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.     

Chiral separation of dansyl amino acids by capillary electrophoresis: Comparison of formamide andN-Methylformamide as background electrolytes

Summary Chiral separation of 12 dansyl amino acids has been achieved by capillary electrophoresis using -cyclodextrin dissolved inN-methylformamide or formamide. The viscosity and the dielectric constants of these two solvents are very different, giving them disimilar electrophoretic properties. Intense electroosmotic flow, high electrophoretic mobilities and high efficiency were achieved inN-methylformamide, but high chiral selector concentration was needed for sufficient resolution. In contrast, the separation of dansyl amino acids in formamide was characterized by longer analysis time and lower efficiency, but the resolution and selectivity of the separation were better and baseline separation could be achieved at lower -cyclodextrin concentrations.     

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.     

Pressurised hot water extraction-microporous membrane liquid-liquid extraction coupled on-line with gas chromatography-mass spectrometry in the analysis of pesticides in grapes

Pressurised hot water extraction-microporous membrane liquid-liquid extraction was coupled on-line with gas chromatography-mass spectrometry (PHWE-MMLLE-GC-MS) for the analysis of pesticides in grapes. MMLLE serves as a trapping step after PHWE. Water from PHWE is directed to the donor side of the membrane unit and the analytes are extracted to the acceptor solution on the other side. The role of MMLLE is to clean and concentrate the extract before on-line transfer to the GC via a sample loop and an on-column interface using partially concurrent solvent evaporation. The extraction conditions were investigated, and then the quantitative features such as linearity, limit of quantification (LOQ), extraction yield and enrichment factors. LOQs in the range 0.3-1.8 microg kg(-1) were achieved. Procymidone and tetradifon were found in the skins of the grapes. The results were in good agreement with those obtained by liquid-solid and ultrasonic extractions.     

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.     

Theoretical (DFT) insights into the mechanism of copper-catalyzed cyclopropanation reactions. Implications for enantioselective catalysis

The mechanism of the copper(I)-catalyzed cyclopropanation reaction has been extensively investigated for a medium-size reaction model by means of B3LYP/6-31G(d) calculations. The starting ethylene complex of the N,N'-dimethylmalonaldiimine--copper (I) catalyst undergoes a ligand exchange with methyl diazoacetate to yield a reaction intermediate, which subsequently undergoes nitrogen extrusion to generate a copper--carbene complex. The cyclopropanation step takes place through a direct carbene insertion of the metal--carbene species to yield a catalyst--product complex, which can finally regenerate the starting complex. The stereochemical predictions of a more realistic model (by considering a chiral bis(oxazoline)--copper (I) catalyst) have been rationalized in terms of steric repulsions, showing good agreement with experimental data.     

Compact sets of compact operators in absence of

We characterize the compactness of a subset of compact operators between Banach spaces when the domain space does not have a copy of