Mathematical models for the elastic beam with structural damping

In this paper the existence, regularity and sharp estimates for the solutions of an abstract second order evolution equation are proved and applications to models of a (possibly non homogeneous) elastic beam with a frequency-proportional damping are given.     

A new optimal electricity market bid model solved through perspective cuts

On current electricity markets the electrical utilities are faced with very sophisticated decision making problems under uncertainty. Moreover, when focusing in the short-term management, generation companies must include some medium-term products that directly influence their short-term strategies. In this work, the bilateral and physical futures contracts are included into the day-ahead market bid following MIBEL rules and a stochastic quadratic mixed-integer programming model is presented. The complexity of this stochastic programming problem makes unpractical the resolution of large-scale instances with general-purpose optimization codes. Therefore, in order to gain efficiency, a polyhedral outer approximation of the quadratic objective function obtained by means of perspective cuts (PC) is proposed. A set of instances of the problem has been defined with real data and solved with the PC methodology. The numerical results obtained show the efficiency of this methodology compared with standard mixed quadratic optimization solvers.     

Electrically Switchable Magnetic Molecules: Inducing a Magnetic Coupling by Means of an External Electric Field in a Mixed‐Valence Polyoxovanadate Cluster

Herein we evaluate the influence of an electric field on the coupling of two delocalized electrons in the mixed‐valence polyoxometalate (POM) [GeV₁₄O₄₀]^8? (in short V₁₄) by using both a t‐J model Hamiltonian and DFT calculations. In absence of an electric field the compound is paramagnetic, because the two electrons are localized on different parts of the POM. When an electric field is applied, an abrupt change of the magnetic coupling between the two delocalized electrons can be induced. Indeed, the field forces the two electrons to localize on nearest‐neighbors metal centers, leading to a very strong antiferromagnetic coupling. Both theoretical approaches have led to similar results, emphasizing that the sharp spin transition induced by the electric field in the V₁₄ system is a robust phenomenon, intramolecular in nature, and barely influenced by small changes on the external structure.     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.     

Synthesis and complete assignment of the 1H and 13C NMR signals of some oxopyrancoumarin and oxofuropyrancoumarin derivatives

The synthesis of four pyranocoumarins starting from phloroglucinol and the complete (1)H and (13)C NMR assignment of seven pyranocoumarins has been performed using 1D and 2D NMR techniques including COSY, HMQC and HMBC experiments.     

Mass spectrometry in the characterization of ambers. I. Studies of amber samples of different origin and ages by laser desorption ionization, atmospheric pressure chemical ionization and atmospheric pressure photoionization mass spectrometry

Amber is a fossil resin constituted of organic polymers derived through complex maturation processes of the original plant resin. A classification of eight samples of amber of different geological age (Miocene to Triassic) and geographical origin is here proposed using direct mass spectrometric techniques, i.e. laser desorption ionization (LDI), atmospheric pressure chemical ionization (APCI) and atmospheric pressure photoionization (APPI), in order to obtain a fingerprint related to the amber origin. Differences and similarities were detected among the spectra with the four methods, showing quite complex spectra, full of ionic species in the mass range investigated (up to m/z 2000). The evaluation required statistical analysis involving multivariate techniques. Cluster analysis or principal component analysis (PCA) generally did not show a clear clustering with respect to the age of samples, except for the APPI method, which allowed a satisfying clustering. Using the total ion current (TIC) obtained by the different analytical approaches on equal quantities of the different amber samples and plotted against the age, the only significant correlation appeared to be that involving APPI. To validate the method, four amber samples from Cretaceous of Spain were analyzed. Also in this case a significant correlation with age was found only with APPI data. PCA obtained with TIC values from all the MS methods showed a fair grouping of samples, according to their age. Three main clusters could be detected, belonging to younger, intermediate and older fossil resins, respectively. This MS analysis on crude amber, either solid or extract, followed by appropriate multivariate statistical evaluation, can provide useful information on amber age. The best results are those obtained by APPI, indicating that the quantity of amber soluble components that can be photoionized decreases with increasing age, in agreement with the formation of highly stable, insoluble polymers.     

