Olga Nikolajevna Bondareva 1937–1991

Obituary

Olga Nikolajevna Bondareva 1937–1991     

Continuous production of inorganic magnetic nanocomposites for biomedical applications by laser pyrolysis

Magnetic composites of Fe-based nanoparticles encapsulated in carbon/silica (C/SiO₂@Fe) or carbon (C@Fe) matrices were prepared by laser-induced pyrolysis of aerosols. The powders were dispersed in aqueous solutions at pH 7 resulting in biocompatible colloidal dispersions with a high resistance to biodegradation. Structural and magnetic properties and the suitability of aqueous dispersions as contrast agent for MRI were analyzed. The results of these characterizations and the NMR relaxivity data are very encouraging for application of laser pyrolysis products in the field of living tissues.     

Center location problems on tree graphs with subtree-shaped customers

We consider the p-center problem on tree graphs where the customers are modeled as continua subtrees. We address unweighted and weighted models as well as distances with and without addends. We prove that a relatively simple modification of Handler’s classical linear time algorithms for unweighted 1- and 2-center problems with respect to point customers, linearly solves the unweighted 1- and 2-center problems with addends of the above subtree customer model. We also develop polynomial time algorithms for the p-center problems based on solving covering problems and searching over special domains.     

Multicriteria Planar Ordered Median Problems

In this paper, we deal with the determination of the entire set of Pareto solutions of location problems involving Q general criteria. These criteria include median, center, or centdian objective functions as particular instances. We characterize the set of Pareto solutions of all these multicriteria problems for any polyhedral gauge. An efficient algorithm is developed for the planar case and its complexity is established. Extensions to the nonconvex case are also considered. The proposed approach is more general than previously published approaches to multicriteria location problems.The research of the third and fourth authors was partially supported by Grants BFM2001-2378, BFM2001-4028, BFM2004-0909, and HA2003-0121.     

The Concept of Proper Solution in Linear Programming

In this paper, we study the optimal solutions of a dual pair of linear programming problems that correspond to the proper equilibria of their associated matrix game. We give conditions ensuring the existence of such solutions, show that they are especially robust under perturbation of right-hand-side terms, and describe a procedure to obtain them.     

Ab initio calculation of temperature effects in the optical response of open-shell sodium clusters

Many properties of atomic clusters have been found to be size dependent, e.g., the optical response. There are, however, factors other than size that can also play an important role in determining the properties of nanoscale systems. Temperature, in particular, has been shown to have a strong effect on the optical response of open-shell sodium clusters. We incorporate the temperature effect on the optical absorption spectra by combining pseudopotentials, Langevin molecular dynamics, and time-dependent density functional theory. We have done calculations for several open-shell sodium clusters, Na(4) (+), Na(7) (+), and Na(11) (+), for which experimental data are available for comparison. We find that the positions of the lower energy peaks of the calculated spectra correspond very well to the peaks in the experimental spectra, although the local density approximation tends to overestimate the gap of the smaller clusters by up to 0.2 eV and underestimate the gap of the largest cluster by 0.4 eV. We fit the width of the peaks in the lower-temperature calculations to the corresponding experimental result to obtain the instrumental linewidth. We then use this same width for the high-temperature calculations and find very good agreement with experiment. Finally, we analyze the transitions that contribute to the observed peaks in the absorption spectra and we plot the effective valence charge density for specific transitions for each cluster. We find that for the two smaller clusters the absorption spectra are dominated by transitions from the occupied levels to a few (three for Na(4) (+) and five for Na(7) (+)) empty levels, although the contribution from transitions to other empty levels can still be significant. In contrast, the absorption spectra for Na(11) (+) come from a greater mixture of transitions as evidenced in the analysis as well as in the plot of the effective valence charge density.     

Revisiting several problems and algorithms in continuous location with \ell _\tau norms

This paper addresses the general continuous single facility location problems in finite dimension spaces under possibly different \(\ell _\tau \) norms, \(\tau \ge 1\) , in the demand points. We analyze the difficulty of this family of problems and revisit convergence properties of some well-known algorithms. The ultimate goal is to provide a common approach to solve the family of continuous \(\ell _\tau \) ordered median location problems Nickel and Puerto (Facility location: a unified approach, 2005) in dimension \(d\) (including of course the \(\ell _\tau \) minisum or Fermat-Weber location problem for any \(\tau \ge 1\) ). We prove that this approach has a polynomial worst case complexity for monotone lambda weights and can be also applied to constrained and even non-convex problems.     

Universal method for the synthesis of arbitrary polarization states radiated by a nanoantenna

Optical nanoantennas efficiently convert confined optical energy into free‐space radiation. The polarization of the emitted radiation depends mainly on nanoantenna shape, so it becomes extremely difficult to manipulate it unless the nanostructure is physically altered. Here, a simple way is demonstrated to synthetize the polarization of the radiation emitted by a single nanoantenna so that every point on the Poincaré sphere becomes attainable. The nanoantenna consists of a single scatterer created on a dielectric waveguide and fed from its both sides so that the polarization of the emitted optical radiation is controlled by the amplitude and phase of the feeding signals. The nanoantenna is created on a silicon chip using standard top‐down nanofabrication tools, but the method is universal and can be applied to other materials, wavelengths and technologies. This work will open the way towards the synthesis and control of arbitrary polarization states in nano‐optics.