Stieltjes Polynomials and Related Quadrature Formulae for a Class of Weight Functions

Consider a (nonnegative) measure with support in the interval such that the respective orthogonal polynomials, above a specific index , satisfy a three-term recurrence relation with constant coefficients. We show that the corresponding Stieltjes polynomials, above the index , have a very simple and useful representation in terms of the orthogonal polynomials. As a result of this, the Gauss-Kronrod quadrature formulae for have all the desirable properties, namely, the interlacing of nodes, their inclusion in the closed interval (under an additional assumption on ), and the positivity of all weights. Furthermore, the interpolatory quadrature formulae based on the zeros of the Stieltjes polynomials have positive weights, and both of these quadrature formulae have elevated degrees of exactness.

     

Theoretical and Experimental Determination of Thermomechanical Properties of Epoxy-SiO2 Nanocomposites

Improvements in the thermomechanical properties of epoxy upon inclusion of well-dispersed SiO₂ nanoparticles have been demonstrated both experimentally and through molecular dynamics simulations. The SiO₂ was represented by two different dispersion models: dispersed individual molecules and as spherical nanoparticles. The calculated thermodynamic and thermomechanical properties were consistent with experimental results. Radial distribution functions highlight the interactions of different parts of the polymer chains with the SiO₂ between 3 and 5 nm into the epoxy, depending on the particle size. The findings from both models were verified against experimental results, such as the glass transition temperature and tensile elastic mechanical properties, and proved suitable for predicting thermomechanical and physicochemical properties of epoxy-SiO₂ nanocomposites.     

Formation of acetamido-Aza-steroids

Beckmann rearrangement of 3α- and 3β-acetamido-5α-androstan-17-one oximes gives homo-aza compounds and the corresponding “second order” Beckmann cleavage ω-cyanoolefin. The mixture of the compounds produced, was separated by column chromatography. The structure of the lactams and the exocyclic nitriles was apparent from ir and nmr spectra.     

Controlling Bivariate Categorical Processes using Scan Rules

In this paper, we introduce a methodology for efficiently monitoring a health process that classify the intervention outcome, in two dependent characteristics, as “absolutely successful”, “with minor but acceptable complications” and “unsuccessful due to severe complications”. The monitoring procedure is based on appropriate 2-dimensional scan rules. The run length distribution is acquired by studying the waiting time distribution for the first occurrence of a 2-dimensional scan in a bivariate sequence of trinomial trials. The waiting time distribution is derived through a Markov chain embedding technique. The proposed procedure is applied on two simulated cases while it is tested against a competing method showing an excellent performance.     

The error norm of quadrature formulae

In certain spaces of analytic functions the error term of a quadrature formula is a bounded linear functional. We give a survey of the methods used in order to compute explicitly, or in some cases estimate, the norm of the error functional. The results, some of which are fairly recent, cover Gauss, Gauss?CLobatto, Gauss?CRadau, Gauss?CKronrod and Fejér type rules.     

Factorizations of EP operators

In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP operators.     

The error norm of Gauss-Radau quadrature formulae for Chebyshev weight functions

In certain spaces of analytic functions the error term of the Gauss-Radau quadrature formula relative to a (nonnegative) weight function is a continuous linear functional. We compute or estimate the norm of the error functional for any one of the four Chebyshev weight functions.     

Total synthesis of epicoccin G

An expedient enantioselective total synthesis of epicoccin G and related dithiodiketopiperazines through a strategy featuring direct two-directional sulfenylation, photooxygenation, and Kornblum-DeLaMare rearrangement is described.     

Oxygen ion diffusion measurements in Bi0.775La0.225O1.5

The oxygen transport properties of the Bi_0.775La_0.225O_1.5 electrolyte material have been investigated. Isotopic exchange depth profiling (IEDP) technique with secondary ion mass spectrometry (SIMS) was used in order to measure the oxygen tracer diffusion coefficient D. The activation energy for oxygen tracer diffusion was found to be 115 ± 2 kJ/mol (1.19 ± 0.02 eV). The measured D values were converted using the Nernst-Einstein relationship to conductivity and compared with data from AC Impedance. The agreement of the two sets of data implies that the material is an oxygen ion conductor.