Mechanistic aspects of radiation-induced oligomerization of 3,4-ethylenedioxythiophene in ionic liquids

Thiophene and its disubstituted derivatives, such as 3,4-ethylenedioxythiophene (EDOT), 3,4-dimethoxythiophene (DMT), 3,4-propylenedioxythiophene (PDOT), and 3,4-butylenedioxythiophene (BuDOT) were oxidized in organic solvents and in ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate (BMIM(+)PF??) at RT and under cryogenic conditions. Their radical cations were spectrally characterized at 77 K. Annealing of the irradiated matrix, which triggers the diffusion processes, led to spontaneous oligomerization. The oxidative coupling between a radical cation and a neutral monomer was identified as the first step of the oligomerization process. The scale of oligomerization could be extended by the addition of chloroform, which acts as a dissociative electron scavenger, whereas the dichloromethylperoxyl radicals formed in the reaction with the dissolved oxygen act as secondary oxidizing agents.     

Laser induced multi-component luminescence of [CuNCS(1,10-phen)P(CH2N(CH2CH2)2O)3]—the first example of CuNCS complexes with diimines and tris(aminomethyl)phosphanes

[CuNCS(phen)P(CH₂N(CH₂CH₂)₂O)₃], a novel mixed-ligand complex of copper(I) isothiocyanate with 1,10-phenanthroline and tris(aminomethyl)phosphane derived from morpholine have been synthesized. It was characterized by elemental analysis, thermogravimetric and differential thermal analyses and studied by NMR, mass, UV–Vis, IR and luminescence spectroscopies. The X-ray structure of the complex was determined. The coordination geometry about the Cu(I) center is pseudo-tetrahedral. The complex exhibits a very weak photoluminescence in the solid state. Surprisingly, the luminescence spectra of the crystalline sample at room and LN temperatures show several bands similarly to absorption(reflectance) spectrum. On the basis of TDDFT calculations we interpreted these bands as of MLLCT type resulting mainly from two transitions: π^?(CuNCS)→π^?(phen) and σ(CuP)→π^?(phen). This strongly suggests that all the ligands are involved into absorption and PL spectra, however their complex character (several bands observed) does not allow the more precise interpretation.     

Approximation of functions from L p (ω) β by matrix means of their Fourier series

We formulate some special conditions for the integrable functions and moduli of continuity. We give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix generate the sequences belonging to the classes MRBVS and MHBVS, We also present some results on norm approximation for functions from the generalized integral Lipschitz classes.     

Improving the Crossing Lemma by Finding More Crossings in Sparse Graphs

Twenty years ago, Ajtai et al. and, independently, Leighton discovered that the crossing number of any graph with v vertices and e > 4v edges is at least ce³/v², where c > 0 is an absolute constant. This result, known as the "Crossing Lemma," has found many important applications in discrete and computational geometry. It is tight up to a multiplicative constant. Here we improve the best known value of the constant by showing that the result holds with c > 1024/31827 > 0.032. The proof has two new ingredients, interesting in their own right. We show that (1) if a graph can be drawn in the plane so that every edge crosses at most three others, then its number of edges cannot exceed 5.5(v-2); and (2) the crossing number of any graph is at least Both bounds are tight up to an additive constant (the latter one in the range ).     

Spectroscopic properties of new luminescent system based on vanadate(V) crystal doped with erbium ions

Er³⁺-doped KCaY(VO₄)₂ microcrystalline samples were synthesized using a high temperature solid-state reaction technique. Spectroscopic properties of Er³⁺: KCaY(VO₄)₂ are studied and the nature of emissions is discussed. A strong green and infrared luminescence were observed under excitation at 314 nm in the O²⁻→V⁵⁺ charge-transfer transitions and direct excitation of Er³⁺ ions at 435 nm. A strong emission lines in the blue region are due to the transitions of VO₄³⁻ ions have been observed at 77 K. The Judd-Ofelt parametrization scheme has been applied to the analysis of the room temperature absorption spectra in order to evaluate the intensity parameters, the branching ratios and the radiative lifetimes of the ⁴I_13/2, ⁴I_11/2, ⁴F_9/2 and ⁴S_3/2 emitting levels. The effective cross-section has been calculated for the ⁴I_13/2→⁴I_15/2 transition, indicating that the title compounds is a promising active medium for application in the three-level laser system. The up-conversion emission in Er³⁺: KCaY(VO₄)₂ was investigated at 300 K. The decay profiles of the Stokes and anti-Stokes emissions were measured and the mechanism of up-conversion luminescence is discussed.     

A note on proving the strong NP-hardness of a scheduling problem with position dependent job processing times

In this paper, we show that the strong NP-hardness proof of the single machine makespan minimization problem with ready times and job processing times described by a non-increasing power function dependent on a job position in a sequence presented in Bachman and Janiak (J Oper Res Soc 55:257–264, 2004) is incorrect. Namely, the applied transformation from 3- Partition problem to the considered scheduling problem is polynomial not pseudopolynomial. Thus, the related problem is NP-hard, but it is not proved to be strongly NP-hard.     

Contribution à la Théorie des Polygones Réguliers

Ohne Zusammenfassung     

Operations research methods in political decisions: a case study on the European Parliament composition

In this paper, we show that operations research methods can be successfully applied to support decision-making in politics on the case study of the apportionment of seats in the European Parliament. The related political constraints and assumptions are quantitatively described and the optimization problem is formulated. On this basis, it is revealed that the current composition of the European Parliament as well as some intuitive propositions do not respect degressive proportionality as far as it was assumed. Nevertheless, our algorithm allows us to find better solutions, and among them, there is only one best allocation, which respects degressive proportionality as far as possible, according to the well known and often applied measures. Namely, over 9 thousands allocations consistent with the political requirement “nobody gains and nobody loses more than one” are referred to over 5.4 millions degressively proportional solutions, and only one allocation is revealed to be the best for all defined criteria under given populations of countries.