The Kramer Sampling Theorem Revisited

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. Besides, it has been the cornerstone for a significant mathematical literature on the topic of sampling theorems associated with differential and difference problems. In this work we provide, in an unified way, new and old generalizations of this result corresponding to various different settings; all these generalizations are illustrated with examples. All the different situations along the paper share a basic approach: the functions to be sampled are obtaining by duality in a separable Hilbert space \(\mathcal {H}\) through an \(\mathcal {H}\) -valued kernel K defined on an appropriate domain.     

Approximation of inverse operators by a new family of high‐order iterative methods

The main goal of this paper is to approximate inverse operators by high‐order Newton‐type methods with the important feature of not using inverse operators. We analyse the semilocal convergence, the speed of convergence, and the efficiency of these methods. We determine that Chebyshev's method is the most efficient method and test it on two problems: one associated to the heat equation and the other one to a boundary value problem. We consider examples with matrices that are close to be singular and/or are badly conditioned. We check the robustness and the stability of the methods by considering situations with many steps and noised data. Copyright © 2013 John Wiley & Sons, Ltd.     

A Lorentz force flow meter for application at blast furnaces: design and calibration

A reference Lorentz force flow meter (LFF) has been developed to measure molten steel mass flow at the end of the runner of an experimental blast furnace. It works according to the principles of Lorentz force velocimetry [1] in which a static magnetic field interacts with a liquid metal stream. The magnetic field lines are generated by an arrangement of permanent magnets and penetrate the entire cross-section of the flow generating eddy currents and a total Lorentz force inside the melt. This force is proportional to the mass flow of the liquid metal and owing Newton's third law, there is a counter force of the same magnitude acting on the magnet system which is connected to a load cell. For accurate flow rate measurements, a “dry and wet calibration” of the LFF needs to be performed [2]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The logic Ł•

The algebraic category is the image of MV, the category whose objects are the MV‐algebras, by the equivalence (cf. 7 , 8 ). In this paper we define the logic ?^? whose Lindenbaum algebra is an MV‐algebra (object of ), and establish a link between ?^? and the infinite valued ?ukasiewicz logic ?. We define U‐operators, that have properties of universal quantifiers, and establish a bijection that maps an MV‐algebra endowed with a U‐operator (cf. 20 - 22 ) into an MV^?‐algebra endowed with a U‐operator. This map extends to a functor that is a categorical equivalence.     

Synthesis,characterization and anticancer activity of new palladacycles derived from chiral α‐diimines

Optically pure α‐diimines quantitatively obtained in solvent‐free conditions starting from 2,3‐butanedione and (S)‐(?)‐1‐phenylethylamine and (S)‐(?)‐1‐(4‐methylphenyl)ethylamine, respectively, yielded the new chiral mono‐Pd complexes 2a–b, which have been partly characterized by IR, ¹H‐ and ¹³C‐NMR spectroscopies along with MS‐FAB⁺ spectrometry. The crystal and molecular structure for palladacycle 2a has been fully confirmed by single‐crystal X‐ray studies. Studies in vitro of 2a–b have displayed growth inhibition against different classes of cancer: leukemia (K‐562 CML), colon cancer (HCT‐15), breast cancer (MCF‐7), central nervous system (U‐251 Glio) and prostate cancer (PC‐3) cell lines. Copyright © 2009 John Wiley & Sons, Ltd.     

Interpretation of vicinal proton–proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors

The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd.     

Evidence of multi-walled carbon nanotube fragmentation induced by sonication during nanotube encapsulation via bulk-suspension polymerization

The synthesis of multi-walled carbon nanotube/polystyrene composites, with nanotube concentrations of 0.04, 0.08 and 0.16 wt%, was carried out by in situ bulk-suspension polymerization with the assistance of sonication. By using this method both encapsulation and exfoliation of the nanotubes into the polymer host were achieved. Evidence of significant nanotube fragmentation was found by scanning electron microscopy; the cause of such fragmentation was attributed to the induction of strong cavitation due to the application of ultrasound during the synthesis. Infrared spectroscopy showed no evidence of the formation of covalent bonds between the nanotubes and the polystyrene during the process of synthesis. The thermal stability was not improved by the inclusion of the nanotubes, it was attributed to the low nanotube concentrations; however, composites glass transition temperature showed improvements.     

Synthesis of (S)-(+)-sotalol and (R)-(−)-isoproterenol via a catalytic enantioselective Henry reaction

A unified approach for the synthesis of (S)-(+)-sotalol and (R)-(?)-isoproterenol has been developed. The enantioselective Henry reaction of the appropriate aldehyde in the presence of a camphor-derived amino pyridine–Cu(II) complex was the key step of the synthesis. The reduction of the nitro group to give the corresponding amino alcohols followed by reductive alkylation of the amine provided the target products with high enantiomeric excesses.