Matrix completion problems over integral domains: The case with a diagonal of prescribed blocks

Let $\mathfrak{R}$ be an arbitrary integral domain, let $\wedge =\{{\lambda }_1\text{,}\dots \text{,}{\lambda }_n\}$ be a multiset of elements of $\mathfrak{R}$, let $\sigma$ be a permutation of $\{1\text{,}\dots \text{,}k\}$ let $n_1\text{,}\dots \text{,}{n}_k$ be positive integers such that $n_1+?+n_k=n$, and for $r=1\text{,}\dots \text{,}k$ let $A_r\in {\mathfrak{R}}^{n_r\times n_{\sigma (r)}}$. We are interested in the problem of finding a block matrix $Q={\left[Q_{\mathit{rs}}\right]}_{r\text{,}s=1}^k\in {\mathfrak{R}}^{n\times n}$ with spectrum $\mathrm{\Lambda }$ and such that $Q_{r\sigma (r)}=A_r$ for $r=1\text{,}\dots \text{,}k$. Cravo and Silva completely characterized the existence of such a matrix when $\mathfrak{R}$ is a field. In this work we construct a solution matrix $Q$ that solves the problem when $\mathfrak{R}$ is an integral domain with two exceptions: (i) $k=2$; (ii) $k\ge 3$, $\sigma (r)=r$ and $n_r>n/2$ for some $r$.What makes this work quite unique in this area is that we consider the problem over the more general algebraic structure of integral domains, which includes the important case of integers. Furthermore, we provide an explicit and easy to implement finite step algorithm that constructs an specific solution matrix (we point out that Cravo and Silva’s proof is not constructive).     

An extension of proximal methods for quasiconvex minimization on the nonnegative orthant

In this paper we propose an extension of proximal methods to solve minimization problems with quasiconvex objective functions on the nonnegative orthant. Assuming that the function is bounded from below and lower semicontinuous and using a general proximal distance, it is proved that the iterations given by our algorithm are well defined and stay in the positive orthant. If the objective function is quasiconvex we obtain the convergence of the iterates to a certain set which contains the set of optimal solutions and convergence to a KKT point if the function is continuously differentiable and the proximal parameters are bounded. Furthermore, we introduce a sufficient condition on the proximal distance such that the sequence converges to an optimal solution of the problem.     

Integrating on-line process control and imperfect corrective maintenance: An economical design

Existing studies of on-line process control are concerned with economic aspects, and the parameters of the processes are optimized with respect to the average cost per item produced. However, an equally important dimension is the adoption of an efficient maintenance policy. In most cases, only the frequency of the corrective adjustment is evaluated because it is assumed that the equipment becomes “as good as new” after corrective maintenance. For this condition to be met, a sophisticated and detailed corrective adjustment system needs to be employed. The aim of this paper is to propose an integrated economic model incorporating the following two dimensions: on-line process control and a corrective maintenance program. Both performances are objects of an average cost per item minimization. Adjustments are based on the location of the measurement of a quality characteristic of interest in a three decision zone. Numerical examples are illustrated in the proposal.     

Efficiency of the medical care industry: Evidence from the Italian regional system

What might be the relation between clinical research and efficiency of medical care suppliers? Is the hypothesis of a positive relation consistent? Considering efficiency as the supplier’s ability to maximize the number of patients hospitalized in a mobility process among regions (i.e. mobility balance), this work aims at highlighting the existence of a positive externality of pharmaceutical clinical research on that kind of efficiency. In other words, an externality is able to affect the patients’ perception of good/bad quality of outputs supplied by the medical care industry, leading their mobility process. Taking Italy and the mobility of patients among regions into account, an Operational Research study will be performed in order to support this assumption.The goal of this work is to show an alternative way to increase the efficiency of medical care suppliers on the market of health care, that is to say, through their competitiveness on the market of human experimentation.     

Nuclear motion effects on the density matrix of crystals: An ab initio Monte Carlo harmonic approach

In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.     

Blue emitting side-chain pendant 4-hydroxy-1,3-thiazoles in polystyrenes synthesized by RAFT polymerization

Blue emitting dyes bearing a luciferin analogous chromophore were attached to a polystyrene backbone. For this purpose, 4-hydroxy-1,3-thiazoles were functionalized with a styrene unit and polymerized using the reversible addition–fragmentation chain transfer (RAFT) polymerization technique. Two different chain transfer agents were investigated and one monomer was studied in terms of its kinetic behavior. The polymerization kinetics are presented and discussed in detail, showing a controlled polymerization behavior, resulting in well-defined copolymers with polydispersity indices below 1.2. The obtained polymers were characterized by size exclusion chromatography (SEC), ¹H NMR, MALDI-TOF MS and UV–vis absorption and fluorescence spectroscopy. In addition, the UV–vis absorption and emission behavior was investigated in thin films.     

