Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.     

Theoretical study of the electronic structure of CnS (n=1-6) thiocumulenes

Linear sulfur-carbon chains C(n)S (n=1-6) of astronomical interest were examined by means of several theoretical methods. The three smallest compounds of the series were chosen to evaluate the performance of several computational models, including Hartree-Fock theory, density functional theory with the Becke's three parameter exchange functional and the correlation functional of Lee, Yang, and Parr (B3LYP), and electron-correlated methods (second-order Moller-Plesset perturbation method (MP2), configuration interaction method including single and double excitations (CISD), and quadratic configuration interaction method including single and double excitations (QCISD) in combination with a large variety of basis sets. The systematic comparison between the experiment and theory indicates that the B3LYP/6-311G** method can be considered suitable for the study of the electronic structures of the C(n)S compounds. The electronic ground states of the C(n)S molecules alternate between 1Sigma and 3Sigma for odd and even values of n, respectively. The B3LYP/6-311G** wave functions for these electronic ground states were analyzed by means of the atoms in molecules (AIM) and natural bond orbital (NBO) methods. Both approaches suggest that the electronic structures for the singlet and triplet compounds must be considered separately. According to the NBO method, singlet compounds can be properly represented by acetylenic structures with alternating single and triple bonds (S[triple bond]C-C[triple bond]C...). However, triplet compounds are better described by means of double bond-double bond cumulenic structures (S=C=C=C=C...) as a consequence of the average between different alpha and beta electronic densities. AIM delocalization indexes and NBO interactions between localized orbitals also indicate that these structures are strongly pi delocalized. Finally, the different singlet and triplet structures proposed provide a consistent explanation for the geometries, dipole moments, and spin-density values of the C(n)S compounds studied.     

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9–10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the ‘1’ and ‘0’ basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

We show that a sizeable electronuclear entanglement of the S = 1/2 and I = 7/2 spins of a vanadyl porphyrin provides the conditions to act as a universal 4-qubit processor, and thus implement quantum error correction at the molecular level.     

Novel analogues of 3-substituted-2,3-dihydro-1,4-dioxino[2,3-b]pyridines: modifications in the dioxane ring

The synthesis of a series of novel analogues of the 3-substituted-2,3-dihydro-1,4-dioxino[2,3-b]pyridine core, modified in the non-aromatic ring, is described. Due to the presence of a versatile hydroxymethyl group in their structure, these novel scaffolds are attractive intermediates for the preparation of potential new therapeutic agents.     

Hexaruthenium carbonyl cluster complexes with basal edge-bridged square pyramidal metallic skeleton: efficient synthesis of 2-imidopyridine derivatives and determination of their reactive sites in carbonyl substitution reactions

The reactions of [Ru(3)(CO)(12)] with half equivalent of 2-amino-6-methylpyridine (H(2)ampy) or 2-aminopyridine (H(2)apy) in refluxing xylene give the hexanuclear products [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-L)(mu-CO)(2)(CO)(14)] (L = ampy, 1; apy, 2). These reactions represent the first high-yield syntheses of hexanuclear complexes with a basal edge-bridged square pyramidal metallic skeleton. Five metal atoms of these complexes are bridged by the N-donor ligand in such a way that the edge-bridging metal atom is attached to the pyridine nitrogen, while the basal atoms of the square pyramid are capped by an imido fragment that arises from the activation of both N-H bonds of the NH(2) group. The reactive sites of these complexes in CO substitution reactions have been determined by studying the reactivity of 1 with triphenylphosphine. Two kinetically controlled monosubstitutions take place on the edge-bridging metal atom in positions cis to the pyridine nitrogen, leading to a mixture of two isomers of formula [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(13)(PPh(3))] (3 and 4). On heating at 80 degrees C, these monosubstituted isomers are transformed, via a dissociative pathway, into the product of thermodynamic control (5), which has the PPh(3) ligand on the apical Ru atom. The di- and trisubstituted derivatives [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(12)(PPh(3))(2)] (6) and [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(11)(PPh(3))(3)] (7) are stepwise formed from 3-5 and PPh(3). Compound 6 has the PPh(3) ligands on the edge-bridging and apical Ru atoms, and compound 7 has an additional PPh(3) ligand on an unbridged basal Ru atom. The compound [Ru(6)(mu(3)-H)(2)(mu(5)-eta(2)-ampy)(mu-CO)(2)(CO)(12)(mu-dppm)] (8), in which a basal and the apical Ru atoms are spanned by the dppm ligand, has been isolated from the reaction of 1 with bis(diphenylphosphino)methane.     

