Duality and equilibrium prices in economics of uncertainty

A random variable (RV) X is given aminimum selling price (S) $$S_U \left( X \right): = \mathop {\sup }\limits_x \left\{ {x + EU\left( {X - x} \right)} \right\}$$ and amaximum buying price (B) $$B_p \left( X \right): = \mathop {\inf }\limits_x \left\{ {x + EP\left( {X - x} \right)} \right\}$$ whereU(·) andP(·) are appropriate functions. These prices are derived from considerations ofstochastic optimization with recourse, and are calledrecourse certainty equivalents (RCE's) of X. Both RCE's compute the “value” of a RV as an optimization problem, and both problems (S) and (B) have meaningful dual problems, stated in terms of theCsiszár φ-divergence $$I_\phi \left( {p,q} \right): = \sum\limits_{i = 1}^n {q_i \phi \left( {\frac{{p_i }}{{q_i }}} \right)} $$ a generalized entropy function, measuring the distance between RV's with probability vectors p and q. The RCES _U was studied elsewhere, and applied to production, investment and insurance problems. Here we study the RCEB _P, and apply it to problems ofinventory control (where the attitude towards risk determines the stock levels and order sizes) andoptimal insurance coverage, a problem stated as a game between the insurance company (setting the premiums) and the buyer of insurance, maximizing the RCE of his coverage.     

Multigrid solvers in reconfigurable hardware

The problem of finding the solution of partial differential equations (PDEs) plays a central role in modeling real world problems. Over the past years, Multigrid solvers have showed their robustness over other techniques, due to its high convergence rate which is independent of the problem size. For this reason, many attempts for exploiting the inherent parallelism of Multigrid have been made to achieve the desired efficiency and scalability of the method. Yet, most efforts fail in this respect due to many factors (time, resources) governed by software implementations. In this paper, we present a hardware implementation of the V-cycle Multigrid method for finding the solution of a 2D-Poisson equation. We use Handel-C to implement our hardware design, which we map onto available field programmable gate arrays (FPGAs). We analyze the implementation performance using the FPGA vendor's tools. We demonstrate the robustness of Multigrid over other similar iterative solvers, such as Jacobi and successive over relaxation (SOR  ), in both hardware and software. We compare our findings with a C++$\mathrm{C}++$ version of each algorithm. The obtained results show better performance when compared to existing software versions.     

Finite Rank Commutators and Semicommutators of Quasihomogeneous Toeplitz Operators

We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols. We show that in this context, the situation is different from the case of harmonic Toeplitz operators. Submitted: July 23, 2007. Accepted: December 4, 2007.     

Synthesis of the tricyclic core of colchicine via a dienyne tandem ring-closing metathesis reaction

The synthesis of the tricyclic framework of colchicine has been achieved using a tandem ring-closing metathesis reaction of dienynes as the key step. In this process, both seven-membered rings B and C were formed in one step. Oxidation of tertiary allylic alcohol derived from the tandem metathesis product furnished an intermediate in the total synthesis of colchicine.     

Group 4 complexes of a new [OSSO]-type dianionic ligand. Coordination chemistry and preliminary polymerization catalysis studies

A straightforward synthesis of a new type of tetradentate dianionic [OSSO]-type ligand is described. This ligand features an ethylenedithiol core bridged via methylene groups to substituted phenols, thus representing an S analogue of the [ONNO]-type Salan ligands. The [OSSO]H2 ligand precursor reacted with titanium(IV) isopropoxide and with zirconium(IV) tert-butoxide to give the corresponding [OSSO]-M(OR)2 complexes, which formed as single C2-symmetric isomers but were fluxional according to variable-temperature NMR. An X-ray structure of [OSSO]-Zr(O-t-Bu)2 supported the fac-fac wrapping mode of the ligand. The dibenzyl complex [OSSO]-Zr(bn)2 that was obtained by a reaction between the ligand precursor and tetrabenzylzirconium was found to be an active 1-hexene polymerization catalyst upon activation with B(C6F5)3, leading to a stereoirregular polymer despite its C2 symmetry.     

Gold-labeled block copolymer micelles reveal gold aggregates at multiple subcellular sites

There is increasing interest in the usefulness of block copolymer micelles as drug delivery vehicles. However, their subcellular distribution has not been explored extensively, mostly because of the lack of adequately labeled block copolymers. In a previous study, we showed that fluorescently labeled block copolymer micelles entered living cells and co-localized with cytoplasmic organelles selectively labeled with fluorescent dyes. The details of the observed co-localizations were, however, limited by the resolution of the fluorescence approach, which is ca. 500 nm. Using transmission electron microscopy (TEM), we established time- and concentration-dependent subcellular distributions of gold-labeled micelles within human embryonic kidney (HEK 293) cells and human lung carcinoma (A549) cells. Gold particles were incorporated into poly(4-vinylpyridine)-block-poly(ethylene oxide) (P4VP21-b-PEO45) micelles. Data from dynamic light scattering (DLS) and TEM analyses revealed that the sizes of the gold particles ranged from 4 to 8 nm. The cells survived up to 24 h in the presence of low gold-labeled micelle concentrations (0.73 microg/mL), but cell death occurred at higher concentrations (i.e., kidney cells are more susceptible than lung cells). Over 24 h periods of equivalent exposure, lung cells internalized significantly more gold-incorporated micelles than kidney cells. Although micelles were added to the cell culture media as dispersed colloidal particles, the presence of serum in these media caused aggregation. These aggregates occurred mainly close to the cell plasma membrane at early times (5-10 min); however, at later times (24 h) aggregated particles were seen inside endosomes and lysozomes. Thus, gold-incorporated (labeled) micelles can serve as a valuable extension of the fluorescence approach to visualizing the localization of micelles in subcellular compartments, improving the resolution by at least 20-fold.