Sequencing games without initial order

In this note we study uncertainty sequencing situations, i.e., one-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (Eur J Oper Res 40:344–351, 1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times.     

Dihalodimethyltin(IV) complexes of 2‐(pyrazol‐1‐ylmethyl)pyridine

Reaction of dichloro‐ and dibromodimethyltin(IV) with 2‐(pyrazol‐1‐ylmethyl)pyridine (PMP) afforded [SnMe₂Cl₂(PMP)] and [SnMe₂Br₂(PMP)] respectively. The new complexes were characterized by elemental analysis and mass spectrometry and by IR, Raman and NMR (¹H, ¹³C) spectroscopies. Structural studies by X‐ray diffraction techniques show that the compounds consist of discrete units with the tin atom octahedrally coordinated to the carbon atoms of the two methyl groups in a trans disposition (Sn? C = 2.097(5), 2.120(5) Å and 2.110(6), 2.121(6) Å in the chloro and in the bromo compounds respectively), two cis halogen atoms (Sn? Cl = 2.4908(16), 2.5447(17) Å; Sn? Br = 2.6875(11), 2.7464(9) Å) and the two donor atoms of the ligand (Sn? N = 2.407(4), 2.471(4) Å and 2.360(5), 2.455(5) Å). In both cases, the Sn? N(pyridine) bond length is markedly longer than the Sn? N(pyrazole) distance. Copyright © 2003 John Wiley & Sons, Ltd.     

How to work with one-dimensional quadratic maps

We analyse some identifiers which can univocally identify hyperbolic components and Misiurewicz points of one-dimensional quadratic maps. After seeing the equivalence among the different identifiers and how to go from one to another, we show which are the best for some specific tasks. Likewise, we present the analytic expressions, some of them shown for the first time in this paper, to calculate these identifiers. Some experimental considerations are taken into account.     

On the power of the zeros of Bessel functions

For ν≥0 let c_νk be the k-th positive zero of the cylinder functionC _v(t)=J _v(t)cosα-Y _v(t)sinα, 0≤α>π whereJ _ν(t) andY _ν(t) denote the Bessel functions of the first and the second kind, respectively. We prove thatC _v,k ^1+H(x) is convex as a function of ν, ifc _νk≥x>0 and ν≥0, whereH(x) is specified in Theorem 1.1.     

A Method for Clustering and Screening of Long-dimensional Chemical Data Based on Fingerprints and Similarity Measurements

A method for the treatment of long-dimensional chemical data arrays is presented in this work with the aim of maximising classification models. The method is based on the construction of fingerprints and the subsequent generation of a similarity matrix. The similarity calculation has been modified through a scaling process to take into account different significance shown by the variables. The method was applied to spectral measurements of wines and several aspects were studied, namely: threshold considered in the construction of fingerprints and patterns, weighting factor used for scaling, normalisation method, etc. The application of both Principal Components Analysis and Soft-Independent Modelling of Class Analogies to the similarity matrices gave better classifications of the information than those obtained using original data.     

Tantalum Clusters in Oxidic Matrices — Synthesis,Crystal Structure and Magnetic Properties of Eu1.83Ta15O32

The mixed‐valent oxotantalate Eu_1.83Ta₁₅O₃₂ was prepared from a compressed mixture of Ta₂O₅ and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, R_F = 0.027 for I > 2σ (I). The structure is isotypic to Ba₂Nb₁₅O₃₂. The salient feature is a [Ta(+8/3)₆O₁₂ⁱO₆^a] cluster consisting of an octahedral Ta₆ core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)₃O₁₃] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu_1.83Ta₁₅O₃₂ is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a M_mol/(N_Aμ_B) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μ_B for free Eu (2+) ions with 4f⁷ configuration in ⁸S_7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers.     

Biological Activity of Flavonoids Copper Complexes

Three flavonoid copper(II) complexes Cu₂(quercetin)(CH₃COO)₃(CH₃OH) ( 1 ), Cu(anthrarufin)(CH₃COO)·1/2H₂O ( 2 ) and Cu(naringin)(OCH₃)(CH₃OH)₂ ( 3 ) have been synthesized and characterized by elemental analysis, IR, electronic absorption and EPR (X‐band) spectroscopy. The complexes have a strong protective action over the Δsod1 mutant of S. cerevisiae against reactive oxygen radicals generated by an external source of free radicals (H₂O₂ or the superoxide‐generating, menadione). On the other hand, the complexes cleave DNA efficiently even in the absence of reducing agents. The main reactive oxygen species responsible for the DNA strand cleavage have been determined using radical scavengers. A probably mechanism of the DNA damage is proposed.     

Highly efficient synthesis of 2′,3′-didehydro-2′,3′-dideoxy-β-nucleosides through a sulfur-mediated reductive 2′,3′-trans-elimination. From iodomethylcyclopropanes to thiirane analogs

Taking into account the thiophilic properties of iodine, a very simple methodology to achieve 2′,3′-didehydro-2′,3′-dideoxy-β-nucleosides in high yield was performed, using mild, and inexpensive conditions, by means of the treatment of 2′-deoxy-3′,5′-dibenzoyl-2′-iodo-β-nucleoside derivatives with NaHS. The process has shown to be highly dependent of the relative geometry between the iodine atom and the adjacent leaving group. In this way, different essays carried out with pyranose derivatives have concluded in no reaction when the vicinal groups to eliminate do not adopt a trans-diaxial disposition. In addition, the treatment of 2-iodomethyl-cyclopropane-1,1-dicarboxylic acid diethyl ester under the same conditions softly and readily leads to the obtention of a mixture of the expected 2-allyl-malonic acid diethyl ester (as the minor product) and the thiirane derivative 2-thiiranylmethyl-malonic acid diethyl ester (as the major product). In this case, the responsible of the reaction progress are the nucleophilic properties of the sulfur atom rather than the thiophilic character of the iodine atom.