Mononuclear lanthanide single-molecule magnets based on polyoxometalates

[ErW10O36]9- is the first polyoxometalate behaving as a single-molecule magnet (SMM). It shows frequency-dependent out-of-phase magnetization and a thermally activated single relaxation process with an effective barrier of 55.8 K. This single lanthanide ion polyoxometalate is the inorganic analogue of the bis(phthalocyaninato)lanthanide SMMs, both exhibiting very similar ligand field symmetries around the lanthanide ion (idealized D4d). It is chemically stable and offers new avenues for organization and processing of single-molecule magnets. Furthermore, it can be made free from nuclear spins and opens the possibility to be used for studies of decoherence on unimolecular qubits.     

Single chain magnets based on the oxalate ligand

The anionic oxalate-bridged bimetallic chain [Co(H2O)2Cr(ox)3]- shows slow relaxation of the magnetization, typical of the so-called single-chain magnets, when crystallized in segregated layers in a mixed salt with the supramolecular cations [C12H24O6K]+ and [(C12H24O6)(FC6H4NH3)]+. This is the first time that such phenomenon has been observed in an oxalate-bridge material. In view of the wide synthetic versatility exhibited by the oxalate ligand, it opens the door for the realization of a complete family of SCM materials whose physical properties might be tuned by the suitable replacement of M3+ ions within the chain. The information extracted from the systematic study of these compounds should provide important information concerning the main parameters that affect the slow-relaxation phenomena in this sort of 1D nanomagnets.     

Synthesis of two new linear trinuclear Cu(II) complexes: mechanism of magnetic coupling through hybrid B3LYP functional and CShM studies

Two new Cu(II) linear trinuclear Schiff base complexes, [Cu3(L)2(CH3COO)2] (1) and [Cu3(L)2(CF3COO)2] (2), have been prepared using a symmetrical Schiff base ligand H2L [where H2L = N,N'-bis(2-hydroxyacetophenone)propylenediimine]. Both of the complexes have been characterized by elemental analyses, Fourier transform IR, UV/vis, and electron paramagnetic resonance spectroscopy. Single-crystal X-ray structures show that the adjacent Cu(II) ions are linked by double phenoxo bridges and a mu(2)-eta(1):eta(1) carboxylato bridge. In each complex, the central copper atom is located in an inversion center with distorted octahedral coordination geometry, while the terminal copper atoms have square-pyramidal geometry. Cryomagnetic susceptibility measurements over a wide range of temperature exhibit a distinct antiferromagnetic interaction of J = -36.5 and -72.3 cm(-1) for 1 and 2, respectively. Density functional theory calculations (B3LYP functional) and continuous-shape measurement (CShM) studies have been performed on the trinuclear unit to provide a qualitative theoretical interpretation of the antiferromagnetic behavior shown by the complexes.     

Spontaneous magnetization in Ni-Al and Ni-Fe layered double hydroxides

Layered double hydroxides containing paramagnetic Ni (II) and diamagnetic/paramagnetic Al (III)/Fe (III) ions have been prepared and characterized. Ni 2Al(OH) 6(NO 3). nH 2O ( 1), Ni 2Fe(OH) 6(NO 3). nH 2O ( 2), Ni 2Fe(OH) 6(C 6H 8O 4) 0.5. nH 2O ( 3), and Ni 2Fe(OH) 6(C 10H 16O 4) 0.5. nH 2O ( 4) were prepared by coprecipitation at controlled pH as polycrystalline materials with the typical brucite-like structure, with alternating layers of hydroxide and the corresponding anions, which determine the interlayer separation. Magnetic studies show the appearance of spontaneous magnetization between 2 and 15 K for these compounds. Interestingly, the onset temperature for spontaneous magnetization follows a direct relationship with interlayer separation, since this is the only magnetic difference between compounds 2, 3, and 4. Magnetic and calorimetric data indicate that long-range magnetic ordering is not occurring in any of these materials, but rather a freezing of the magnetic system in 3D due to the magnetic disorder and competing intra- and interlayer interactions. Thus, these hydrotalcite-like magnetic materials can be regarded as spin glasses.