On price competition in location-price models with spatially separated markets

In this paper we study price competition for two types of location-price models in which facility locations are set up and price decisions have to be made in order to maximise profit. We discuss the existence and determination of equilibrium prices in a general location space when facilities have different production costs. It is assumed that each price is bounded from below and demand for a single homogeneous product is price-inelastic. When facilities set mill prices, a price equilibrium rarely exists and necessary conditions for existence are obtained. In particular, when the location space is a tree network, we give a characterisation of the locations for which a unique equilibrium exists for two competitors. With spatial price discrimination, though equilibrium prices might not exist, it is shown that ε-equilibrium prices always exist for any locations of the facilities. A characterisation of ε-equilibrium is also given. Then the location-price problem is reduced to a location problem. A comparison of results with the two types of price determination is also presented. This work has been supported by the Ministry of Science and Technology of Spain under the research project BEC2002-01026, in part financed by the European Regional Development Fund (ERDF).     

Synthesis of pyrazolo[3,4-b][1,4]diazepines and pyrazolo[3,4-b]pyrazines

The synthesis and structure elucidation of new pyrazolo[3,4-b][1,4]diazepines and pyrazolo[3,4-b]pyrazines are reported and the characterisation of isomers and tautomers by proton and carbon-13 nmr are discussed. In some case only NOE experiments allow us to identify the isomeric structure.     

Templating Schiff-base lateral macrobicycles: an experimental and theoretical structural study of the intermediates

In this paper, we report a structural study both in the solid state and in solution of barium complexes with the diamine N,N'-bis(2-aminobenzyl)-4,13-diaza-18-crown-6 (L(2)), that allows us to rationalize the template effect of the metal ion in the synthesis of Schiff-base lateral macrobicycles resulting from the condensation of L(2) with different dicarbonyl compounds. The X-ray crystal structures of [Ba(L(2))(ClO(4))](ClO(4)) (3) [triclinic space group P1 with Z = 2, a = 10.467(2) A, b = 10.4755(2) A, c = 16.9911(3) A, alpha = 85.075(1) degrees, beta = 80.907(1) degrees, and gamma = 61.627(4) degrees ] and [Ba(L(2))(NCS)(H(2)O)](SCN) (4) [monoclinic space group P2(1)/n with Z = 4, a = 9.954(5) A, b = 29.193(5) A, c = 11.313(5) A, and beta = 91.371(5) degrees ] demonstrate that in the solid state the barium(II) ion induces an anti conformation of the receptor in the complexes. Variable temperature (1)H and (13)C NMR data point out that in solution compounds 3 and 4 exist as a mixture of syn and anti isomers. The presence of the syn isomer in solution, independent of the counterion employed (perchlorate or thiocyanate), accounts for the effectiveness of the barium(II) ion as a template agent in the synthesis of the lateral macrobicycles resulting from the condensation of L(2) with different dicarbonyl compounds. Density functional theory calculations (at the B3LYP/LanL2DZ level) for [Ba(L(2))](2+) predict the syn conformation to be more stable both in vacuo and in solution (PCM model). In order to asses which of the two isomers predominates in acetonitrile solution, the (13)C NMR shielding tensors of the two isomers of [Ba(L(2))](2+) were calculated for the in vacuo optimized structures by using the GIAO method, and the results were compared with the experimental ones. According to these analyses, a syn stereochemistry is assigned to the major species in solution.     

Some aspects of the enthalpy of dilution of biological polyelectrolytes

It is shown that calorimetric experiments on the dilution process of polyelectrolytes, i.e. on the excess enthalpy of electrostatic origin, can give information on the conformational state of the polymer. Analytical expression are obtained relating the enthalpy of dilution to the charge density on the polymer, from Manning's theory. The experimental data reported on some ionic biopolymers are interpreted on the basis of the theoretical prediction of the electrostatic contribution to the enthalpy of dilution in water of a polyelecrolytic salt and of a weak polyacid. The procedure outlined provides a means of calculating the actual charge/per unit length and of disclosing possible non-electrostatic effects arising from conformational transitions.     

