Angular self-intersections for closed geodesics on surfaces

In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon's definition of intersection forms for surfaces.

     

Optical absorption spectra of linear and cyclic thiophenes—selection rules manifestation

We theoretically study the size-dependent relation between absorption spectra of thiophene-based oligomers and the corresponding cyclothiophenes. In our approach based on a Frenkel exciton Hamiltonian, we demonstrate that the geometry and selection rules determine the observed relations between the spectra.     

Novel acrylic macromonomer with amphiphilic character derived from Triton X‐100: Radical copolymerization with methyl methacrylate and thermal properties

This article explores the synthesis of a novel methacrylic macromonomer with an amphiphilic character derived from poly(ethylene glycol) tert‐octylphenyl ether (MT) and its respective homopolymer. To know their reactivity in radical copolymerization reactions with methyl methacrylate (MMA), a model monomer (MTm) was synthesized to determine the reactivity ratios and compare them with the low molar fractions of copolymers of MT with MMA because they were difficult to isolate. They were r_MTm = 0.97 and r_MMA = 0.95. The compositional diagrams when representing the weight fraction of MT and MTm in the feed and the copolymer suggested that a clear correlation exists between the experimental points of the model monomer MTm and the macromonomer MT ones, suggesting that the length of the side poly(ethylene oxide) chain does not affect the reactivity of the methacrylic double bond in the prepared monomers for this type of polymerization reaction. The reactivity ratios of the copolymers have a tendency for the formation of random or Bernoullian copolymers. The glass‐transition temperatures (T_g's) of the prepared copolymers were determined by differential scanning calorimetry, deviated from the Fox equation, and discussed on the basis of treatments that consider the influence of the monomeric units along the copolymer chains, determining the T_g of the corresponding alternating dyads. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1641–1649, 2003     

Generalized Mukai conjecture for special Fano varieties

Let X be a Fano variety of dimension n, pseudoindex i _X and Picard number ρ_X. A generalization of a conjecture of Mukai says that ρ_X(i _X −1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i _X ≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρ_X> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.     

The communication complexity of private value single-item auctions

This paper is concerned with information revelation in single-item auctions. We compute how much data needs to be transmitted in three strategically equivalent auctions—the Vickrey auction, the English auction and the recently proposed bisection auction—and show that in the truth-telling equilibrium the bisection auction is the best performer.     

Chemometric approaches in environmental problems concerning PCDD and PCDF. Data interpretation and source correlation. Mechanisms of formation and destruction in MSW combustion process

Summary The role of multivariate analysis methods in evaluating, rationalizing, and working out complex environmental problems is discussed. The discussion is organized in two sections; a literature analysis of the application of chemometric methods to PCDD/PCDF data interpretation and source correlation and a review of the role of chemometric methods in analysing the results obtained by the Authors studying PCDD/PCDF formation and destruction mechanisms in MSW combustion processes.     

Limonene concentration in lemon (Citrus volkameriana) peel oil as a function of ripeness

The dependence of the limonene content of lemon (Citrus volkameriana) peel oil on the degree of ripeness of the fruit has been studied by using steam distillation and cold pressing to extract the oils from lemon fruit peel at different stages of maturation (green, greenish-yellow, and yellow-orange peel coloration). Samples of essential oils were analyzed by high resolution GC and GC-MS, using tetradecane as internal standard for quantitation. Forty components were detected; thirty eight were positively identified by comparison of their mass spectra (El, 70 eV) and Kováts retention indexes (determined using a non-logarithmic scale on capillary columns coated with both polar (DB-Wax) and non-polar (DB-1) stationary phases) with those of standards and with data reported in the literature. The limonene concentration reached a maximum level of 79.4% when the fruit was in the intermediate maturation stage characterized by greenish-yellow coloration.     

The diastereoselective synthesis of functionalised isoxazolidines using a Cope elimination/intramolecular nitrone cycloaddition strategy

Functionalised hydroxylamine derivatives of (S)-prolinol prepared by a Cope elimination have been found to undergo oxidation to the nitrone either in the presence of air or a catalytic quantity of TPAP. These undergo intramolecular cycloaddition to give tricyclic isoxazolidines with high diastereoselectivity.