Abstract functions with continuous differences and Namioka spaces

Let be a semigroup and a topological space. Let be an Abelian topological group. The right differences of a function are defined by for . Let be continuous at the identity of for all in a neighbourhood of . We give conditions on or range under which is continuous for any topological space . We also seek conditions on under which we conclude that is continuous at for arbitrary . This led us to introduce new classes of semigroups containing all complete metric and locally countably compact quasitopological groups. In this paper we study these classes and explore their relation with Namioka spaces.

     

A generic framework for time-stepping partial differential equations (PDEs): general linear methods,object-oriented implementation and application to fluid problems

Time-stepping algorithms and their implementations are a critical component within the solution of time-dependent partial differential equations (PDEs). In this article, we present a generic framework – both in terms of algorithms and implementations – that allows an almost seamless switch between various explicit, implicit and implicit–explicit (IMEX) time-stepping methods. We put particular emphasis on how to incorporate time-dependent boundary conditions, an issue that goes beyond classical ODE theory but which plays an important role in the time-stepping of the PDEs arising in computational fluid dynamics. Our algorithm is based upon J.C. Butcher's unifying concept of general linear methods that we have extended to accommodate the family of IMEX schemes that are often used in engineering practice. In the article, we discuss design considerations and present an object-oriented implementation. Finally, we illustrate the use of the framework by applications to a model problem as well as to more complex fluid problems.     

Surface hydration of crystalline and amorphous silicas

The surface properties of three SiO₂ samples, one crystalline (quartz) and two amorphous, with a large difference in particle size, have been investigated by thermal analysis, adsorption calorimetry and infrared spectroscopy. The variation in the silanol group population upon thermal treatment has been followed via the evolution of the i.r. bands at 3745–3750 cm^–1 (free hydroxyl groups) and 3650-3550 cm^–1 (adjacent pairs of SiOH) and the evolution of the heat of adsorption of water with coverage on the outgassed samples.The adsorption capacities increase in the sequence high surface area amorphous sample T=673 K) brings about dehydroxylation leaving only isolated silanols on the high surface area amorphous silica, and partial dehydroxylation of the low surface area material. Quartz is totally hydrophilic, as its regular structure probably stabilizes the hydroxyl layers at the surface.

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Zusammenfassung Die Oberflächeneigenschaften von einer kristallinen (Quarz) und zwei amorphen SiO₂-Proben mit großen Unterschieden in der Partikelgröße wurden durch thermische Analyse, Adsorptionskalorimetrie und Infrarotspektroskopie untersucht. Bei thermischer Behandlung eintretende Veränderungen in der Silanolgruppenpopulation wurden durch Messung der IR-Banden bei 3745–3750 cm^–1 (freie Hydroxylgruppen) und 3650–3550 cm^–1 (benachbarte SiOH-Paare) und der Adsorptionswärme von Wasser an ausgeheitzten Proben untersucht. Die Adsorptionskapazitäten nehmen in folgender Reihenfolge ab: amorphe Probe mit großer Oberfläche > amorphe Probe mit geringer Oberfläche > Quarz. Dehydroxylierung der Oberfläche hat zunehmenden hydrophoben Charakter (Gestalt der Isothermen, Adsorptionswärme kleiner als Kondensationswärme von Wasser) zur Folge. Bei der gleichen thermischen Behandlung (673 K) werden bei amorphen Siliciumdioxid mit großer Oberfläche eine nur isolierte Hydroxylgruppen zurücklassende Dehydroxylierung und bei Material mit kleiner Oberfläche eine teilweise Dehydroxylierung beobachtet. Quarz ist vollkommen hydrophyl, da die reguläre Struktur wahrscheinlich die Hydroxylschichten an der Oberfläche stabilisiert.

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, , (), — . 3745–3750 ^–1 ( ) 3650–3550 ^–1 ( SiOH), . < < . ( , ). (T=673 K) . , , , .

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This research was supported by the Ministry of Public Education within a national programme relating to the structure and reactivity of surfaces.     

Potential-Derived point-charge model study of electrostatic interaction energies in some hydrogen-bonded systems

Mulliken's atomic charges (MC ) and potential derived (PD ) point charges obtained from STO -3G wave functions are used to study the electrostatic interaction energies for a series of representative hydrogenbonded complexes. The results of the above-mentioned models are compared with the more accurate results of segmental multipole moment (SMM ) expansion, and it is shown that the PD model is superior to the Mc model. The results of PD model are shown to be well correlated with the results of SMM expansion technique. Results of our calculations using 6-31G and 6-31G** PD charges are also reported here. Electrostatic interaction energies obtained using 6-31G** PD charges are compared with the 6-31G** SCF interaction energies available for the nine hydrogen-bonded dimers of ammonia, water, and hydrogen fluoride and a good con-elation between the two is shown. The interrelationship between the results of different basis sets are also examined for the PD point-charge model. The electrostatic interaction energies obtained using STO -3G PD model are shown to be well correlated to the results of 6-31G and 6-31G** PD models.     

