Systems of proportionally modular Diophantine inequalities

The set of integer solutions to the inequality ax mod b≤c x is a numerical semigroup. We study numerical semigroups that are intersections of these numerical semigroups. Recently it has been shown that this class of numerical semigroups coincides with the class of numerical semigroups having a Toms decomposition. The first author was (partially) supported by the Centro de Matemática da Universidade do Porto (CMUP), financed by FCT (Portugal) through the programmes POCTI and POSI, with national and European Community structural funds. The last three authors are supported by the project MTM2004-01446 and FEDER funds. The authors would like to thank the referee for her/his comments and suggestions.     

Convergence and optimization of the parallel method of simultaneous directions for the solution of elliptic problems

For the solution of elliptic problems, fractional step methods and in particular alternating directions (ADI) methods are iterative methods where fractional steps are sequential. Therefore, they only accept parallelization at low level. In [T. Lu, P. Neittaanmäki, X.C. Tai, A parallel splitting-up method for partial differential equations and its applications to Navier–Stokes equations, RAIRO Modél. Math. Anal. Numér. 26 (6) (1992) 673–708], Lu et al. proposed a method where the fractional steps can be performed in parallel. We can thus speak of parallel fractional step (PFS) methods and, in particular, simultaneous directions (SDI) methods. In this paper, we perform a detailed analysis of the convergence and optimization of PFS and SDI methods, complementing what was done in [T. Lu, P. Neittaanmäki, X.C. Tai, A parallel splitting-up method for partial differential equations and its applications to Navier–Stokes equations, RAIRO Modél. Math. Anal. Numér. 26 (6) (1992) 673–708]. We describe the behavior of the method and we specify the good choice of the parameters. We also study the efficiency of the parallelization. Some 2D, 3D and high-dimensional tests confirm our results.     

Treatment of PVC using an alternative low energy ion bombardment procedure

In many applications, polymers have progressively substituted traditional materials such as ceramics, glasses, and metals. Nevertheless, the use of polymeric materials is still limited by their surface properties. Frequently, selective modifications are necessary to suit the surface to a given application. Amongst the most common treatments, plasma immersion ion implantation (PIII) has attracted the attention of many researchers owing to its versatility and practicality. This method, however, requires a power supply to provide high voltage (tens of kV) negative pulses, with a controlled duty cycle, width and frequency. Owing to this, the implementation of PIII on the industrial scale can become economically inviable. In this work, an alternative plasma treatment that enables low energy ion bombardment without the need of a high voltage pulse generator is presented. To evaluate the efficiency of the treatment of polymers, polyvinylchloride, PVC, specimens were exposed to 5 Pa argon plasmas for 3600 s, at excitation powers, P, of between 10 and 125 W. Through contact angle and atomic force microscopy data, the influence of P on the wettability, surface free energy and roughness of the samples was studied. Surface chemical composition was measured by X-ray photoelectron spectroscopy, XPS. To evaluate the effect of aging under atmospheric conditions, contact angle and XPS measurements were performed one and 1334 days after the treatment. The plasma potential and ion density around the driven electrode were determined from Langmuir probe measurements while the self-bias potential was derived with the aid of an oscilloscope. From these data it was possible to estimate the mean energy of ions bombarding the PVC surface. Chlorine, carbon and oxygen contamination were detected on the surface of the as-received PVC. Upon exposure to the plasma, the proportion of chlorine was observed to decrease while that of oxygen increased. Consequently, the wettability and surface energy increased after the treatment but such modifications were not stable after aging: the contact angle increased for all the samples, modifying the initially hydrophilic surface into a highly hydrophobic one. Consistently, the surface composition also changed after aging: there was carbon enrichment due to further losses of oxygen and chlorine. Another relevant factor for the elevation of θ was the change in morphology induced by the treatment. At greater powers, the uniform matrix of the PVC was transformed into a columnar structure containing randomly distributed sharp pillars. Interpretation of such results is proposed in terms of the total energy deposited in the solid by ionic collisions.     

Dense numerical semigroups

Semigroup Forum - A numerical semigroup S is dense if for all $$s\in S\backslash \{0\}$$ we have $$\left\{ s-1,s+1\right\} \cap S\ne \emptyset $$ . We give algorithms to compute the whole set of...     

