Addendum to: Comparison between different types of abstract integrals in riesz spaces

In [3] we did not give explicitly the definition of measurability for realvalued functions, with respect to finitely additive measures with values in a Dedekind complete Riesz space. We note that, in [3], all involved functions are intended to be measurable. We now report the definition of measurability, which we gave in [2] (Definition 3.2).     

Tutte uniqueness of line graphs

We prove that if a graph H has the same Tutte polynomial as the line graph of a d-regular, d-edge-connected graph, then H is the line graph of a d-regular graph. Using this result, we prove that the line graph of a regular complete t-partite graph is uniquely determined by its Tutte polynomial. We prove the same result for the line graph of any complete bipartite graph.     

The synthesis of (4S,5S)-(−)-isocytoxazone

(4S,5S)-(?)-Isocytoxazone, which is needed for a configurational study, was synthesized from the commercially available (1S,2S)-(+)-2-amino-1-(4-nitrophenyl)-1,3-propanediol in which the p-nitro substituent was replaced by a p-methoxyl group; the thus prepared p-methoxyphenyl amino diol was cyclized via an N-Boc derivative.     

Synthesis of new 2-oxosparteine derivatives

For the first time, substituents to the 3-position of 2-oxosparteine have been introduced. The synthesis of 3-phenylthiolupanine, 3,3-di(phenylthio)lupanine, 3-dehydrolupanine, 3-bromodehydro-lupanine and 2-thiono-3-dehydrosparteine has been described. The stereochemistry of these compounds has been determined and by NMR spectroscopy and X-ray crystallography.     

Mass spectrometric study of glucose and cellobiose produced during enzymatic hydrolysis of α‐cellulose extracted from oak late‐wood annual rings

We present the first results concerning interannual variations in concentrations of glucose and cellobiose, obtained through enzymatic hydrolysis of α‐cellulose. The α‐cellulose was extracted from late‐wood of oak. The tree‐ring chronologies, wood components and their physical and chemical properties provide information about the ecosystem in which the tree grew, and thus information regarding climate variability and the impact of human activity in the past. The large molecular size and insolubility make it difficult to determine precisely the chemical and physical properties of the intact cellulose polymer. Enzymatic hydrolysis is the principal method of degradation of cellulose. In this study the feasibility has been examined of characterizing α‐cellulose through analysis by mass spectrometry (MS) of the degradation products from hydrolysis. Degradation of α‐cellulose was possible without using alkaline or acid buffers. Analysis by MS provided the opportunity to obtain information on the biodegradation of saccharides. The presence of cellobiose and glucose in the degradation product was evidenced by the mass spectra. We have compared the abundances of these glucose and cellobiose ions with carbon isotope ratios, the efficiency of extraction of α‐cellulose from the wood and tree‐ring width indices. The challenge is to establish, with respect to climate changes and environmental conditions, the significance of the variations from one year to another in the observed abundances of glucose and cellobiose ions. Copyright © 2009 John Wiley & Sons, Ltd.     

Gold‐ or Platinum‐Catalyzed Cascade Processes of Alkynol Derivatives Involving Hydroalkoxylation Reactions Followed by Prins‐Type Cyclizations

An efficient method for the synthesis of [3.3.1]bicyclic compounds from easily available alkynol derivatives has been developed. The reaction is based on a gold‐ or platinum‐catalyzed tandem process that involves an intramolecular hydroalkoxylation of a triple bond followed by a Prins‐type cyclization. The reaction has been carried out with differently substituted alkynol derivatives and oxygen‐, nitrogen‐, and carbon‐centered nucleophiles. The incorporation of halogen atoms as nucleophiles and elimination reactions has also been studied. Enantiomerically pure [3.3.1]bicyclic systems were easily synthesized from the chiral pool.     

The duality of option investment strategies for hedge funds

This paper explores the structure of optimal investment strategies using stochastic programming and duality theory in investment portfolios containing options for a hedge fund manager who attempts to beat a benchmark. Explicit optimal conditions for option investments are obtained for several models. This research was supported by Inquire, the Social Sciences and Humanities Research Council of Canada, the Natural Sciences and Engineering Research Council of Canada, the National Center of Competence in Research FINRISK, a research instrument of the Swiss National Science Foundation, and MIT’s Sloan School of Management. J. R. Rodríguez-Mancilla thanks Gabriel Casillas-Olvera, Deputy Manager of Risk Control at Banco de Mexico, who read several drafts of this paper and made many helpful comments. The opinions in this paper do not necessarily represent those of Banco de México.     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.