A conformal group approach to the Dirac–Kähler system on the lattice

Starting from the representation of the (n  ? 1) + n  ? dimensional Lorentz pseudo‐sphere on the projective space , we propose a method to derive a class of solutions underlying to a Dirac–Kähler type equation on the lattice. We make use of the Cayley transform to show that the resulting group representation arises from the same mathematical framework as the conformal group representation in terms of the general linear group . That allows us to describe such class of solutions as a commutative n  ? ary product, involving the quasi‐monomials ) with membership in the paravector space . Copyright © 2016 John Wiley & Sons, Ltd.     

Structural,magnetic, and vibrational properties of stoichiometric clusters of CrN

We performed density‐functional‐theoretic calculations to investigate the structural, magnetic and vibrational properties of the stoichiometric clusters (CrN)_n ( ). We show that the building block of the ground‐state structures of these clusters is a square CrNCrN unit; the only exception with n > 2 occurs for (CrN)₃, but this cluster has an isomer not very far in energy from the ground state consisting of a pair of CrNCrN squares sharing a CrN bond. In the smaller CrN, (CrN)₂, and (CrN)₃ clusters the magnetic moments of the N atoms are non‐negligible and antiparallel to those of the Cr atoms, but for the larger species (CrN)₄, (CrN)₅, (CrN)₆, and (CrN)₉ the cluster magnetic moments are almost entirely due to the Cr atoms. Lack of imaginary vibrational frequencies in the predicted ground‐state structures of (CrN)_n ( ) confirms that they are mechanically stable equilibrium states. © 2015 Wiley Periodicals, Inc.     

Mixed micelle formation between amino acid-based surfactants and phospholipids

The mixed micelle formation in aqueous solutions between an anionic gemini surfactant derived from the amino acid cystine (C(8)Cys)(2), and the phospholipids 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC, a micelle-forming phospholipid) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC, a vesicle-forming phospholipid) has been studied by conductivity and the results compared with the ones obtained for the mixed systems with the single-chain surfactant derived from cysteine, C(8)Cys. Phospholipid-surfactant interactions were found to be synergistic in nature and dependent on the type of phospholipid and on surfactant hydrophobicity. Regular solution theory was used to analyse the gemini surfactant-DHPC binary mixtures and the interaction parameter, β(12), has been evaluated, as well as mixed micelle composition. The results have been interpreted in terms of the interplay between reduction of the electrostatic repulsions among the ionic head groups of the surfactants and steric hindrances arising from incorporation of the zwitterionic phospholipids in the mixed micelles.     

Novel pyrazoline and pyrazole porphyrin derivatives: synthesis and photophysical properties

2-Vinyl-5,10,15,20-tetraphenylporphyrinatozinc(II) reacts with nitrile imines, generated in situ from ethyl hydrazono-α-bromoglyoxylates, affording the corresponding pyrazolines in good to excellent yields. Treatment of pyrazoline derivatives with DDQ affords the corresponding pyrazole derivatives with moderate to excellent yields. When the hydrolysis of ester group in the pyrazoline derivatives was considered, it was observed the concomitant oxidation of the heterocyclic unit, which allowed directly obtaining porphyrin-pyrazole derivatives with a carboxylic group, in very good yields.The photophysical properties of the pyrazoline and pyrazole porphyrin derivatives show that the influence of the heterocyclic substituents is limited by the tendency of these molecules to aggregate. All other properties and especially the triplet kinetics remain unaffected. The adducts with low tendency to aggregate showed very high singlet oxygen yield, which makes these compounds interesting for their use as photosensitizers for PDT.     

Evaluation of intramolecular energy transfer process in the lanthanide(III) bis- and tris-(TTA) complexes: Photoluminescent and triboluminescent behavior

This work reports the energy transfer mechanism process of [Eu(TTA)₂(NO₃)(TPPO)₂] (bis-TTA complex) and [Eu(TTA)₃(TPPO)₂] (tris-TTA complex) based on experimental and theoretical spectroscopic properties, where TTA=2-thienoyltrifluoroacetone and TPPO=triphenylphosphine oxide. These complexes were synthesized and characterized by elemental analyses, infrared spectroscopy and thermogravimetric analysis. The theoretical complexes geometry data by using Sparkle model for the calculation of lanthanide complexes (SMLC) is in agreement with the crystalline structure determined by single-crystal X-ray diffraction analysis. The emission spectra for [Gd(TTA)₃(TPPO)₂] and [Gd(TTA)₂(NO₃)(TPPO)₂] complexes are associated to T→S₀ transitions centered on coordinated TTA ligands. Experimental luminescent properties of the bis-TTA complex have been quantified through emission intensity parameters Ω_λ (λ=2 and 4), spontaneous emission rates (A_rad), luminescence lifetime (τ), emission quantum efficiency (η) and emission quantum yield (q), which were compared with those for tris-TTA complex. The experimental data showed that the intensity parameter value for bis-TTA complex is twice smaller than the one for tris-TTA complex, indicating the less polarizable chemical environment in the system containing nitrate ion. A good agreement between the theoretical and experimental quantum yields for both Eu(III) complexes was obtained. The triboluminescence (TL) of the [Eu(TTA)₂(NO₃)(TPPO)₂] complexes are discussed in terms of ligand-to-metal energy transfer.     

A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity Active-Set Algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.     

Porphyrin and phthalocyanine glycodendritic conjugates: synthesis, photophysical and photochemical properties

Synthesis of water soluble porphyrin and phthalocyanine derivatives with, respectively, eight and sixteen galactose units has been carried out. The combined preliminary photophysical and photochemical features of the new products suggest that they might be promising photodynamic therapeutic agents.     

Solutions for the Klein–Gordon and Dirac Equations on the Lattice Based on Chebyshev Polynomials

The main goal of this paper is to adopt a multivector calculus scheme to study finite difference discretizations of Klein–Gordon and Dirac equations for which Chebyshev polynomials of the first kind may be used to represent a set of solutions. The development of a well-adapted discrete Clifford calculus framework based on spinor fields allows us to represent, using solely projection based arguments, the solutions for the discretized Dirac equations from the knowledge of the solutions of the discretized Klein–Gordon equation. Implications of those findings on the interpretation of the lattice fermion doubling problem is briefly discussed.