Densities of maximal embedding dimension numerical semigroups

We define the density of a numerical semigroup and study the densities of all the maximal embedding dimension numerical semigroups with a fixed Frobenius number, as well as the possible Frobenius number for a fixed density. We also prove that for a given possible density, in the sense of Wilf’s conjecture, one can find a maximal embedding dimension numerical semigroup with that density.     

A polynomial algorithm for a continuous bilevel knapsack problem

In this note, we analyze a bilevel interdiction problem, where the follower’s program is a parametrized continuous knapsack. Based on the structure of the problem and an inverse optimization strategy, we propose for its solution an algorithm with worst-case complexity $O\left(n^2\right)$.     

A note on concentrations for integral two-scale problems

This work is devoted to the characterization of the asymptotic behavior, as \({\{\varepsilon_n\}}\) goes to zero, of a family of integral functionals of the form \({\int_{\Omega}f(x,\langle x/\varepsilon_n \rangle, \nabla u_{n}(x))\, dx}\) in terms of measures of oscillation and concentration associated to the sequence \({\{(\langle x/\varepsilon_n\rangle, \nabla u_{n}(x))\}}\).     

Synthesis and structure of 2-substituted pyrene-derived scaffolds

Pyrenes bear a propensity to form fluorescent excimers, and thus this chromophore is often found in sensors and fluorescent probes. 2-Functionalized pyrenes are of particular interest, however the preparation of these scaffolds is not trivial, involving synthetic routes that require 4,5,9,10-tetrahydropyrene as a key intermediate. Herein, the development and optimization of routes for the synthesis of 2-functionalized pyrene-derived building blocks, with potential to be used as tags in the preparation of fluorescent probes, is described. Additionally, the crystal structures of ethyl 4,5,9,10-tetrahydro-2-pyrene-5-oxopentanoate and 2-acetyl-4,5,9,10-tetrahydropyrene revealed distinct conformations of the saturated tetrahydropyrene rings.     

Synthesis of 5-substituted 2,3-dihydrobenzofurans in a one-pot oxidation/cyclization reaction

Variously substituted 2,3-dihydrobenzofurans have been synthesized according to a sequential one-pot oxidation/cyclization procedure between para-aminophenol derivatives and an azadiene.     

Characteristics of fixed-shape pulses emerging from pulsating,erupting, and creeping solitons

It is known that one of the impacts of combined higher-order effects, namely the intrapulse Raman scattering, third-order dispersion, and self-steepening, on the plain-pulsating, erupting, and creeping soliton solutions of the complex Ginzburg–Landau equation is the change of its periodic behavior and its transformation into fixed-shape solutions. In this work, we numerically find the regions in the parameters space in which these solutions exist. We also characterize their velocities, shapes, and chirp.     

Electrospray ionization mass spectrometric analysis of newly synthesized α,β‐unsaturated γ‐lactones fused to sugars

Knowledge of the fragmentation mechanisms of lactones and their behaviour under electrospray ionization (ESI) conditions can be extended to larger and more complex natural products that contain an α,β‐unsaturated γ‐lactone moiety in their structure. Moreover, little is known about the gas‐phase behaviour of α,β‐unsaturated γ‐lactones linked or fused to sugars. Therefore, five α,β‐unsaturated γ‐lactones (butenolides) fused to a pyranose ring, recently synthesized compounds with potential relevance regarding their biological properties, were investigated using ESI‐MS and ESI‐MS/MS in both positive and negative ion modes. Their fragmentation mechanisms and product ion structures were compared. It was observed that two isomers could be unambiguously distinguished in the negative ion mode by the fragmentation pathways of their deprotonated molecules as well as in the positive ion mode by the fragmentation pathways of either the protonated or the sodiated molecule. Fragmentation mechanisms are proposed taking into account the MS/MS data and semi‐empirical calculations using the PM6 Hamiltonean. The semi‐empirical calculations were also very useful in determining the most probable protonation and cationization sites. Copyright © 2010 John Wiley & Sons, Ltd.     

Growth of (Perylene)2 [Pd(mnt)2] crystals

The conditions for the growth of (Perylene)₂ [Pd(mnt)₂] crystals either by chemical oxidation and electrochemical routes are described. The electrocrystallisation is limited by close proximity of the oxidation potentials of the perylene donor and [Pd(mnt)₂]^? anion, and depending on the experimental conditions different morphologies can be obtained. (Per)₂ [Pd(mnt)₂] crystals obtained by elecrocrystallisation were found to be mainly of the β-polymorph with properties comparable to the Cu, Ni and Pt analogues previously described at variance with those obtained by chemical oxidation which are mainly of the α-polymorph .