The Brjuno Functions and Their Regularity Properties

We show that various possible versions of the Brjuno function, based on different kinds of continued fraction developments, are all equivalent and we study their regularity (L ^p, BMO and H?lder) properties, through a systematic analysis of the functional equation which they fulfill. Received: 21 March 1995 / Accepted: 8 August 1996     

Quality assurance of e-learning in developing countries

In this paper some of the aspects of implementing measures for quality assurance of e-learning in developing countries are discussed. Also the main problems of establishing quality assurance of e-learning are illustrated. The advantages of adopting international measures of quality assurance in those countries together with several recommendations for the future and our conclusion are then given.     

Liquid-phase epitaxy of multicomponent layer-based porous coordination polymer thin films of [M(L)(P)0.5] type: importance of deposition sequence on the oriented growth

The progressive liquid-phase layer-by-layer (LbL) growth of anisotropic multicomponent layer-based porous coordination polymers (PCPs) of the general formula [M(L)(P)(0.5)] (M: Cu(2+), Zn(2+); L: dicarboxylate linker; P: dinitrogen pillar ligand) was investigated by using either pyridyl- or carboxyl-terminated self-assembled monolayers (SAMs) on gold substrates as templates. It was found that the deposition of smooth, highly crystalline, and oriented multilayer films of these PCPs depends on the conditions at the early growth cycles. In the case of a two-step process with an equimolar mixture of L and P, growth along the [001] direction is strongly preferred. However, employing a three-step scheme with full separation of all components allows deposition along the [100] direction on carboxyl-terminated SAMs. Interestingly, the growth of additional layers on top of previously grown oriented seeding layers proved to be insensitive to the particular growth scheme and full retention of the initial orientation, either along the [001] or [100] direction, was observed. This homo- and heteroepitaxial LbL growth allows full control over the orientation and the layer sequence, including introduction of functionalized linkers and pillars.     

A simple chemical model for clathrate hydrate inhibition by polyvinylcaprolactam

A dimeric model compound gives structural insight into the mode of interaction of low dosage hydrate inhibitors with water.     

Post-synthetic modification of epitaxially grown, highly oriented functionalized MOF thin films

Thin films of MOFs grown on solid substrates offer a huge potential with regard to tailoring the properties of a surface, in particular if used in connection with post-synthesis modification (PSM). Here, we report on the PSM of surface-supported crystalline MOFs, with target molecules using an amine-based coupling strategy.     

Efficacy of 2-Hydroxyflavanone in Rodent Models of Pain and Inflammation: Involvement of Opioidergic and GABAergic Anti-Nociceptive Mechanisms

The current work examined the pharmacological potential of a selected flavanone derivative 2-hydroxyflavanone as a promising remedy for the treatment and management of pain. The selected flavanone derivative (2-HF) was evaluated for its analgesic and anti-inflammatory potentials following standard pharmacological protocols including hot plate, acetic acid-induced writhing and tail immersion tests. Naloxone and pentylenetetrazol were used to evaluate the potential implication of GABAergic and opioidergic mechanisms. The anti-inflammatory potential of 2-HF was confirmed using carrageenan-, serotonin- and histamine-induced paw edema models as well as a xylene-induced ear edema model. Furthermore, the anti-neuropathic potential of 2-HF was tested using a cisplatin-induced neuropathic pain model. Our sample, at the tested concentrations of 15, 30 and 45 mg kg⁻¹, showed considerable analgesic, anti-inflammatory effects, as well as efficacy against neuropathic pain. Naloxone and pentylenetetrazol at 1 and 15 mg kg⁻¹ antagonized the anti-nociceptive activities of 2-hydroxyflavanone indicating the involvement of opioidergic and GABAergic mechanisms. In the static allodynia model, combination of gabapentin 75 mg kg⁻¹ with 2-HF at 15, 30, 45 mg kg⁻¹ doses exhibited considerable efficacy. In cold allodynia, 2-hydroxyflavanone, at doses of 15, 30 and 45 mg kg⁻¹ and in combination with gabapentin (75 mg kg⁻¹), demonstrated prominent anti-allodynic effects. The paw withdrawal latency was considerably increased in gabapentin + cisplatin treated groups. Moreover, cisplatin + 2-hydroxyflavanone 15, 30, 45 mg kg⁻¹ showed increases in paw withdrawal latency. Likewise, considerable efficacy was observed for 2-hydroxyflavanone in thermal hyperalgesia and dynamic allodynia models. Our findings suggest that 2-hydroxyflavanone is a potential remedy for pain syndrome, possibly mediated through opioidergic and GABAergic mechanisms.     

Effect of ZnO Nanofiller on Structural and Electrochemical Performance Improvement of Solid Polymer Electrolytes Based on Polyvinyl Alcohol–Cellulose Acetate–Potassium Carbonate Composites

In this study, a solution casting method was used to prepare solid polymer electrolytes (SPEs) based on a polymer blend comprising polyvinyl alcohol (PVA), cellulose acetate (CA), and potassium carbonate (K₂CO₃) as a conducting salt, and zinc oxide nanoparticles (ZnO-NPs) as a nanofiller. The prepared electrolytes were physicochemically and electrochemically characterized, and their semi-crystalline nature was established using XRD and FESEM. The addition of ZnO to the polymer–salt combination resulted in a substantial increase in ionic conductivity, which was investigated using impedance analysis. The size of the semicircles in the Cole–Cole plots shrank as the amount of nanofiller increased, showing a decrease in bulk resistance that might be ascribed to an increase in ions due to the strong action of the ZnO-NPs. The sample with 10 wt % ZnO-NPs was found to produce the highest ionic conductivity, potential window, and lowest activation energy (E_a) of 3.70 × 10^–3 Scm^–1, 3.24 V, and 6.08 × 10^–4 eV, respectively. The temperature–frequency dependence of conductivity was found to approximately follow the Arrhenius model, which established that the electrolytes in this study are thermally activated. Hence, it can be concluded that, based on the improved conductivity observed, SPEs based on a PVA-CA-K₂CO₃/ZnO-NPs composite could be applicable in all-solid-state energy storage devices.     

The cohomological equation for Roth-type interval exchange maps

We exhibit an explicit class of minimal interval exchange maps (i.e.m.'s) for which the cohomological equation

has a bounded solution provided that the datum belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The proof is purely dynamical and is based on a renormalization argument and on Gottshalk-Hedlund's theorem. If the datum is more regular the loss of differentiability in solving the cohomological equation will be the same.

The class of interval exchange maps is characterized in terms of a diophantine condition of Roth type imposed to an acceleration of the Rauzy-Veech-Zorich continued fraction expansion associated to . More precisely one must impose a growth rate condition for the matrices appearing in the continued fraction algorithm together with a spectral gap condition (which guarantees unique ergodicity) and a coherence condition. We also prove that the set of Roth-type interval exchange maps has full measure.

In the appendices we construct concrete examples of Roth-type i.e.m.'s and we show how the growth rate condition alone does not imply unique ergodicity.