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.     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

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.     

Gas phase activation energy for unimolecular dissociation of biomolecular ions determined by focused RAdiation for gaseous multiphoton ENergy transfer (FRAGMENT)

We present a novel approach for the determination of activation energy for the unimolecular dissociation of a large (>50 atoms) ion, based on measurement of the unimolecular dissociation rate constant as a function of continuous-wave CO(2) laser intensity. Following a short ( approximately 1 s) induction period, CO(2) laser irradiation produces an essentially blackbody internal energy distribution, whose 'temperature' varies inversely with laser intensity. The only currently available method for measuring such activation energies is blackbody infrared radiative dissociation (BIRD). Compared with BIRD, FRAGMENT: (a) eliminates the need to heat the surrounding ion trap and vacuum chamber to each of several temperatures (each requiring hours for temperature equilibration); (b) offers a three-fold wider range of effective blackbody temperature; and (c) extends the range of applications to include initially cold ions (e.g., gas-phase H/D exchange). Our FRAGMENT-determined activation energy for dissociation of protonated bradykinin, 1.2 +/- 0.1 eV, agrees within experimental error to the value, 1.3 +/- 0.1 eV, previously reported by Williams et al. from BIRD experiments. Copyright 1999 John Wiley & Sons, Ltd.     

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.     

Relations between different types of spectra and spectral characterizations

In the study of the asymptotic behaviour of solutions of differential-difference equations the -spectrum has been useful, where and implies Fourier transform , with given , φ∈L ^∞(ℝ,X), X a Banach space, (half)line. Here we study and related concepts, give relations between them, especially weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =  ; also  = Beurling spectrum of “φ modulo ” (Chill-Fasangova). If satisfies a Loomis type condition (L _U ), then countable and uniformly continuous ∈U are shown to imply ; here (L _U ) usually means , indefinite integral Pf of f in U imply Pf in (the Bohl-Bohr theorem for = almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes , ℳ ^m U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with in some we show . With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral integro-differential-difference systems. Also many examples and special cases are discussed.