Dendrites and light open mappings

It is shown that a metric continuum is a dendrite if and only if for every compact space and for every light open mapping such that there is a copy of in for which the restriction is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.

     

Openness of induced projections

For continua and it is shown that if the projection has its induced mapping open, then is -smooth. As a corollary, a characterization of dendrites in these terms is obtained.

     

Twenty years of linear programming based portfolio optimization

Markowitz formulated the portfolio optimization problem through two criteria: the expected return and the risk, as a measure of the variability of the return. The classical Markowitz model uses the variance as the risk measure and is a quadratic programming problem. Many attempts have been made to linearize the portfolio optimization problem. Several different risk measures have been proposed which are computationally attractive as (for discrete random variables) they give rise to linear programming (LP) problems. About twenty years ago, the mean absolute deviation (MAD) model drew a lot of attention resulting in much research and speeding up development of other LP models. Further, the LP models based on the conditional value at risk (CVaR) have a great impact on new developments in portfolio optimization during the first decade of the 21st century. The LP solvability may become relevant for real-life decisions when portfolios have to meet side constraints and take into account transaction costs or when large size instances have to be solved. In this paper we review the variety of LP solvable portfolio optimization models presented in the literature, the real features that have been modeled and the solution approaches to the resulting models, in most of the cases mixed integer linear programming (MILP) models. We also discuss the impact of the inclusion of the real features.     

The interactions of saturated fatty acids at the dodecane/water interface and their sodium salts at the air/water interface

The interfacial tension of lauric, myristic and palmitic acids at the dodecane/water interface and of their sodium salts at the air/water interface were measured using the Du Noüy (ring) method. On the basis of these results the standard free energies of adsorption (ΔG⁰_ad) and of micellization (ΔG⁰_mic) of the above mentioned systems were calculated. According to deviations of the Langmuir isotherm, the corresponding interactions were discussed from the dependence of the standard free energy of adsorption on the interface coverage (Θ).