New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

AlIII‐Catalysed Formation of Poly(limonene)carbonate: DFT Analysis of the Origin of Stereoregularity

Amino‐triphenolate derived Al^III complexes combined with suitable nucleophiles have been investigated as binary catalysts for the coupling of limonene oxide and carbon dioxide to afford alternating polycarbonates. These catalysts are able to produce stereoregular, perfectly alternating trans‐polymers from cis‐limonene oxide, whereas the pure trans isomer and cis/trans mixture give rise to lower degrees of stereoregularity. The best Al^III catalyst shows the potential to mediate the conversion of both stereoisomers of limonene oxide with high conversion levels of up to 71 % under neat conditions, indicating the high degree of robustness and atom‐efficiency of this catalytic process. Computational studies have revealed unique features of the binary catalyst system, among which is the preferred nucleophilic attack on the quaternary carbon centre in the limonene oxide substrate.     

Synthesis and characterization of new galactosylated-based N2O-donors tridentate ligands

The synthesis and characterization of three novel N₂O-donor ligands containing the group 4-[1-β-d-2,3,4,6-tetra-O-acetyl-galactosyl)]benzaldehyde are presented. The insertion of this group was designed to increase the absorption of the prodrug in tumor cells, and is part of an ongoing work in our group with tridentate ligands to develop potential cobalt(III) prodrugs. The synthetic route described here allowed the isolation of pure ligands with yields ranged 81–89%. Finally, compounds were characterized by IR, NMR and HRMS (ESI⁺).     

Incremental Tuning Up of Fluorous Phenazine Acceptors

In a simple, one‐step direct trifluoromethylation of phenazine with CF₃I we prepared and characterized nine (poly)trifluoromethyl derivatives with up to six CF₃ groups. The electrochemical reduction potentials and gas‐phase electron affinities show a direct, strict linear relation to the number of CF₃ groups, with phenazine(CF₃)₆ reaching a record‐high electron affinity of 3.24 eV among perfluoroalkylated polyaromatics.     

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.     

<Emphasis Type="Italic">p</Emphasis>-adic valuation of exponential sums associated to trinomials and some consequences

In this paper, we compute the p-adic valuation of exponential sums associated to trinomials \(F\left( X \right) = a{X^{{d_1}}} + b{X^{{d_2}}} + c{X^{{d_3}}}\) over Fp. As a byproduct of our results, we obtain restrictions for permutation polynomials of type \(a{X^{{d_1}}} + b{X^{{d_2}}} + c{X^{{d_3}}}\) over F_p.