the minimality ...