Inhibitor‐Induced Dimerization of an Essential Oxidoreductase from African Trypanosomes

Trypanosomal and leishmanial infections claim tens of thousands of lives each year. The metabolism of these unicellular eukaryotic parasites differs from the human host and their enzymes thus constitute promising drug targets. Tryparedoxin (Tpx) from Trypanosoma brucei is the essential oxidoreductase in the parasite's hydroperoxide‐clearance cascade. In vitro and in vivo functional assays show that a small, selective inhibitor efficiently inhibits Tpx. With X‐ray crystallography, SAXS, analytical SEC, SEC‐MALS, MD simulations, ITC, and NMR spectroscopy, we show how covalent binding of this monofunctional inhibitor leads to Tpx dimerization. Intra‐ and intermolecular inhibitor–inhibitor, protein–protein, and inhibitor–protein interactions stabilize the dimer. The behavior of this efficient antitrypanosomal molecule thus constitutes an exquisite example of chemically induced dimerization with a small, monovalent ligand that can be exploited for future drug design.     

Poly(9‐undecyl‐9‐methyl‐fluorene) and poly(9‐pentadecyl‐9‐methyl‐fluorene): Synthesis,solution structure,and effect of side chain asymmetry on aggregation behavior

We report on solution aggregates and backbone conformation of poly(9‐undecyl‐9‐methyl‐fluorene) (PF1‐11) and poly(9‐pentadecyl‐9‐methyl‐fluorene) (PF1‐15), having two different side chains compared with poly(9,9‐dihexylfluorene) (PF6) and poly(9,9‐dioctylfluorene) (PF8) with two identical side chains. In the poor solvent methylcyclohexane (MCH), X‐ray scattering indicates that PF1‐11 and PF1‐15 appear as three‐dimensional aggregates (5–10 nm wide and thick), forming ribbon‐like agglomerates (correlation lengths of 100 nm). PF6 and PF8 appear as two‐dimensional aggregates (>10 nm wide and 2–3 nm thick) involving ribbon‐like agglomerates (correlation lengths much greater than 100 nm). Upon heating, all aggregates undergo a gel–sol transition which occurs at lower temperatures for PF1‐11 and PF1‐15 (<60°C) than for PF6 and PF8 (>80°C). In the good solvent toluene, PF1‐11 and PF1‐15 form networks of cylindrical particles. The mesh size and the cylinder radius are smaller in 24°C toluene (60 nm, 0.5 nm) than in 60°C MCH (300 nm, 1–2 nm). Nuclear magnetic resonance spectra in toluene‐d₈ together with density functional theory calculations suggest higher torsion angles between polymer repeat units for PF6, PF8, and PF1‐11 (less planar conformation) and a gauche arrangement of the dihedral angles between the bridge carbon atom and the side chain methylene groups in PF1‐15. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 826–837     

Global strong solutions for the incompressible micropolar fluids equations

Archiv der Mathematik - We study the Cauchy problem for the system of equations describing the nonstationary flow of micropolar incompressible fluids in $$\mathbb {R}^3$$ . We show the global...     

Synthesis and characterization of poly(ethylene glycol) diacrylate copolymers containing azobenzene groups prepared by frontal polymerization

A novel polymer matrix containing amino–nitro substituted azobenzene groups was obtained by frontal polymerization. (E)‐2‐(Ethyl(4‐((4‐nitrophenyl)diazenyl)phenyl)amino)ethyl methacrylate (MDR‐1) was copolymerized with poly(ethylene glycol) diacrylate (PEGDA) using this easy and fast polymerization technique. The effect of the amount of the incorporated azo‐monomer into the polymer matrix was studied in detail and correlated to front velocity, maximum temperature, initiator concentration, and monomer conversion. The obtained materials were characterized by infrared spectroscopy (Fourier transform infrared), and their thermal properties were studied by thermogravimetric analysis and differential scanning calorimetry. Moreover, the optical properties of the polymers were studied by absorption spectroscopy in the UV–Vis region. Absorption spectra of the copolymers exhibit a significant blue shift of the absorption bands with respect to the azo‐monomer, due to the presence of H‐aggregates. Cubic nonlinear optical (NLO) characterizations of the PEGDA/MDR‐1 copolymers were performed according to the Z‐Scan technique. It has been proven that samples with higher MDR‐1 content (0.75 mol %) exhibited outstandingly high NLO‐activity with negative NLO‐refractive coefficients in the promising range of n₂ = ?8.057 × 10^?4 esu. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Fabrication of functional nanostructured coatings by a combined sol–gel and plasma-enhanced chemical vapour deposition method

Nanostructures have a wide range of potential applications in industry because they can impart novel mechanical or functional properties to coatings such as abrasion resistance, UV shielding, superhydrophobicity. In this work we present a method for the fabrication of nanostructured coatings with improved mechanical properties, in which sol–gel nanoparticles are deposited on a surface and embedded in a ceramic film by plasma-enhanced chemical vapour deposition. This synthetic strategy is applied to the fabrication of transparent nanostructured antiscratch coatings.