A method for portfolio choice

This paper shows how one can use the theory of hidden Markov models for portfolio optimization. We illustrate our method by a ball and urn experiment. An application to historical data is examined. Copyright © 2003 John Wiley & Sons, Ltd.     

The Immersed Interface Method for a Nonlinear Chemical Diffusion Equation with Local Sites of Reactions

A diffusion equation with nonlinear localized chemical reactions is considered in this paper. As a result of the reactions, although the equation is parabolic, the derivatives of the solution are discontinuous across the interfaces (local sites of reactions). A second-order accurate immersed interface method is constructed for the diffusion equation involving interfaces. The new method is more accurate than the standard approach and it does not require the interfaces to be grid points. Several experiments that confirm second-order accuracy are presented. The efficiency of the proposed algorithm is also demonstrated for solving blow up problems. The proposed technique could be extended for construction of efficient numerical algorithms on uniform grids for the present equations with moving interfaces [9] but more analysis is required.     

Novel Lipophilic Fluorophores with Highly Acidity-Dependent Two-Photon Response

Lipophilic fluorophores are widely implemented in nonlinear microscopy; however, few existing membrane-specific probes combine the high brightness of two-photon excited fluorescence (2PEF) with pH sensitivity. Herein we describe four novel two-photon excited fluorophores, based on a coumarin 151 core structure, where lipophilicity is induced by a covalently attached phosphazene moiety. Changing the environmental acidity using trifluoromethanesulfonic (triflic) acid leads to profound changes in the linear fluorescence and 2PEF characteristics, due to chromophores’ switching between neutral- and protonated forms. We characterize this dependence by measuring the two-photon absorption (2PA) spectra over the region λ_2PA=550–1000 nm, observing 2PA cross sections of σ_2PA=10–20 GM, with an associated 2PEF brightness of 10–13 GM, in neutral solutions of both acetonitrile and n-octanol. Although quantum chemical modelling and NMR measurements show that, at high chromophore concentrations, protonation may be accompanied by a dimerization process, these dimers likely do not form at the lower concentrations used in optical spectroscopy.     

Low-Flammable Parahydrogen-Polarized MRI Contrast Agents

Many MRI contrast agents formed with the parahydrogen-induced polarization (PHIP) technique exhibit biocompatible profiles. In the context of respiratory imaging with inhalable molecular contrast agents, the development of nonflammable contrast agents would nonetheless be highly beneficial for the biomedical translation of this sensitive, high-throughput and affordable hyperpolarization technique. To this end, we assess the hydrogenation kinetics, the polarization levels and the lifetimes of PHIP hyperpolarized products (acids, ethers and esters) at various degrees of fluorine substitution. The results highlight important trends as a function of molecular structure that are instrumental for the design of new, safe contrast agents for in vivo imaging applications of the PHIP technique, with an emphasis on the highly volatile group of ethers used as inhalable anesthetics.     

The First Molybdenum(VI) and Tungsten(VI) Oxoazides MO2(N3)2, MO2(N3)2⋅2 CH3CN, (bipy)MO2(N3)2, and [MO2(N3)4]2− (M=Mo,W)

Molybdenum(VI) and tungsten(VI) dioxodiazide, MO₂(N₃)₂ (M=Mo, W), were prepared through fluoride–azide exchange reactions between MO₂F₂ and Me₃SiN₃ in SO₂ solution. In acetonitrile solution, the fluoride–azide exchange resulted in the isolation of the adducts MO₂(N₃)₂⋅2 CH₃CN. The subsequent reaction of MO₂(N₃)₂ with 2,2′‐bipyridine (bipy) gave the bipyridine adducts (bipy)MO₂(N₃)₂. The hydrolysis of (bipy)MoO₂(N₃)₂ resulted in the formation and isolation of [(bipy)MoO₂N₃]₂O. The tetraazido anions [MO₂(N₃)₄]²⁻ were obtained by the reaction of MO₂(N₃)₂ with two equivalents of ionic azide. Most molybdenum(VI) and tungsten(VI) dioxoazides were fully characterized by their vibrational spectra, impact, friction, and thermal sensitivity data and, in the case of (bipy)MoO₂(N₃)₂, (bipy)WO₂(N₃)₂, [PPh₄]₂[MoO₂(N₃)₄], [PPh₄]₂[WO₂(N₃)₄], and [(bipy)MoO₂N₃]₂O by their X‐ray crystal structures.     

Kinetics of the solvolyses of benzhydryl derivatives: basis for the construction of a comprehensive nucleofugality scale

A series of 21 benzhydrylium ions (diarylmethylium ions) are proposed as reference electrofuges for the development of a general nucleofugality scale, where nucleofugality refers to a combination of leaving group and solvent. A total of 167 solvolysis rate constants of benzhydrylium tosylates, bromides, chlorides, trifluoroacetates, 3,5-dinitrobenzoates, and 4-nitrobenzoates, two-thirds of which have been determined during this work, were subjected to a least-squares fit according to the correlation equation log k(25 degrees C) = sf(Nf + Ef), where sf and Nf are nucleofuge-specific parameters and Ef is an electrofuge-specific parameter. Although nucleofuges and electrofuges characterized in this way cover more than 12 orders of magnitude, a single set of the parameters, namely sf, Nf, and Ef, is sufficient to calculate the solvolysis rate constants at 25 degrees C with an accuracy of +/-16 %. Because sf approximately 1 for all nucleofuges, that is, leaving group/solvent combinations, studied so far, qualitative discussions of nucleofugality can be based on Nf.