Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from f+; g. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Influence of dopants on the properties of maghemite

Preparatiun or aci cular maghemi te containing dopan ls li ke Mg. i and Gd and their characleris,llion us ing different analytica l techniques have been reported. These in vestigat ions reveal that the addition of dopants li ke Mg. Ni and Gd modifies the magnetic properties without cfrecting any structural changes. The opt ical bandgaps of these doped compositions have ,li S() hecn determ ined. Evidence is ,li so av,li lab le from spectroscopic investi gations suggest ing thalmaghcllli te prepared vi,l the ()xa l,ltc precursor route does nm exhi bit a hydrogen fe rrite structure