Matrix pencil methodologies for computing the greatest common divisor of polynomials: hybrid algorithms and their performance

The computation of the greatest common divisor (GCD) of several polynomials is a problem that emerges in many fields of applications. The GCD computation has a non-generic nature and thus its numerical computation is a hard problem. In this paper we examine the family of matrix pencil methods for GCD computation and investigate their performance as far as their complexity, error analysis and their effectiveness for evaluating approximate solutions. The relative merits of the various variants of such methods are examined for the different cases of sets of polynomials with varying number of elements and degree. The developed algorithms combine symbolical and numerical programming and this is what we define here as hybrid computations. The combination of numerical operations with symbolical programming can improve the nature of the methods and guarantees the stability of the algorithm. Furthermore, it emphasizes the significance of hybrid computations in complex problems such as the computation of GCD. All methods are tested thoroughly for several sets of polynomials and the results are presented in tables.     

Studies on the usability of recycled PET for food packaging applications

The need of and opportunities for recycling of plastics for food packaging have been recognized, and a lot of work to find meaningful and cost-effective solutions to this issue is in progress. The safety of recycled plastics for food contact use is largely dictated by the ability of post-consumer contaminants to absorb into recycled materials and later diffuse from recycled plastics into the food. The objective of the present study was to establish a suitable analytical approach to identifying and quantifying any chemical substances that derive from the earlier use and remain in the polyethylene terephthalate (PET). A simple gas chromatographic technique using flame ionization detection was developed to allow quantification of solvent extractable compounds in a series of recycled PET samples. Identification of the nature and extent of contaminants in the PET samples was also attempted using GC/MS analysis.     

The concept of physical metric in rate-independent generalized plasticity

A new internal variable formulation of rate-independent generalized plasticity is presented. The formulation relies crucially on the consideration of the physical (referential) metric as a primary internal variable and does not invoke any decomposition of the kinematical quantities into elastic and plastic parts. On the basis of a purely geometrical argument, namely the invariance of a set under the action of the flow of a vector field, the transition to classical plasticity is demonstrated. The covariant balance of energy is systematically employed for the derivation of the mechanical state equations. It is shown that unlike the case of finite elasticity, in finite plasticity the covariant balance of energy does not yield the Doyle?CEricksen formula, unless a further assumption is made. As an application, a material model is developed and is tested numerically for the solution of several problems of large-scale plastic flow.     

Interfacial properties of (Ag + CuO) brazes used as sealing materials in SOFC stacks

Ceramic insulation layers in combination with air braze filler metals were investigated as material compositions suitable for joining the metallic components in planar solid oxide fuel cell stacks. This paper reports on a series of wetting experiments for determination of the interfacial properties of pure Ag and Ag + CuO brazes in contact with the oxides MgO, MgAl₂O₄, Al₂O₃ and the mixture MgO + MgAl₂O₄, as well as with ferritic steel at 1273 K. The long-term stability of the ceramic/Ag + CuO/steel joints after exposure for longer periods of time (1000 h) at 1073 K is also assessed. The influence on joining of CuO additions in the noble metal was investigated following two different routes. The first one involved melting of Ag + 4 wt% CuO brazes on the surface of solid substrates (ceramic, steel), and the second one involved melting of pure Ag on the substrates coated with a thin CuO_x layer. No differences in the values of the measured contact angles were observed. Furthermore, it was found that the reactions taking place at the interface braze/steel at the initial stage of brazing is extended in the case of Ag + 4 wt% CuO during the long-term exposure at envisaged operating temperature limiting the stability of the joint.     

Error sources and error propagation in the Levinson-Durbinalgorithm

It is proved that there are two types of numerical error, due to finite precision, in the Levinson-Durbin algorithms; an erratic and a systematic one. The erratic one depends on the value the input autocorrelation accidentally takes at an iteration, and, essentially, it affects only the results obtained at this particular recursion. On the contrary, the systematic numerical error increases with the information the system carries and propagates essentially throughout the algorithm. It is shown that, for both types of error, as well as the overall one, there are specific intermediate quantities, calculated in the evolution of the algorithm, which may serve as precise indicators of the exact number of erroneous digits with which the various quantities are computed including the PARCOR coefficients and the filter coefficients. Therefore, the generated numerical error can be accurately traced     

A general class of nonparametric control charts

In this article, we introduce a new general class of nonparametric Shewhart‐type control charts using the lengths of runs of test sample observations between successive observations of a reference sample. Several control charts that have appeared in the literature are members of the new family. In addition, 3 new nonparametric control charts that belong to the class are introduced and studied. Numerical results depict that the proposed charts attain competitive in‐control and out‐of‐control performance as compared with existing nonparametric charts.     

A multiscale virtual element method for the analysis of heterogeneous media

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples.     

Physical characterization of Y<Subscript>2</Subscript>O<Subscript>3</Subscript>–CeO<Subscript>2</Subscript>–TiO<Subscript>2</Subscript> (YCT) mixed oxides and Ni/YCT cermets as anodes in solid oxide fuel cells

Mixed oxides in the binary Y₂O₃–CeO₂ (YC) and ternary Y₂O₃–CeO₂–TiO₂ (YCT) systems as well as the corresponding Ni cermets were evaluated in terms of application as anodes in solid oxide fuel cells (SOFCs) between 650 and 900 °C. X-ray diffraction (XRD) analysis of the YCT powders calcined up to 1,400 °C showed the cubic fluorite structure of YC and also the formation of an additional phase with pyrochlore structure. The thermal expansion of the ceramics measured in air and Ar/4% H₂ showed no significant differences in the temperature range of 25–800 °C. The absolute values of the total electrical conductivity of the ceramics measured between 450 and 900 °C in Ar/4% H₂ increased by about 1–2 orders of magnitude compared to those measured in air. Ni/Y_0.20Ce_0.80O_1.9 and Ni/Y_0.20C_0.75Ti_0.05O_1.9 cermets with 40 vol% Ni exhibited improved long-term stability regarding their electrical conductivity after annealing at 1,000 °C. The diffusion coefficient of Ce in the 8YSZ electrolyte was measured by compatibility tests. Electrochemical measurements on single SOFCs showed high polarization resistance at the anode/electrolyte interface.