A discrete long-term location–price problem under the assumption of discriminatory pricing: Formulations and parametric analysis

We consider a competitive location problem in which a new firm has to make decisions on the locations of several new facilities as well as on its price setting in order to maximise profit. Under the assumption of discriminatory prices, competing firms set a specific price for each market area. The customers buy one unit of a single homogeneous price-inelastic product from the facility that offers the lowest price in the area the consumers belong to. Three customer choice rules are considered in order to break ties in the offered prices. We prove that, considering long-term competition on price, this problem can be reduced to a problem with decisions on location only. For each one of the choice rules the location problem is formulated as an integer programming model and a parametric analysis of these models is given. To conclude, an application with real data is presented.     

A Schiff base lateral macrobicycle derived from 4,13‐diaza‐18‐crown‐6 in its protonated form

In the structure of the title compound, 28,31,36,39‐tetraoxa‐9,17,42‐triaza‐1,25‐diazoniapentacyclo[23.8.5.1^11,15.0^3,8.0^18,23]nonatriaconta‐3,5,7,9,11,13,15,16,18,20,22‐undecene bis(perchlorate), C₃₃H₄₃N₅O₄²⁺·2ClO₄⁻ or (H₂L)(ClO₄)₂, the cation and one of the two independent anions lie on crystallographic twofold axes, while the second perchlorate anion is disordered about a centre of inversion. The conformation of the macrobicycle L is conditioned by two strong intramolecular hydrogen‐bonding interactions involving the pivot and imine N atoms, and is quite different from that observed when a metal ion is placed inside its cavity. The two imine groups are not coplanar with the pyridine moiety, and the deviation from planarity is considerably larger than that found in the corresponding Ba complex. Moreover, the fold of the macrobicycle in H₂L²⁺ causes a significant approach of the two pivot N atoms compared with their disposition in the Ba complex. This is the first X‐ray crystal structure analysis of an uncoordinated Schiff base lateral macrobicycle.     

The triterpenes 3β-lup-20(29)-en-3-ol and 3β-lup-20(29)-en-3-yl acetate and the carbohydrate 1,2,3,4,5,6-hexa-O-acetyl-dulcitol as photosynthesis light reactions inhibitors

Three compounds were isolated from Maytenus acanthophylla Reissek (Celastraceae): the pentacyclic triterpenes lup-20(29)-en-3β-ol (lupeol, 1) and 3β-lup-20(29)-en-3-yl acetate (2) and the carbohydrate 1,2,3,4,5,6-hexa-O-acetyldulcitol (3); lupeol was also isolated from Xylosma flexuosa. The compounds' structures were elucidated by spectroscopic and spectrometric analysis. Compound 1 acts as an energy transfer inhibitor, interacting with isolated CF? bound to thylakoid membrane, and dulcitol hexaacetate 3 behaves as a Hill reaction inhibitor and as an uncoupler, as determined by polarography. Chlorophyll a (Chl a) fluorescence induction kinetics from the minimum yield F? to the maximum yield F(M )provides information of the filling up from electrons coming from water to plastoquinone pool with reducing equivalents. In this paper we have examined the effects of compounds 1 and 3 on spinach leaf discs. Compound 1 induces the appearance of a K-band, which indicates that it inhibits the water splitting enzyme. In vivo assays measuring the fluorescence of chl a in P. ixocarpa leaves sprayed with compound 1, showed the appearance of the K-band and the PSII reaction centers was transformed to "heat sinks" or silent reaction centers unable to reduce Q(A). However, 3 also induced the appearance of a K band and a new band I appears in P. ixocarpa plants, therefore it inhibits at the water splitting enzyme complex and at the PQH? site on b?f complex. Compounds 1 and 3 did not affect chlorophyll a fluorescence of L. perenne plants.     

Positively charged lanthanide complexes with cyclen-based ligands: synthesis, solid-state and solution structure, and fluoride interaction

The syntheses of a new cyclen-based ligand L(2) containing four N-[2-(2-hydroxyethoxy)ethyl]acetamide pendant arms and of its lanthanide(III) complexes [LnL(2)(H(2)O)]Cl(3) (Ln = La, Eu, Tb, Yb, or Lu) are reported, together with a comparison with some Ln(III) complexes of a previously reported analogue L(1) in which two opposite amide arms have been replaced by coordinating pyridyl units. The structure and dynamics of the La(III), Lu(III), and Yb(III) complexes in solution were studied by using multinuclear NMR investigations and density functional theory calculations. Luminescence lifetime measurements in H(2)O and D(2)O solutions of the [Ln(L(2))(H(2)O)](3+) complexes (Ln = Eu or Tb) were used to investigate the number of H(2)O molecules coordinated to the metal ion, pointing to the presence of an inner-sphere H(2)O molecule in a buffered aqueous solution. Fluoride binding to the latter complexes was investigated using a combination of absorption spectroscopy and steady-state and time-resolved luminescence spectroscopy, pointing to a surprisingly weak interaction in the case of L(2) (log K = 1.4 ± 0.1). In contrast to the results in solution, the X-ray crystal structure of the lanthanide complex showed the ninth coordination position occupied by a chloride anion. In the case of L(1), the X-ray structure of the [(EuL(1))(2)F] complex features a bridging fluoride donor with an uncommon linear Eu-F-Eu entity connecting two almost identical [Eu(L(1))](3+) units. Encapsulation of the F(-) anion within the two complexes is assisted by π-π stacking between the pyridyl rings of two complexes and C-H···F hydrogen-bonding interactions involving the anion and the pyridyl units.     