The highest water exchange rate ever measured for a Gd(III) chelate

The complex [Gd(L)(H2O)]3- (H(6)L =N,N'-bis(6-carboxy-2-pyridylmethyl)ethylenediamine-N,N'-methylenephosphonic acid) displays the highest water exchange rate ever measured for a Gd(III) chelate (k(298)(ex)= 8.8 x 10(8) s(-1)), which is attributed to the flexibility of the metal coordination environment.     

Using Interval Analysis for Solving Planar Single-Facility Location Problems: New Discarding Tests

Interval analysis is a powerful tool which allows the design of branch-and-bound methods able to solve many global optimization problems. The key to the speed of those methods is the use of several tests to discard boxes or parts of boxes in which no optimal point may occur. In this paper we present three new discarding tests for two-dimensional problems which are specially suitable for planar single-facility location problems. The usefulness of the new tests is shown by a computational study.     

Binuclear Co(II), Ni(II), Cu(II) and Zn(II) complexes with Schiff-bases derived from crown ether platforms: Rare examples of ether oxygen atoms bridging metal centers

Bibracchial lariat ethers L³ and L⁴, derived from the condensation of N,N′-bis(2-aminobenzyl)-1,10-diaza-15-crown-5 or N,N′-bis(2-aminobenzyl)-4,13-diaza-18-crown-6 with salicylaldehyde, form binuclear complexes with Co(II), Ni(II), Cu(II) and Zn(II). Our studies show that the different denticity and crown moiety size of the two related receptors give rise to important differences on the structures of the corresponding complexes. Single crystal X-ray diffraction analysis shows that the [Ni₂(L³)(H₂O)₂]²⁺ and [Cu₂(L³)(NO₃)]⁺ complexes constitute a rare example in which an oxygen atom of the crown moiety is bridging the two six coordinate metal ions. In contrast, none of the oxygen atoms of the crown moiety is acting as a bridging donor atom in the [Co₂(L⁴)(CH₃CN)₂]²⁺, [Cu₂(L⁴)]²⁺ and [Zn₂(L⁴)]²⁺ complexes. This is attributed to the larger size the crown moiety and the higher denticity of L⁴ compared to L³. In [Co₂(L⁴)(CH₃CN)₂]²⁺ the metal ions show a distorted octahedral coordination, while in the Cu(II) and Zn(II) analogues the metal ions are five-coordinated in a distorted trigonal bipyramidal environment. In [Cu₂(L³)(NO₃)]⁺ the coordinated nitrate anion acts as a bidentate bridging ligand, which results in the formation of a 1D coordination polymer.     

Liquid chromatograpic-mass spectrometric analysis of phenolics and free radical scavenging activity of rosemary extract from different raw material

The antioxidant activity of rosemary (Rosmarinus officinalis) extract from different raw materials has been studied. Extracts were prepared from wild or drip-irrigated plants, as well as from the by-product resulting from the distillation of the aromatic essential oil. The radical scavenging activity of rosemary extracts was compared with that of antioxidants widely used in food, such as BHT and delta-tocopherol, using an optimization of the method based on the reduction of the radical 2,2-diphenyl-1-picrylhydrazyl (DPPH). The results pointed the excellent antioxidant activity of the crude fresh rosemary extracts, which was almost identical to that of pure delta-tocopherol, and higher than that of BHT; extracts prepared from distilled rosemary showed the lowest activity, although they are also of interest due to the low cost of the raw material. High performance liquid chromatography (HPLC) combined with diode array (DAD) and electrospray (ESI)-ion trap-MS detection was used to separate and identify the compounds present in the rosemary extracts. Rosmarinic acid, carnosic acid and seven of their terpene-type metabolites, and seven flavones were identified. The drying and/or distillation treatments used with the plant material strongly affected the content of the two compounds of higher antioxidant activity: rosmarinic acid and carnosic acid.     

Two-sided Two-cosided Hopf Modules and Yetter–Drinfeld Modules for Quasi-Hopf Algebras

For a quasi-Hopf algebra H, an H-bicomodule algebra and an H-bimodule coalgebra C we will show that the category of two-sided two-cosided Hopf modules is equivalent to the category of right–left generalized Yetter–Drinfeld modules . Using alternative versions of this result we will recover the category isomorphism between the categories of left–left and left–right Yetter–Drinfeld modules over a quasi-Hopf algebra.