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.     

Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

On the summability of the formal solutions for some PDEs with irregular singularity

In this Note, we consider some classes of nonlinear partial differential equations with regular singularity with respect to t=0 and irregular one with respect to x=0. Our purpose is to establish a result which is similar to the k-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or k-summable with respect to x in all other directions. To cite this article: Z. Luo et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Study of a vibrating plate: comparison between experimental (ESPI) and analytical results

Real-time electronic speckle pattern interferometry (ESPI) was used for tuning and visualization of natural frequencies of a trapezoidal plate. The plate was excited to resonant vibration by a sinusoidal acoustical source, which provided a continuous range of audio frequencies. Fringe patterns produced during the time-average recording of the vibrating plate—corresponding to several resonant frequencies—were registered. From these interferograms, calculations of vibrational amplitudes by means of zero-order Bessel functions were performed in some particular cases. The system was also studied analytically. The analytical approach developed is based on the Rayleigh–Ritz method and on the use of non-orthogonal right triangular co-ordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated by using the Gram–Schmidt procedure. A high degree of correlation between computational analysis and experimental results was observed.     

Damping of coupled phonon-plasmon modes

The effect of free carriers on the dispersion and damping of coupled phonon-plasmon modes is considered in the long-wave approximation. The electron and phonon scattering rate, as well as Landau damping, is taken into account.     

Elastoplastic torsion theory for whisker crystals

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1991.     

A generalization of the H-theorem to steady non-equilibrium states. Part 1: A basic decomposition and the linear case

A generalized relative entropy functional is associated to the evolution of gas in a container with (generally) non-uniform boundary data. A decomposition for its rate in ‘bulk’ and in ‘boundary’ terms is given; for the linear case both have a definite sign. The relation with the strong L₁ stability is pointed out.     

Two-dimensional autocorrelation function analysis of smoked foil patterns

Digital image processing techniques have been applied to the analysis of cellular smoked foil patterns from gaseous detonations. In particular, the two-dimensional autocorrelation function is applied to digital cell pattern images and an orientational correlation parameter is calculated. Taking line profiles along the directions of highest correlation provides an unbiased method of determining the mean cell size in each of the two principal directions. By analyzing the width, amplitude and angular position of the orientational correlation plots, information can be extracted concerning the cellular pattern regularity, the relative angular correlation between two sets of transverse waves in two directions, and the mean shape or elongation of the cells within the pattern. The technique is applied to smoked foils from oxyacetylene mixtures with argon dilutions ranging from 0 to 75% to quantify the increase in regularity with argon dilution. This method provides a simple and useful way of analyzing cellular patterns and constitutes a promising technique for improving smoked foil diagnostics.