Macrocyclic receptor showing extremely high Sr(II)/Ca(II) and Pb(II)/Ca(II) selectivities with potential application in chelation treatment of metal intoxication

Herein we report a detailed investigation of the complexation properties of the macrocyclic decadentate receptor N,N'-Bis[(6-carboxy-2-pyridil)methyl]-4,13-diaza-18-crown-6 (H(2)bp18c6) toward different divalent metal ions [Zn(II), Cd(II), Pb(II), Sr(II), and Ca(II)] in aqueous solution. We have found that this ligand is especially suited for the complexation of large metal ions such as Sr(II) and Pb(II), which results in very high Pb(II)/Ca(II) and Pb(II)/Zn(II) selectivities (in fact, higher than those found for ligands widely used for the treatment of lead poisoning such as ethylenediaminetetraacetic acid (edta)), as well as in the highest Sr(II)/Ca(II) selectivity reported so far. These results have been rationalized on the basis of the structure of the complexes. X-ray crystal diffraction, (1)H and (13)C NMR spectroscopy, as well as theoretical calculations at the density functional theory (B3LYP) level have been performed. Our results indicate that for large metal ions such as Pb(II) and Sr(II) the most stable conformation is Δ(δλδ)(δλδ), while for Ca(II) our calculations predict the Δ(λδλ)(λδλ) form being the most stable one. The selectivity that bp18c6(2-) shows for Sr(II) over Ca(II) can be attributed to a better fit between the large Sr(II) ions and the relatively large crown fragment of the ligand. The X-ray crystal structure of the Pb(II) complex shows that the Δ(δλδ)(δλδ) conformation observed in solution is also maintained in the solid state. The Pb(II) ion is endocyclically coordinated, being directly bound to the 10 donor atoms of the ligand. The bond distances to the donor atoms of the pendant arms (2.55-2.60 ?) are substantially shorter than those between the metal ion and the donor atoms of the crown moiety (2.92-3.04 ?). This is a typical situation observed for the so-called hemidirected compounds, in which the Pb(II) lone pair is stereochemically active. The X-ray structures of the Zn(II) and Cd(II) complexes show that these metal ions are exocyclically coordinated by the ligand, which explains the high Pb(II)/Cd(II) and Pb(II)/Zn(II) selectivities. Our receptor bp18c6(2-) shows promise for application in chelation treatment of metal intoxication by Pb(II) and (90)Sr(II).     

Defects in rutile and anatase polymorphs of TiO2: kinetics and thermodynamics near grain boundaries

The direct consequence of irradiation on a material is the creation of point defects-typically interstitials and vacancies, and their aggregates-but it is the ultimate fate of these defects that determines the material's radiation tolerance. Thus, understanding how defects migrate and interact with sinks, such as grain boundaries, is crucial for predicting the evolution of the material. We examine defect properties in two polymorphs of TiO(2)-rutile and anatase-to determine how these materials might respond differently to irradiation. Using molecular statics and temperature accelerated dynamics, we focus on two issues: how point defects interact with a representative grain boundary and how they migrate in the bulk phase. We find that grain boundaries in both polymorphs are strong sinks for all point defects, though somewhat stronger in rutile than anatase. Further, the defect kinetics are very different in the two polymorphs, with interstitial species diffusing quickly in rutile while oxygen defects-both interstitials and vacancies-are fast diffusers in anatase. These results allow us to speculate on how grain boundaries will modify the radiation tolerance of these materials. In particular, grain boundaries in rutile will lead to a space charge layer at the boundary and a vacancy-rich damage structure, while in anatase the damage structure would likely be more stoichiometric, but with larger defects consisting primarily of Ti ions.     

The optimal combination: Grammatical swarm,particle swarm optimization and neural networks

Social behaviour is mainly based on swarm colonies, in which each individual shares its knowledge about the environment with other individuals to get optimal solutions. Such co-operative model differs from competitive models in the way that individuals die and are born by combining information of alive ones. This paper presents the particle swarm optimization with differential evolution algorithm in order to train a neural network instead the classic back propagation algorithm. The performance of a neural network for particular problems is critically dependant on the choice of the processing elements, the net architecture and the learning algorithm. This work is focused in the development of methods for the evolutionary design of artificial neural networks. This paper focuses in optimizing the topology and structure of connectivity for these networks.     

Identification of vortex cores of three-dimensional large-vortical structures

In this paper, we propose a nonlocal method to identify vortex cores in three-dimensional flows as a complement to the existing list of local and nonlocal methods of the bibliography. The method is based on the vector field of the instantaneous rotation of a particle around a center. This center is defined using the Darboux vector field along the path-particle lines; the vortex core is detected using their Frenet–Serret frame. We illustrate the application of the method to identify the core of large-vortical structures in analytical and numerically simulated laminar and turbulent natural convection flows.     

Search for new d0 half-metallic materials: theoretical investigation on KCaC1−xSix (x = 0; 0.25; 0.5; 0.75 and 1) compounds

In recent years, the investigations on d⁰ half-metallic materials have become the new trend in the search of novel materials for applications in spintronic devices. In this work, the structural, electronic and magnetic properties of KCaC${}_{1?x}$Si_x (x = 0; 0.25; 0.5; 0.75 and 1) compounds have been theoretically studied using the full-potential linearized augmented plane wave (FP-LAPW) method within framework of the density functional theory. The generalized gradient approximation scheme as proposed by Wu-Cohen (GGA-WC) and Tran-Blaha modified Becke-Johnson exchange potential with improved parameterization by Koller are adopted for the treatment of electron exchange-correlation. All considered materials show half-metallic characteristics with semiconducting majority spin channel and metallic minority one. The total spin magnetic moment is 1μ_B for ternary alloys and 4μ_B for quaternary compounds. Our obtained results suggest that these materials could be promising candidate for spintronic applications.     

Matrix approach to discrete fractional calculus II: Partial fractional differential equations

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359–386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.