Application of autoregressive spectral analysis to missing data problems

Time series solutions for spectral analysis in missing data problems use reconstruction of the missing data, or a maximum likelihood approach that analyzes only the available measured data. Maximum likelihood estimation yields the most accurate spectra. An approximate maximum likelihood algorithm is presented that uses only previous observations falling in a finite interval to compute the likelihood, instead of all previous observations. The resulting nonlinear estimation algorithm requires no user-provided initial solution, is suited for order selection, and can give very accurate spectra even if less than 10% of the data remains.     

Finite sample properties of ARMA order selection

The cost of order selection is defined as the loss in model quality due to selection. It is the difference between the quality of the best of all available candidate models that have been estimated from a finite sample of N observations and the quality of the model that is actually selected. The order selection criterion itself has an influence on the cost because of the penalty factor for each additionally selected parameter. Also, the number of competitive candidate models for the selection is important. The number of candidates is, of itself, small for the nested and hierarchical autoregressive/moving average (ARMA) models. However, intentionally reducing the number of selection candidates can be beneficial in combined ARMA(p,q) models, where two separate model orders are involved: the AR order p and the MA order q. The selection cost can be diminished by creating a nested sequence of ARMA(r,r-1) models. Moreover, not evaluating every combination (p,q) of the orders considerably reduces the required computation time. The disadvantage may be that the true ARMA(p,q) model is no longer among the nested candidate models. However, in finite samples, this disadvantage is largely compensated for by the reduction in the cost of order selection by considering fewer candidates. Thus, the quality of the selected model remains acceptable with only hierarchically nested ARMA(r,r-1) models as candidates.     

Performance of simple response method for the establishment and adjustment of calibration intervals

Managing calibration intervals in order to fulfill requirements of quality-oriented organizations is discussed in this paper. In particular, the simple response method is considered. According to this technique, the interval between successive calibrations is adjusted adaptively on the basis of the outcome of the last calibration process. An original analysis is presented about the properties of such calibration interval handling methods. Finally, directions are given on how to tune its parameters optimally, in order to meet desired levels of long-term measurement reliability.     

Implementation of a mechanics-based system for estimating the strength of timber

The most accurate way of determining the strength of lumber requires destructive testing. An intelligent mechanics-based lumber-grading system was developed to provide a better estimation of the strength of a board nondestructively. This system processed X-ray-extracted geometric features (of 1080 boards that eventually underwent destructive strength testing) by using finite element methods to generate associated stress fields. The stress fields were then fed to a feature-extracting-processor, which produced 26 strength predicting features. The best strength predicting features were determined from the coefficient of determination (correlation r/sup 2/) between the features and actual strengths of the boards. The coefficients of determination of each feature (or combination of features), with the actual strength of the board, were calculated and compared. A coefficient of determination of 0.4158 was achieved by using a longitudinal (along the local grain angle) maximum stress concentration (MSC) feature to predict the estimated strength of lumber.     

Preparation of Nickel, Iron, and Cobalt Nanopowders via Reduction of Salts with Sodium Dissolved in Liquid Ammonia

Nickel, iron, and cobalt powders are prepared via reduction of salts with sodium dissolved in liquid ammonia. The low temperature of the process and the ability of liquid ammonia to stabilize dangling chemical bonds notably reduce the growth rate of metal particles and prevent their aggregation. The magnetic properties of the nanopowders are investigated.     

Composition, Structure, and Thermal Expansion of Ca3Fe4S3O6 and CaFeSO

The iron calcium oxysulfides Ca₃Fe₄S₃O₆ and CaFeSO are synthesized by reacting mixtures of CaO and FeS in an inert atmosphere. Their elemental compositions and lattice parameters are determined by x-ray microanalysis and x-ray diffraction. From the temperature-dependent lattice parameters of the oxysulfides (measured up to 1020 K), their thermal expansion coefficients are evaluated.     

Fixed mesh front‐tracking methodology for finite element simulations

A direct front‐tracking method using an Eulerian–Lagrangian formulation is developed in two space dimensions. The front‐tracking method is general in that it can track any type of interface once its local velocity is specified or has been determined by calculation. The method uses marker points to describe the interface position and tracks the interface evolution on a fixed finite‐element mesh, including growth, contraction, splitting and merging. Interfacial conditions are applied directly at the interface position. The method is applied to three scenarios that involve different interface conditions and are based on energy and mass diffusion. The three calculations are for the dendritic solidification of a pure substance, the cellular growth of an alloy, and the Ostwald ripening of silica particles in silicon. Numerical results show that very complicated interface morphologies and topological changes can be simulated properly and efficiently. Copyright © 2004 John Wiley & Sons, Ltd.     

Thomas Fincke und die <Emphasis Type="Italic">Geometria rotundi</Emphasis>

Thomas Fincke (January 6^th, 1561–April 24^th, 1656), born in Flensburg (Germany), was one of the very most important and significant scientists in Denmark during the seventeenth century, a mathematician and astrologer and physician in the beginning of modern science, a representative of humanism and an influentual academic organizer. He studied in Strasbourg (since 1577) and Padua (since 1583) and received his M.D. in Basel (1587), he practised as a physician throughout his life (since 1587 or 1590) and became a professor at Copenhagen (1591). But he was best known because of his Geometriae rotundi libri XIIII (1583), a famous book on plane and spherical trigonometry, based not on Euclid but on Petrus Ramus. In this influentual work, in which Fincke introduced the terms tangent and secant and probable first noticed the Law of Tangents and the so-called Newton-Oppel-Mauduit-Simpson-Mollweide-Gauss-formula, he showed himself to be „abreast of the mathematics of his time“.      

The Simulation of Impact Loads on Beam-type Structures using a Pseudo-dynamic Procedure

Abstract:  This study proposes an alternate method for the analysis of beams with solid cross-section or built as a framed structure and subjected to transverse impact loads from an external striker. The procedure used in the analysis is a combination of two essential tools using pseudo-dynamic techniques. The method reported here involves only one degree of freedom for the structure modelling and assumes an elastic contact between an external striker and the beam structure, which in reality does not happen. As only one degree of freedom is considered in the analysis, some important limitations are inherent to the method proposed here. Essentially, there is the difficulty of modelling the displacement field associated with the transient structure behaviour accurately, as a consequence of fast-rate impact loads. Another difficulty faced by the method refers to a local structure behaviour associated with contact loads. The present method can deal with large displacements in transversely loaded beams associated to a collapse mechanism having a simple geometry and defined with precision from a single parameter. This ensures reasonable accuracy in the evaluation of the strain energy absorbing capacity of transversely impacted beam structures using a single degree of freedom model in a pseudo-dynamic procedure.