Martingale representation for Poisson processes with applications to minimal variance hedging

We consider a Poisson process η on a measurable space equipped with a strict partial ordering, assumed to be total almost everywhere with respect to the intensity measure λ of η. We give a Clark-Ocone type formula providing an explicit representation of square integrable martingales (defined with respect to the natural filtration associated with η), which was previously known only in the special case, when λ is the product of Lebesgue measure on R₊ and a σ-finite measure on another space X. Our proof is new and based on only a few basic properties of Poisson processes and stochastic integrals. We also consider the more general case of an independent random measure in the sense of Itô of pure jump type and show that the Clark-Ocone type representation leads to an explicit version of the Kunita-Watanabe decomposition of square integrable martingales. We also find the explicit minimal variance hedge in a quite general financial market driven by an independent random measure.     

Boxicity of Leaf Powers

The boxicity of a graph G, denoted as boxi(G), is defined as the minimum integer t such that G is an intersection graph of axis-parallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T such that the leaves of the tree correspond to the vertices of G and two vertices in G are adjacent if and only if their corresponding leaves in T are at a distance of at most k. Leaf powers are used in the construction of phylogenetic trees in evolutionary biology and have been studied in many recent papers. We show that for a k-leaf power G, boxi(G)??? k?1. We also show the tightness of this bound by constructing a k-leaf power with boxicity equal to k?1. This result implies that there exist strongly chordal graphs with arbitrarily high boxicity which is somewhat counterintuitive.     

Thermal behaviour of nickel(II) sulphate,nitrate and halide complexes containing ammine and ethylenediamine as ligands

Thermal behaviour of nickel amine complexes containing SO₄ ²⁻, NO₃ ⁻, Cl⁻ and Br⁻ as counter ions and ammonia and ethylenediamine as ligands have been investigated using simultaneous TG/DTA coupled with mass spectroscopy (TG/DTA–MS). Evolved gas analyses detected various transient intermediates during thermal decomposition. The nickel ammonium sulphate complex produces NH, N, S, O and N₂ species. The nickel ammonium nitrate complex generated fragments like N, N₂, NO, O₂, N₂O, NH₂ and NH. The halide complexes produce NH₂, NH, N₂ and H₂ species during decomposition. The ligand ethylenediamine is fragmented as N₂/C₂H₄, NH₃ and H₂. The residue hexaamminenickel(II) sulphate produces NiO with crystallite size 50 nm. Hexaammine and tris(ethylenediamine)nickel(II) nitrate produce NiO in the range 25.5 nm and 23 nm, respectively. The halide complexes produce nano sized metallic nickel (20 nm) as the residue. Among the complexes studied, the nitrate containing complexes undergo simultaneous oxidation and reduction.     

Thermolysis reaction of 2-acetyl-1-oxo-five-, six-, and seven-membered ring

The rates of gas-phase thermolysis reactions of 2-acetylcyclopentanone 1,2-acetylcyclohexanone 2, N-acetylcaprolactam 3,2-acetylbutyrolactone 4,2-acetyl-2-methylbutyrolactone 5, and 3-acetyl-2-oxazolidinone 6 have been measured over a temperature range of 50 K. They undergo unimolecular first-order elimination reactions for which log A = 11.7, 11.7, 11.2, 11.4, 11.5, and 11.1 s^?1 and E_a = 193.4, 189.5, 153.2, 201.0, 206.8, and 176.1 kJ mol^?1, respectively. The effect of the ring size together with the effect of a heteroatom in the ring on the rate of thermolysis reactions for compound 1–6 is the subject of this work. © 1995 John Wiley & Sons, Inc.     

Tuning the enantioselective N-acetylation of racemic amines: a spectacular salt effect

We have described a spectacular salt effect in the kinetic resolution of (+/-)-1-phenylethylamine, which leads to an increase in reactivity, high levels of selectivity, and a complete reversal of the stereoselectivity. By tuning the reaction conditions, we were able to increase the selectivity factor of (1S,2S)-1 to s = 115.     

Chemical failure modes of AlQ3-based OLEDs: AlQ3 hydrolysis

Tris(8-hydroxyquinoline)aluminum(III), AlQ3, is used in organic light-emitting diodes (OLEDs) as an electron-transport material and emitting layer. The reaction of AlQ3 with trace H2O has been implicated as a major failure pathway for AlQ3-based OLEDs. Hybrid density functional calculations have been carried out to characterize the hydrolysis of AlQ3. The thermochemical and atomistic details for this important reaction are reported for both the neutral and oxidized AlQ3/AlQ3+ systems. In support of experimental conclusions, the neutral hydrolysis reaction pathway is found to be a thermally activated process, having a classical barrier height of 24.2 kcal mol(-1). First-principles infrared and electronic absorption spectra are compared to further characterize AlQ3 and the hydrolysis pathway product, AlQ2OH. The activation energy for the cationic AlQ3 hydrolysis pathway is found to be 8.5 kcal mol(-1) lower than for the neutral reaction, which is significant since it suggests a role for charge imbalance in promoting chemical failure modes in OLED devices.     

A mechanistic rationalization of unusual kinetic behavior in proline-mediated C-O and C-N bond-forming reactions

Kinetic evidence supports the role of the reaction product in the catalytic cycle of proline-mediated alpha-aminoxylation and alpha-amination reactions, providing both design principles as well as a model for the evolution of efficiency in catalysis.     

Quantum chemical studies of semiconductor surface chemistry using cluster models

Modern quantum chemical methods can be used to investigate many properties of novel molecules and materials with predictive power. We have carried out accurate quantum chemical calculations with cluster models to investigate chemical reactions on semiconductor surfaces. The structure–property relationships that emerge from these studies are illustrated with particular emphasis on silicon as well as indium phosphide surface chemistry. Some new strategies that we have developed to provide a proper balance between covalent and dative bonding in compound semiconductors are discussed. Embedded cluster models have been used in some cases to include the effects of the surroundings on the active region. The structural and mechanistic understanding that emerges from our studies is illustrated by selected results on atomic layer deposition of Al₂O₃ on silicon and hydrogenation of P-rich and In-rich indium phosphide surfaces.