Decomposition methods for large linear discrete ill-posed problems

The solution of large linear discrete ill-posed problems by iterative methods continues to receive considerable attention. This paper presents decomposition methods that split the solution space into a Krylov subspace that is determined by the iterative method and an auxiliary subspace that can be chosen to help represent pertinent features of the solution. Decomposition is well suited for use with the GMRES, RRGMRES, and LSQR iterative schemes.     

The Augmentation Quotients of the Groups of Order 25, II

We have described the structure of Q _n (G) = Δ ⁿ (G)/Δ ⁿ⁺¹(G) for 35 particular classes of groups G with order 2⁵ in the previous article. In this article, the structure of Q _n (G) for all the remaining classes of groups G with order 2⁵ are presented.     

Reject inference,augmentation, and sample selection

Many researchers see the need for reject inference in credit scoring models to come from a sample selection problem whereby a missing variable results in omitted variable bias. Alternatively, practitioners often see the problem as one of missing data where the relationship in the new model is biased because the behaviour of the omitted cases differs from that of those who make up the sample for a new model. To attempt to correct for this, differential weights are applied to the new cases. The aim of this paper is to see if the use of both a Heckman style sample selection model and the use of sampling weights, together, will improve predictive performance compared with either technique used alone. This paper will use a sample of applicants in which virtually every applicant was accepted. This allows us to compare the actual performance of each model with the performance of models which are based only on accepted cases.     

Hypersonic jet control effectiveness

The present study aims to identify some of the parameters which determine the upstream extent and the lateral spreading of the separation front around an under-expanded transverse jet on a slender blunted cone. The tests were conducted in the Cranfield hypersonic facility at , to and at , . Air was used as the working gas for both the freestream and the jet. Schlieren pictures were used for the visualisation of the three-dimensional structures around the jet. Pressure, normal force and pitching moment measurements were conducted to quantitatively study the interaction region and its effects on the vehicle. An analytical algorithm has been developed to predict the shape of the separation front around the body. Received 18 August 1995 / Accepted 27 June 1996     

On Certain Quotients of Lower Central Factors of a Normal Subgroup of a Free Group

We compute subgroups of the normal subgroup R of a free group F determined by certain ideals contained in the augmentation ideal Δ(R) and then prove certain subquotients of R to be free Abelian.     

Heat transfer augmentation between impinging circular air jet and flat plate using finned surfaces and vortex generators

An experimental investigation is performed to study the effect of the finned surfaces and surfaces with vortex generators on the local heat transfer coefficient between impinging circular air jet and flat plate. Reynolds number is varied between 7000 and 30,000 based on the nozzle exit condition and jet to plate spacing between 0.5 and 6 nozzle diameters. Thermal infrared imaging technique is used for the measurement of local temperature distribution on the flat plate. Fins used are in the form of cubes of 2 mm size spaced at a pitch of 5 mm on the target plate and hexagonal prism of side 2.04 mm and height of 2 mm spaced at a pitch of 7.5 mm. Vortex generators in the form of a equilateral triangle of side 4 mm are used. Effect of number of rows of vortex generators, radius of a row, number of vortex generators in a row and inclination angle (i.e., the angle between the plane of the target plate and the plane of the vortex generators) on Nusselt number is studied. It is observed that the heat transfer coefficient between the impinging jet and the target plate is sensitive to the shape of the fin. The increase in the heat transfer coefficient up to 77% depending on the shape of the fin, nozzle plate spacing and the Reynolds number is observed. The augmentation in the heat transfer for the surfaces vortex generators are higher than that of the finned surfaces. The heat transfer augmentation in case of vortex generator is as high as 110% for a single row of six vortex generators at a radius of 1 nozzle diameter as compared to the smooth surface at a given nozzle plate spacing of 1 nozzle diameter and a Reynolds number of 25,000 at extreme radial location.     

Data for the gas-liquid chromatographic analysis of essential oils. Determination of the composition of the essential oil of Marjoram

Summary By identification of the essential oil component ‘cis-sabinene hydrate acetate’ of marjoram we demonstrate that the mass spectrum—furnish to the chemical composition and molecular configuration of compounds—can lead to incorrect qualitative identification if retention data are not taken into consideration. We studied also the temperature-dependence of the retention data of different compounds, and our measurements showed that because of the different temperature-dependence, a change in the temperature of the analysis results in a change in order of elution. The use of this phenomenon, originating from the change of the retention data, both increases the safety of qualitative identification and aids determination of the optimum measurement conditions in both isothermal and temperature-programmed modes of operation. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001     

Robust calibrations on reduced sample sets for API content prediction in tablets: Definition of a cost-effective NIR model development strategy

Owing to spectral variations from other sources than the component of interest, large investments in the NIR model development may be required to obtain satisfactory and robust prediction performance. To make the NIR model development for routine active pharmaceutical ingredient (API) prediction in tablets more cost-effective, alternative modelling strategies were proposed. They used a massive amount of prior spectral information on intra- and inter-batch variation and the pure component spectra to define a clutter, i.e., the detrimental spectral information. This was subsequently used for artificial data augmentation and/or orthogonal projections. The model performance improved statistically significantly, with a 34–40% reduction in RMSEP while needing fewer model latent variables, by applying the following procedure before PLS regression: (1) augmentation of the calibration spectra with the spectral shapes from the clutter, and (2) net analyte pre-processing (NAP). The improved prediction performance was not compromised when reducing the variability in the calibration set, making exhaustive calibration unnecessary. Strong water content variations in the tablets caused frequency shifts of the API absorption signals that could not be included in the clutter. Updating the model for this kind of variation demonstrated that the completeness of the clutter is critical for the performance of these models and that the model will only be more robust for spectral variation that is not co-linear with the one from the property of interest.     

The index of merit of kth-copy integration lattices

r2d2lri   is an automatic two-dimensional cubature algorithm that demonstrates the practical value of using an augmentation sequence consisting of (2^k)²$(2^k{)}^2$-copy lattices as a basis for numerical integration. This paper investigates use of similar embedded augmentation sequences in higher dimensions by developing theoretical results relating to the index of merit of s  -dimensional (2^k)^s$(2^k{)}^s$-copy lattices generated from rank-1 simple lattices. The theoretical results can be used to guide the search for good augmentation sequences in s dimensions in the sense of high index of merit.