Overviewing the transition of Markowitz bi-criterion portfolio selection to tri-criterion portfolio selection

Over sixty years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an overview on how Markowitz's risk-return (bi-criterion) portfolio selection can be extended to tri-criterion portfolio selection. With a focus on the geometry of the extension, many graphs are used to illustrate

INVESTIGATIONS OF THE NEGATIVE DIFFERENTIAL CONDUCTIVITY AND CURRENT BISTABILITY IN DOUBLE BARRIER n+ GaAs/(AlGa)As/GaAs/(AlGa)As/n+ GaAs RESONANT TUNNELLING DEVICES USING HIGH MAGNETIC FIELDS

Conductivité négative différentielle (CND) et bistabilité en courant dans une structure tunnel résonnante ont été étudiées par l'effet oscillatoire dans le courant magnétotunnel avec J||B. Les mesures montrent que la bistabilité est associée avec l'accumulation et l'éjection de charge négative du puits. CND associé avec la deuxième sous-bande du puits est observée à plus grand voltage (~ 1 V). Les magnéto-oscillations indiquent la présence du tunnel séquentiel à cette région.Negative differential conductivity (NDC) and current bistability in a resonant tunnelling device are investigated by examining the oscillatory structure in the magnetotunnelling current for J ||B. The data support the conclusion that bistability is associated with build-up and ejection of negative space charge from the well. The charge density of 2D electrons in the contact accumulation layer is measured directly. NDC due to tunnelling into the second sub-band of the well is observed at high bias (~ 1 V). The associated magneto-oscillations indicate the presence of sequential tunnelling in this region of the I(V) curves