Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.     

Potenzsummenformeln im 17. Jahrhundert

Interest in power series of natural numbers is to be seen not only against the background of their application to the quadrature-problem of parabolas and hyperbolas, as with Fermat, but it is fueled as well by purely number-theoretic interests, which were accompanied by number-mystical speculations, as with Johannes Faulhaber. On another level the seventeenth-century works on power series of natural numbers show quite clearly how long heuristic methods were regarded as powerful in proofs, and how much the introduction of rigorous methods of proof depended on the communications system of mathematicians.     

Photoinduced switch of a DNA/RNA inactive molecule into a classical intercalator

Spectroscopic titrations and thermal denaturation experiments show that "acyclic" analogue 1 does not bind to ds-DNA, but under same conditions "cyclic" 2 strongly interacts with ds-DNA and ds-RNA by intercalation into the double helix. Besides, 2 is significantly more effective in inhibition of the tumor cell growth in vitro than 1. We have shown that it is possible to efficiently and irreversibly convert "DNA inactive" compound 1 into "DNA active" compound 2 by light irradiation of the aqueous solutions of the former. This strategy offers a new and attractive approach to photoinduced anticancer therapy.     

Energy spectrum of α particles emitted from sources of different thicknesses

The shape of the energy distribution of all particles emitted by sources of different thicknesses was investigated. The energy distribution N(E) dE found can be expressed by a semi-empirical formula, which on the whole agrees with experiment. The source of particles was uranium oxide U ₃ 0 ₈.The energy distribution was measured with AGFA K2 nuclear emulsions 200 thick. Altogether 3,602 trajectories of particles in the nuclear emulsions of five plates were measured.The author would like to thank Prof. Dr. V. Petrílka, M. Rozko and L. Drka for remarks and their interest in this paper. He also thanks R. Krejí, J. Lejnarová and H. Koutová for carefully and promptly measuring the trajectories and for help in realizing the experiments.     

The Reaction of 3-Formylchromone with ortho-Substituted Anilines. Preparation of a Tetraaza [14]annulene

The reactions of 3-formylchromone ( 1 ) with 1, 2-phenylenediamine, 2-amino-diphenylamine and 2-aminophenol were reinvestigated and shown to yield 1, 8-dihydro-6, 13-di (2-hydroxybenzoyl)-dibenzo [b, i]-l, 4, 8, 11-tetraazacyclotetradeca- 4, 6, 11,13-tetraene ( 7 ), 3-[2-(1-phenyl)benzimidazolyl]chromone ( 10b ) and 3-(2-hydroxyphenyl)iminomethylchromone ( 4 ), respectively at variance with earlier reports. Compound 4 reacts with ethanol to give 2-ethoxy-3-[(2-hydroxyphenyl)-aminomethylidene]chroman-4-one ( 5b ). Dehydrogenation of 7 produces 3-(2-benz-imidazolyl)chromone ( 10a ), also at variance with earlier reports. The structures have been elucidated with the aid of NMR. and mass spectra. The reaction mechanism is discussed.     

Condensed phases in flame spectrometry: an equilibrium model of the acetylene flame

An equilibrium model for a wet acetylene flame has been used for the calculation of the distribution of carbon, aluminium and silicon between gaseous and condensed phases. Calculated values of free atom vapour fractions are in agreement with published experimental data. It is thermodynamically probable that the formation of condensed phases limits atom vapour formation. There is a relationship between the position of an element in the Periodic Table and the nature of the condensed phase.     

Interior numerical approximation of boundary value problems with a distributional data

We study the approximation properties of a harmonic function u ∈ H^1?k(Ω), k > 0, on a relatively compact subset A of Ω, using the generalized finite element method (GFEM). If Ω = ??, for a smooth, bounded domain ??, we obtain that the GFEM‐approximation u_S ∈ S of u satisfies ‖u ? u_S‖ ≤ Ch^γ‖u‖, where h is the typical size of the “elements” defining the GFEM‐space S and γ ≥ 0 is such that the local approximation spaces contain all polynomials of degree k + γ. The main technical ingredient is an extension of the classical super‐approximation results of Nitsche and Schatz (Applicable Analysis 2 (1972), 161–168; Math Comput 28 (1974), 937–958). In addition to the usual “energy” Sobolev spaces H¹(??), we need also the duals of the Sobolev spaces H^m(??), m ∈ ?₊. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Electrospray deposition, model, and experiment: toward general control of film morphology

Poly(vinylidene fluoride) film formation with electrospray deposition has been studied with support of a droplet evaporation model. The input parameters of the model consist basically of the solvent, the solute concentration, the flow rate, and the solution conductivity. The model provides the droplet size, the solute concentration, the droplet velocity, and the shear stress of the droplet at impact as a function of the distance between the nozzle and the substrate. With some additional experimental information such as the size change of the film with spray distance and the viscosity of the solution, the growth rate of the film and the shear rate of the droplet at impact can be determined. Growth rate is shown to define distinct regimes of film formation. In those regimes, only a single factor or a limited number of factors controls the film morphology. The most important factors include the shear rate and the surface energy. It is found that at a specific range of growth rates only the shear rate determines the morphology of the polymer film. Growth rate, as the defining quantity of film morphology, is not limited to polymer solutions. Therefore, the growth rate, in combination with the control factors mentioned above, functions as a general framework through which understanding and control of film formation with electrospray deposition can be improved.     

Approximate analysis of single-server tandem queues with finite buffers

In this paper, we study single-server tandem queues with general service times and finite buffers. Jobs are served according to the Blocking-After-Service protocol. To approximately determine the throughput and mean sojourn time, we decompose the tandem queue into single-buffer subsystems, the service times of which include starvation and blocking, and then we iteratively estimate the unknown parameters of the service times of each subsystem. The crucial feature of this approach is that in each subsystem successive service times are no longer assumed to be independent, but a successful attempt is made to include dependencies due to blocking by employing the concept of Markovian Arrival Processes. An extensive numerical study shows that this approach produces very accurate estimates for the throughput and mean sojourn time, outperforming existing methods, especially for longer tandem queues and for tandem queues with service times with a high variability.     

Reversible Optical Writing and Data Storage in an Anthracene‐Loaded Metal–Organic Framework

Metal–organic frameworks (MOFs) enable the design of host–guest systems with specific properties. In this work, we show how the confinement of anthracene in a well‐chosen MOF host leads to reversible yellow‐to‐purple photoswitching of the fluorescence emission. This behavior has not been observed before for anthracene, either in pure form or adsorbed in other porous hosts. The photoresponse of the host–guest system is caused by the photodimerization of anthracene, which is greatly facilitated by the pore geometry, connectivity, and volume as well as the structural flexibility of the MOF host. The photoswitching behavior was used to fabricate photopatternable and erasable surfaces that, in combination with data encryption and decryption, hold promise in product authentication and secure communication applications.