Asymptotic formula for the error in cardinal interpolation

Summary. We give the asymptotic formula for the error in cardinal interpolation. We generalize the Mazur Orlicz Theorem for periodic function. Received February 22, 1999 / Revised version received October 15, 1999 / Published online March 20, 2001     

q-quantum plane,ψ(q)-umbral calculus, and all that

It is known that one can formulateq-extended finite operator calculus with help of “quantumq-plane”q-commuting variablesA, B : AB − qBA ≡ [A, B]q=0. We shall recall this simple fact in its natural entourage which is the so-calledψ(q)-extension of Rota’s finite operator calculus. We aim to convince the audience that this is a natural and elementary method for formulation and treatment ofq-extended and possiblyR-extended orψ(q)-extended models for quantum-likeψ(q)-deformed oscillators. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

Nitration of Porphyrin Systems: A Toolbox of Synthetic Methods

This review addresses nitration reactions of porphyrin derivatives. Simple porphyrins modifications afford valuable intermediates in this area of chemistry. They are useful materials for further transformations, as the NO₂ group introduced into parent porphyrin system increases its electrophilic character, thus allowing a broad spectrum of subsequent reactions, e. g. reduction of NO₂ to NH₂, subsequent diazotisation, nucleophilic substitution of hydrogen (in ortho-position to NO₂), a variety of cyclizations, etc. Such reactions are often utilized in the first steps of the designed syntheses, leading to attractive and useful target porphyrin molecules. This approach (via nitro-derivatives) allows synthesizing numerous porphyrin-like compounds of a high degree of complexity, and has thus become one of the methods choice. The substitution by NO₂ group can take place at all positions of the porphyrin systems: four meso-positions (5, 10, 15, 20) and eight positions β (2, 3, 7, 8, 12, 13, 17, 18). The third possibility includes the nitration in meso-aryl rings attached to positions 5, 10, 15, and 20. The latter derivatives (meso-aryl substituted ones) are a large, well-known group of synthetic porphyrins. The nitration reactions described herein follow three various mechanisms: (a) radical, (b) via π-cation radicals and π-dications, and (c) electrophilic. All the above cases are discussed in detail. According to our knowledge, this is the first such systematic account concerning these reactions.     

A dynamic analysis of a coupled beam/slider system

The paper deals with transverse vibration of a beam with moving boundary conditions. In order to examine the transfer of energy between a moving support and a vibrating beam under assumption of zero slope of the beam elastic line at the moving support, dynamic analysis of a coupled beam/slider system is carried out. The moving support is modelled as a slider attached to a spring which realizes definite boundary conditions. Equations of motion are derived using Hamilton’s principle. Because length of the beam varies appropriate transformations of time and position variables are made to convert the solution space into a rectangle and, subsequently, to solve the partial differential equation of transverse vibration of the beam using the FDM. The phenomenon of the energy flow between the slider and the beam is a subject of the detailed analysis. The beam vibration with a fixed formula of length is examined, too. The dynamic characteristics of the system is brought forward from spectral analysis of numerical solutions.     

Spectroscopic and photopolymerization studies of benzyl methacrylate/poly(benzyl methacrylate) two‐component system

The influence of the viscosity of a two‐component system on its molecular dynamics (on the basis of hypersonic wave velocity and attenuation coefficient) and photopolymerization kinetics was studied. The system investigated represented the solution of poly(benzyl methacrylate), PBzMA (MW = 70000) in its monomer, benzyl methacrylate (BzMA). The viscosity of the system was varied by adding various amounts of the polymer to the monomer (10–50 wt %). The molecular dynamics in the neat BzMA was studied by the proton Nuclear Magnetic Resonance (NMR) spin‐lattice relaxation time measurements and the wide‐line ¹H NMR spectroscopy in a wide range of temperature. Information on the local dynamics in liquid BzMA above its melting temperature was gained from the high‐resolution ¹H and ¹³C NMR spectra. The hypersonic wave velocity and the attenuation coefficient were investigated in the appropriate temperature range related to a viscoelastic relaxation process by the Brillouin light scattering method. The kinetic measurements have demonstrated that the photopolymerization rate rapidly increases and the monomer conversion decreases with increasing polymer‐to‐monomer ratio; this effect has been noted in the whole range of polymer concentration and reaction temperature studied. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1336–1348, 2010     

Did Günter Nimtz discover tachyons?

It is argued that in the famous G. Nimtz experiment tachyons were produced and annihilated. We base our considerations on the new version of Special Relativity elaborated recently by one of the authors.     

Influence of inner transducer properties on EMF response and stability of solid-contact anion-selective membrane electrodes based on metalloporphyrin ionophores

The performance of solid-contact coated-wire-type electrodes with plasticized poly(vinyl chloride) membranes containing metalloporphyrins as anion-selective ionophores is reported. The membranes are deposited on transducers based on graphite pastes and graphite rods. The hydrophobicity of the underlying conductive transducer surface is found to be a key factor that influences the formation of an aqueous layer beneath the polymer film. Elimination of this ill-defined water layer greatly improves the electrochemical properties of the ion-sensors, such as electromotive force stability and lifetime. Only highly lipophilic electrode substrates, namely graphite paste with mineral oil, were shown to prevent the formation of aqueous layer underneath the ion-sensing membrane. The possibility of employing Co(III)-tetraphenylporphyrin both as NO₂ ⁻ selective ionophore and as electron- and ion-conducting species to ensure ion-to-electron translation was also discussed based on the results of preliminary experiments.