Facile large-scale fabrication of proton conducting channels

A new approach to the facile large-scale fabrication of robust silicon membranes with artificial proton conducting channels is presented. Ordered two-dimensional macroporous silicon was rendered proton conducting by growing a thick uniform polyelectrolyte brush using surface-initiated atom transfer radical polymerization throughout the porous matrix. The fabricated silicon-poly(sulfopropyl methacrylate) hybrid membranes were evaluated for their proton conductivity, ion exchange capacity, and water uptake. With proton conductivities in the range of 10(-2) S/cm, these proof-of-concept experiments highlight a promising alternative for producing tailorable proton conducting membranes. This approach constitutes a benchmark for the preparation and study of model systems and, in addition, for the large-scale fabrication of membranes suitable for a wide range of technological applications.     

Proton and calcium-gated ionic mesochannels: phosphate-bearing polymer brushes hosted in mesoporous thin films as biomimetic interfacial architectures

Rational construction of interfaces based on multicomponent responsive systems in which molecular transport is mediated by structures of nanoscale dimensions has become a very fertile research area in biomimetic supramolecular chemistry. Herein, we describe the creation of hybrid mesostructured interfaces with reversible gate-like transport properties that can be controlled by chemical inputs, such as protons or calcium ions. This was accomplished by taking advantage of the surface-initiated polymerization of 2-(methacryloyloxy)ethyl phosphate (MEP) monomer units into and onto mesoporous silica thin films. In this way, phosphate-bearing polymer brushes were used as "gatekeepers" located not only on the outer surface of mesoporous thin films but also in the inner environment of the porous scaffold. Pore-confined PMEP brushes respond to the external triggering chemical signals not only by altering their physicochemical properties but also by switching the transport properties of the mesoporous film. The ion-gate response/operation was based on the protonation and/or chelation of phosphate monomer units in which the polymer brush works as an off-on switch in response to the presence of protons or Ca(2+) ions. The hybrid meso-architectured interface and their functional features were studied by a combination of experimental techniques including ellipso-porosimetry, cyclic voltammetry, X-ray reflectivity, grazing incidence small-angle X-ray scattering, X-ray photoelectron spectroscopy, and in situ atomic force microscopy. In this context, we believe that the integration of stimuli-responsive polymer brushes into nanoscopic supramolecular architectures would provide new routes toward multifunctional biomimetic nanosystems displaying transport properties similar to those encountered in biological ligand-gated ion channels.     

Hydrophilic/hydrophobic features of TiO2 nanoparticles as a function of crystal phase, surface area and coating, in relation to their potential toxicity in peripheral nervous system

The hydrophilic/hydrophobic properties of a variety of commercial TiO(2) nanoparticles (NP), to be employed as inorganic filters in sunscreen lotions, were investigated both as such (dry powders) and dispersed in aqueous media. Water uptake and the related interaction energy have been determined by means of adsorption microcalorimetry of H(2)O vapor, whereas dispersion features in aqueous solutions were investigated by dynamic light scattering and electrokinetic measurements (zeta potential). The optimized dispersions in cell culture medium were employed to assess the possible in vitro neuro-toxicological effect on dorsal root ganglion (DRG) cells upon exposure to TiO(2)-NP, as a function of crystal phase, surface area and coating. All investigated materials, with the only exception of the uncoated rutile, were found to induce apoptosis on DRG cells; the inorganic/organic surface coating was found not to protect against the TiO(2)-induced apoptosis. The risk profile for DRG cells, which varies for the uncoated samples in the same sequence as the photo-catalytic activity of the different polymorphs: anatase-rutile>anatase>rutile, was found not to be correlated with the surface hydrophilicity of the uncoated/coated specimens. Aggregates/agglomerates hydrodynamic diameter was comprised in the ~200-400 nm range, compatible with the internalization within DRG cells.     

Harmonic analysis and asymptotic behavior of solutions to the abstract cauchy problem

LetC _ub ( $\mathbb{J}$ , X) denote the Banach space of all uniformly continuous bounded functions defined on $\mathbb{J}$ 2 ε {?⁺, ?} with values in a Banach spaceX. Let ? be a class fromC _ub( $\mathbb{J}$ ,X). We introduce a spectrumsp?(φ) of a functionφ εC _ub (?,X) with respect to ?. This notion of spectrum enables us to investigate all twice differentiable bounded uniformly continuous solutions on ? to the abstract Cauchy problem (*)ω′(t) =Aω(t) +φ(t),φ(0) =x,φ ε ?, whereA is the generator of aC ₀-semigroupT(t) of bounded operators. Ifφ = 0 andσ(A) ∩i? is countable, all bounded uniformly continuous mild solutions on ?⁺ to (*) are studied. We prove the bound-edness and uniform continuity of all mild solutions on ?⁺ in the cases (i)T(t) is a uniformly exponentially stableC ₀-semigroup andφ εC _ub(?,X); (ii)T(t) is a uniformly bounded analyticC ₀-semigroup,φ εC _ub (?,X) andσ(A) ∩i sp(φ) = Ø. Under the condition (i) if the restriction ofφ to ?⁺ belongs to ? = ?(?⁺,X), then the solutions belong to ?. In case (ii) if the restriction ofφ to ?⁺ belongs to ? = ?(?⁺,X), andT(t) is almost periodic, then the solutions belong to ?. The existence of mild solutions on ? to (*) is also discussed.