Synthesis and Characterization of the Monomer 2,2′ diallylbisphenol-A (ABFA) for obtaining Proton Exchange Membranes based on Crosslinked Sulphonated Poly(Arylene ether sulphone)s

Summary: In the present work, a methodology of synthesis and characterization of the monomer 2,2′ diallylbisphenol-A (ABFA) was developed, aiming at getting a precursor, with adequate purity, for obtaining cross-linked membranes based on sulphonated poly(arylene ether sulphone)s. The monomer synthesis involved the synthesis of 2,2′ bis(4-allyloxiphenyl)propane (Bisphenol-A, diallyl ether - BFAAE), from Bisphenol-A (BFA), followed by Claisen rearrangement of BFAAE, for the production of the target compound 2,2′ diallylbisphenol-A (ABFA). All the compounds, reagent BFA and obtained products, intermediate product BFAAE and final product ABFA, were characterized by FTIR (Fourier Transform infrared spectroscopy), TGA (Thermo-gravimetric analysis) and HPLC (High-performance liquid chromatography). The compound BFAAE was obtained with a yield of 94.5% and a purity of 97.3%, the latter characterized by TGA and by HPLC. The structure of the product was confirmed by FTIR. The thermal Claisen rearrangement process was conducted by using Differential Scanning Calorimetry (DSC) technique, from a factorial experiment planning, with two factors and three levels, with temperature and time being the variables. The above cited techniques were used for monitoring the Claisen rearrangement and for the characterization of the final product. The best results yield ABFA purity between 85 and 90%, approximately, for 220 °C/60min, 230 °C/30min and 210 °C/90min conditions. The obtained results suggest that, in the studied range, polymerization and degradation of the monomer ABFA occur, simultaneously to its formation.     

Heptabismuthate [Bi7I24]3–: a main group element anderson-type structure and its relationships with the polyoxometalates

We describe the unique structural and electronic arrangement in the heptanuclear polyiodobismuthate [Bi(7)I(24)](3-) which displays striking similarities with the Anderson-type structures found in polyoxometalates. This main group element anion is part of the complex [Bi(OAc)(2)(thf)(4)](3)[Bi(7)I(24)] (1) which has been characterized by X-ray crystallography. We investigated the structure, stability, and bonding of [Bi(7)I(24)](3-) using relativistic dispersion-corrected density functional theory in combination with a quantitative energy decomposition and electron localization function analysis in order to better understand the main features of this isopolyanion. A comparative analysis of the properties of [Bi(7)I(24)](3-) and previously reported high-nuclearity [Bi(n)X(3n+m)](m-) anions, in the gas phase and in solution, has been performed, in the latter case to track the macroscopic solvent effects. [Bi(7)I(24)](3-) is the largest building block in the class of trianionic iodobismuthates and the sole heptanuclear framework in the family of iodobismuthates.     

Flexible and dynamic thermal behavior of self-catenated [{Ni3(H2O)3(Bpa)4}(V6O18)]·8H2O constructed from 10-c heterometallic inorganic-organic clusters

The hydrothermal treatment of Ni(NO(3))(2)·6H(2)O, NaVO(3), and Bpa (1,2-Di(pyridyl)ethane) (C(12)H(12)N(2)) at 120 °C during 3 days leads to green single crystals of the title compound. The single crystal X-ray diffraction reveals that [{Ni(3)(H(2)O)(3)(Bpa)(4)}(V(6)O(18))]·8H(2)O crystallizes in the monoclinic system, P2(1)/c space group, with a = 13.5536 (2), b = 19.0463 (2), c = 27.7435 (3) ?, β = 112.3880 (10)°, V = 6622(3) ?(3), with R1(obs) = 0.0558, wR2(obs) = 0.1359, for 10278 observed reflections. The complexity of the crystal structure is based on different points, as the existence of: both "gauche" and "trans" conformations of the organic ligand, the [V(12)O(36)](-12) cycles, formed by 12 corner-sharing VO(4) tetrahedra, and, finally, the combination of both three-dimensional metal-organic and inorganic substructures, giving rise to a self-catenated highly connected net. The crystallization water molecules are semi-encapsulated in the channels along the [100] direction, and their loss gives rise to a dynamical and reversible structural contraction. Moreover, after the removal of the crystallization water molecules, the compound exhibits a negative thermal behavior in the 85-155 °C temperature range, and irreversible structural transformation due to the loss of coordinated water molecules up to 200 °C. The IR and UV-vis spectra were determined for the as-synthesized sample, after the removal of crystallization water molecules and after the irreversible transformation due to the loss of coordinated water molecules. The thermal evolution of χ(m) was adjusted to a magnetic model considering an isotropic dimer plus two Ni(II) d(8) isolated octahedra.     

Architectures,stability and optimization for clock distribution networks

Synchronous telecommunication networks, distributed control systems and integrated circuits have its accuracy of operation dependent on the existence of a reliable time basis signal extracted from the line data stream and acquirable to each node. In this sense, the existence of a sub-network (inside the main network) dedicated to the distribution of the clock signals is crucially important. There are different solutions for the architecture of the time distribution sub-network and choosing one of them depends on cost, precision, reliability and operational security. In this work we expose: (i) the possible time distribution networks and their usual topologies and arrangements. (ii) How parameters of the network nodes can affect the reachability and stability of the synchronous state of a network. (iii) Optimizations methods for synchronous networks which can provide low cost architectures with operational precision, reliability and security.