Hermite-based Appell polynomials: Properties and applications

By employing certain operational methods, the authors introduce Hermite-based Appell polynomials. Some properties of Hermite-Appell polynomials are considered, which proved to be useful for the derivation of identities involving these polynomials. The possibility of extending this technique to introduce Hermite-based Sheffer polynomials (for example, Hermite-Laguerre and Hermite-Sister Celine's polynomials) is also investigated.     

Olefin epoxidation with H2O2 in the presence of Mn(II) dicarboxylate coordination polymer catalysts

Abstract  

The Mn(II) dicarboxylate coordination polymers [Mn(μ-terephthalate)(H₂O)₂] _n , [Mn(μ-oxalate)(H₂O)₂] _n , and [Mn(μ-d-(−)-tartrate)] _n were prepared in water and characterized by FT-IR spectroscopy and CHN analysis. Particles of the terephthalate catalyst were also synthesized, by reaction of terephthalic acid and MnCl₂·4H₂O by a sonochemical method. The catalytic potential of these coordination polymers as slow-release sources of catalytically active Mn species was tested in the oxidation of cyclooctene to its epoxide in acetonitrile, using hydrogen peroxide as oxygen source. For the terephthalate species the catalytic activity was found to increase with increasing dielectric constant and dipole moment of the solvent (being highest in acetonitrile), with reaction temperature to a maximum at 60 °C, and with an imidazole co-catalyst (highest activity found for a imidazole-to-catalyst molar ratio of 20:1). Good activity with more than 64% conversion in 24 h was obtained for epoxidation of cyclooctene and cyclohexene, whereas low yields only were obtained from aryl-substituted olefins. Some exo versus endo regioselectivity was found for norbornene.     

Aircraft and crew scheduling for fractional ownership programs

Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods. Our computational results using real and randomly generated data indicate that these models are quite effective in finding optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits.     

Palladium–dppb–borate‐catalyzed regioselective synthesis of cinnamate esters by alkoxycarbonylation of phenylacetylene

The regioselective alkoxycarbonylation of phenylacetylene into various cinnamate esters was achieved with a catalyst system formed from palladium (II), 1,4‐bis(diphenylphosphino) butane (dppb) and salicylborate complex in acetonitrile as a solvent. The influence of various parameters on the overall conversion of phenylacetylene and the selectivity of the reaction were studied systematically by varying the type of palladium complex, acids promoter, CO pressure, temperature and the reaction time. This investigation allowed us to obtain the predominant formation of cinnamate esters with excellent selectivity (90–96%). Copyright © 2008 John Wiley & Sons, Ltd.     

Gas chromatographic technique for determination of Irgafos 168 in polyolefin samples after conversion to the related phenolic compound by saponification

A gas chromatographic technique is reported for the determination of a secondary antioxidant, Irgafos 168, in polymeric samples. Irgafos 168 [tris(2,4-di-tert-butyl phenyl)phosphite] is extracted by dissolution/precipitation, saponified to 2,4-di-tert-butyl phenol by refluxing in the presence of methanolic potassium hydroxide, and determined by gas chromatography-flame ionization detection. The method’s repeatability is good, and the relative standard deviation is 7.5% (between runs) and 15.5% (between days). This method was applied to the determination of Irgafos 168 in commercial polymers, and the obtained results were in relatively good agreement with those obtained by the previously reported spectrophotometric method. Correspondence: Mir Ali Farajzadeh, Department of Chemistry, Faculty of Science, Urmia University, Urmia, Iran     

Algebraic properties of separated power series

We study the commutative algebra of rings of separated power series over a ring E and that of their extensions: rings of separated (and more specifically convergent) power series from a field K with a separated E-analytic structure. Both of these collections of rings already play an important role in the model theory of non-Archimedean valued fields and we establish their algebraic properties. This will make a study of the analytic geometry over such fields through the classical methods of algebraic geometry possible.     

Novel phthalocyanines with naphthalenic substituents

Phthalocyanines with four naphthyl-malonic ester groups on the periphery were synthesized by cyclotetramerization of 4-(1,1-dicarbethoxy-2-(1-naphthyl)-ethyl)-phthalonitrile. The new compounds were characterized by spectroscopic methods. The electronic spectra exhibit intense π–π* transitions from the naphthyl moiety together with the characteristic Q and B bands of the phthalocyanine core. The electrochemical properties of the 2,9,17,23-tetra-(1,1-(dicarbethoxy)-2-(1-naphthyl)-ethyl) phthalocyaninato copper(II) complex were studied by cyclic voltammetry.     

Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system

The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 67–84, 2006.     

The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel

In this investigation, the peristaltic flow of a third order fluid in an asymmetric channel is considered in the presence of a slip condition. The series solution of the stream function and longitudinal pressure gradient is given under long wave length and low Reynolds number approximations. Pressure rise and frictional forces per wave length are analyzed through numerical integration. Pumping and trapping phenomena are examined and the obtained results are compared with those of no-slip condition. Comparison is made with the results of no-slip and viscous fluid cases.