Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

On the synthesis of 3(5)-carbomethoxy-4-hetarylpyrazoles

3(5)-Carbomethoxy-4-hetarylpyrazoles 3 can be obtained by the aromatization of the corresponding cis-3-benzamido-3-carbomethoxy-4-hetaryl-Δ¹-pyrazolines 2 obtained by 1,3-dipolar cycloaddition of diazo-methane with methyl Z-2-benzamido-3-hetarylpropenoates 1. An explanation, based on FMO theory, for the different reactivity of the dipolarophiles with diazomethane is given.     

AlPO-Catalysed asymmetric Diels-Alder reactions of cyclopentadiene with chiral acrylates

Reactions of cyclopentadiene with several chiral acrylates are studied and compared with the same reactions catalysed by Zn(II)-exchanged K10 montmorillonite. In general, amorphous AlPO₄ is a more efficient catalyst than the clay. In particular, the reaction of cyclopentadiene with (−)-8-phenylmenthyl acrylate leads to 74% diastereomeric excess (d.e.) in methylene chloride at low temperatures. This result constitutes the highest asymmetric induction described to date for a solid-catalysed asymmetric Diels-Alder reaction. When the reactions are carried out in the absence of a solvent a noticeable decrease in selectivity is observed, probably due to an extensive competition of the non-catalysed reaction.     

The first immobilization of pyridine-bis(oxazoline) chiral ligands

[formula: see text] A chiral pyridine-bis(oxazoline) ligand, functionalized with a vinyl group in the pyridine ring, can be polymerized with styrene and divinylbenzene to obtain supported chiral ligands. As proof of the usefulness of this supported ligands, the corresponding ruthenium complexes are catalysts for the cyclopropanation reaction of styrene with ethyl diazoacetate with up to 85% ee.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.     

Control over the Self‐Assembly Modes of PtII Complexes by Alkyl Chain Variation: From Slipped to Parallel π‐Stacks

We report the self‐assembly of a new family of hydrophobic, bis(pyridyl) Pt^II complexes featuring an extended oligophenyleneethynylene‐derived π‐surface appended with six long (dodecyloxy ( 2 )) or short (methoxy ( 3 )) side groups. Complex 2 , containing dodecyloxy chains, forms fibrous assemblies with a slipped arrangement of the monomer units (d_Pt???Pt≈14 Å) in both nonpolar solvents and the solid state. Dispersion‐corrected PM6 calculations suggest that this organization is driven by cooperative π–π, C?H???Cl and π–Pt interactions, which is supported by EXAFS and 2D NMR spectroscopic analysis. In contrast, nearly parallel π‐stacks (d_Pt???Pt≈4.4 Å) stabilized by multiple π–π and C?H???Cl contacts are obtained in the crystalline state for 3 lacking long side chains, as shown by X‐ray analysis and PM6 calculations. Our results reveal not only the key role of alkyl chain length in controlling self‐assembly modes but also show the relevance of Pt‐bound chlorine ligands as new supramolecular synthons.     

Structural and Kinetic Aspects of Blood Plasma Protein Adsorption on the Surface of Hydrophobic Polymers

Abstract

Due to the wide use of polymers in medicine, researchers are required to solve a very important problem–to understand the interaction between materials of nonphysiological origin and the surrounding biological liquids, and tissues, particularly blood.