Stopping rule for variable selection using stepwise discriminant analysis

Summary In general, when characterizing samples, such as ceramic samples or other types of samples, for first time by means of chemical elements, the analyst measures a large number of variables, many of which may not be very informative. In fact, some may even be unrelated to the issue at hand and blur the picture instead of making it clearer. In subsequent studies the analyst may wish to measure fewer variables for several reasons, such as being very time consuming; in cases where measurement time is important, such as on-line monitoring; in order to reduce cost or effort; etc. Therefore, the hope is to determine those variables that are most relevant without losing essential information and to remove the less productive information. The problem is how to perform this in an objective way and to capture crucial information using a multivariate analysis. This paper aims to describe and illustrate a stopping rule for the identification of redundant variables, and the selection of variable subsets, preserving multivariate data structure using stepwise discriminant analysis, selecting those variables that are in some senses adequate for discrimination purposes. One illustrative example using data sets obtained via INAA of ceramic samples from two archaeological sites is provided.     

Statistical Analysis of the Effect of Mineral Admixtures on the Strength of the Interfacial Transition Zone

Microscopic evidence indicates that the thickness of the interfacial transition zone (ITZ) between the aggregate and the cement paste is modified when mineral admixtures partially replace portland cement. Unfortunately, there is limited information on the significance of these microscopic modifications to the mechanical properties of the ITZ. This research reports experimental results on the shear and tensile strength of the ITZ as affected by the addition of the following mineral admixtures: silica fume, fly ash, and natural pozzolan. Statistical analysis was used to identify the significant parameters affecting the tensile and shear strength of the ITZ. Experimental results indicate that not only does the incorporation of silica fume and fly ash increase the strength of the ITZ, these mineral admixtures have a greater influence on the strength increase of the ITZ than in the strength increase of the cement paste.     

A study of the mechanism and kinetics of interaction between nepheline powder and ammonium hydrofluoride

Behavior of a skeleton silicate, nepheline, in the reaction of fluorination with ammonium hydrofluoride was studied by means of differential-thermal, X-ray phase, and chemical analyses, IR spectroscopy, and scanning electron microscopy.     

Homogeneous renewal equation

Let F be a non-arithmetic distribution on the line , and W be the class of bounded functions w without discontinuity of the second kind such that

.In this paper, we show that the solution of the homogeneous renewal equation w = w F in the class W is a constant-function.     

Convergence of multistep discretizations of DAEs

Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that avoid discretization of the constraint. A freer use of e.g. explicit methods for the non-stiff differential part of the DAE is then possible.Dedicated to Germund Dahlquist on the occasion of his 70th birthdayThis author thanks the Centro de Estadística y Software Matemático de la Universidad Simón Bolivar (CESMa) for permitting her free use of its research facilities.Partial support by the Swedish Research Council for Engineering Sciences TFR under contract no. 222/91-405.     

Cold compaction of ceramic powder: Computational analysis of the effect of pressing method and die shape

This paper deals with a computational analysis of the influence of the pressing method and part geometry on the final density distribution in the cold compaction process of ceramic alumina powders. The analysis is based on the explicit finite-element model proposed and validated in a previous study. The mechanical behavior of the processing material is described using a multisurface elastoplastic model, the modified Drucker-Prager/Cap model Published in Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 129–134, October 2007.