Warm-Start Heuristic for Stochastic Portfolio Optimization with Fixed and Proportional Transaction Costs

We consider a probabilistic portfolio optimization model including fixed and proportional transaction costs. We derive a deterministic equivalent of the probabilistic model for fat-tailed portfolio returns. We develop a method which finds provably near-optimal solutions in minimal amount of time for industry-sized (up to 2000 assets) problems. To solve the mixed-integer nonlinear programming (MINLP) deterministic formulation equivalent to the stochastic problem, we design a mathematical programming-based warm-start heuristic. The tests show the computational efficiency of the heuristic which is more than an order of magnitude faster than Cplex in finding high-quality solutions.     

The Dirichlet problem for the fractional Laplacian: Regularity up to the boundary

We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u   is a solution of (−Δ)^su=g${(-\mathrm{\Delta })}^{s}u=g$ in Ω  , u≡0$u\equiv 0$ in Rⁿ\Ω${\mathbb{R}}^n\backslash \Omega$, for some s∈(0,1)$s\in (0,1)$ and g∈L^∞(Ω)$g\in L^{\infty }(\Omega )$, then u   is C^s(Rⁿ)$C^s({\mathbb{R}}^n)$ and u/δ^s_|Ω$u/{\delta }^s{|}_{\Omega }$ is C^α$C^{\alpha }$ up to the boundary ∂Ω   for some α∈(0,1)$\alpha \in (0,1)$, where δ(x)=dist(x,∂Ω)$\delta (x)=\mathrm{dist}(x,\partial \Omega )$. For this, we develop a fractional analog of the Krylov boundary Harnack method.     

Nanotubes from misfit layered compounds

Abstract

First, the mechanisms leading to the formation of nanotubes from layered (2-D) materials are briefly discussed. Two main mechanisms are evoked: (1) The asymmetry of the layer along the c-axis, which leads to spontaneous folding, as revealed first by Pauling in 1930; (2) The seaming of the layer due to the abundance of dangling bonds in the rim atoms of the 2-D nanoclusters. This mechanism was discussed first in connection with carbon fullerenes and carbon nanotubes, some 30 years ago and was further extended to inorganic 2-D materials in 1992. In the second part of this work, the formation mechanism of nanotubes from misfit layered compounds (MLC) is deliberated. Here, the two forces are shown to work in synergy leading to facile formation of nanotubes from ternary misfit compounds. This synergy is demonstrated through the versatile chemistry, which has been employed to synthesize MLC nanotubes. Furthering in complexity, few recent examples of nanotubes from quaternary chalcogenide-based MLC are briefly discussed.     

The synthesis of tetradentate salens derived from (3R,4R)-N-substituted-3,4-diaminopyrrolidines and their application in the enantioselective trimethylsilylcyanation of aromatic aldehydes

The in situ formed Ti(IV) complexes of pyrrolidine-based chiral salen ligands derived from natural l-tartaric acid were evaluated as catalysts in the enantioselective trimethylsilylcyanation of aromatic aldehydes. The different activity and selectivity of the catalysts in the formation of the products were found to be dependent on the N-substituent of the pyrrolidine.     

A unifying approach to abstract matrix algebra preconditioning

In earlier papers Tyrtyshnikov [42] and the first author [14] considered the analysis of clustering properties of the spectra of specific Toeplitz preconditioned matrices obtained by means of the best known matrix algebras. Here we generalize this technique to a generic Banach algebra of matrices by devising general preconditioners related to “convergent” approximation processes [36]. Finally, as case study, we focus our attention on the Tau preconditioning by showing how and why the best matrix algebra preconditioners for symmetric Toeplitz systems can be constructed in this class. Received April 25, 1997 / Revised version received March 13, 1998     

Fibre-optic pH sensor for sea-water monitoring using a single dye

A sensor for the continuous monitoring of pH in sea water, having the configuration of a probe, is described. The characteristics of this probe, which uses phenol red adsorbed on Amberlite resin as a chemichromatic element on top of an optical fibre, are reported and the effects of interfering parameters (variable salinity and temperature of sea water) are assessed. The possibility of enhancing the working range is discussed, and a procedure for rendering the range suitable for marine monitoring is presented.     

Laser printing of enamels on tiles

A Nd:YAG laser beam is used as a tool to print patterns of coloured enamels on tile substrates. For this, the laser beam is scanned over a layer of raw enamel previously sprayed on the tile surface. The possibility to focus the laser energy to heat a small zone without affecting the rest of the piece presents some advantages in front of traditional furnace techniques in which the whole piece has to be heated; among them, energy saving and the possibility to apply enamels with higher melting temperatures than those of the substrate. In this work, we study the effects of laser irradiation of a green enamel, based in chromium oxide pigment and lead frit, deposited on a white tile substrate. Lines obtained with different combinations of laser beam power and scan speeds were investigated with the aim to optimize the process from the point of view of the quality of the patterns. For this purpose, the morphology of the lines and their cross-sections is studied. The results show that lines with good visual properties can be printed with the laser. The characteristics of the marked lines were found to be directly related with the accumulated energy density delivered. Moreover, there is a linear relationship between the accumulated energy density and the volume of melted material. A minimum accumulated energy density is required to melt a shallow zone of the glazed substrate to allow the adhesion of the enamelled lines.