Determination of mercury in soils and sediments by graphite furnace atomic absorption spectrometry with slurry sampling

A graphite furnace atomic absorption spectrometric procedure for the determination of mercury is presented, in which the samples are suspended in a solution containing hydrofluoric and nitric acids. Silver nitrate (4% m/v) and potassium permanganate (3%) are incorporated, in the order specified, and aliquots are directly introduced into the graphite furnace. A fast heating programme with no conventional pyrolysis step is used. The detection limit for mercury in a 125 mg ml⁻¹ suspension is 0.1 μg g⁻¹. Calibration is performed by using aqueous standards. The reliability of the procedure is proved by analysing certified reference materials.     

Skew-symmetric derivations of a complex Lie algebra

Let be a complex Lie algebra, its underlying real Lie algebra, a real form of and ·, · the euclidean product induced by the real part of an hermitian inner product on . Let aut be the Lie algebra of skew-symmetric derivations of . We give necessary and sufficient conditions to ensure that aut is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups.     

Iron-57 Mössbauer spectroscopic studies of materials of composition Fe x NbTiP3O12: materials with low concentrations of iron and the effects of treatment in air

The⁵⁷Fe Mössbauer spectrum recorded from the material of composition Fe_0.25NbTiP₃O₁₂ shows the presence of Fe²⁺ in a distribution of approximately octahedral type I sites within the channels of the NbTiP₃O₁₂ structure. A comparison of the results with those recorded from the material Fe_0.33NbTiP₃O₁₂ demonstrates the existence of an upper limit to the occupation by the Fe²⁺ species of the type I sites. Lattice parameter measurements and⁵⁷Fe Mössbauer spectroscopy show that treatment of Fe_0.25NbTiP₃O₁₂ in air induces the migration of the incorporated iron from the channels to form macroscopic -Fe₂O₃.     

A closed model category for ()-connected spaces

For each integer , we give a distinct closed model category structure to the category of pointed spaces such that the corresponding localized category is equivalent to the standard homotopy category of -connected CW-complexes. The structure of closed model category given by Quillen to is based on maps which induce isomorphisms on all homotopy group functors and for any choice of base point. For each , the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on for .

     

Development and validation of a liquid chromatography-ultraviolet absorbance detection assay using derivatisation for the novel marine anticancer agent ES-285 x HCl [(2S,3R)-2-amino-3-octadecanol hydrochloride] and its pharmaceutical dosage form

ES-285 x HCl [(2S,3R)-2-amino-3-octadecanol hydrochloride] is a novel investigational anticancer agent, which has shown in vitro and in vivo cytotoxic activity against various tumor cell lines with selectivity for certain solid tumors. The pharmaceutical development of ES-285 x HCl warranted the availability of an assay for the quantification and purity determination of ES-285 x HCl active pharmaceutical ingredient (API) and its pharmaceutical dosage form. A liquid chromatographic method (LC) comprising of derivatisation of ES-285 x HCl with phenylisothiocyanate and UV-detection was developed. The method was found to be linear, precise and accurate. The assay also proved selectivity as determined by analysing ES-285 x HCl in combination with 15 analogues and in combination with hydroxypropyl-beta-cyclodextrin, the excipient used in the lyophilised pharmaceutical dosage form. Stress testing showed that the degradation products were separated from the parent compound, confirming its stability indicating capacity. The method was found robust as determined with design of experiments (DoE), which made it possible to predict system suitability responses in worst case experimental conditions and to define criteria for system suitability testing.