‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkin...

In this article we extend and implement the forward search algorithm for identifying atypical subjects/observations in factor analysis models. The forward search has been mainly developed for detecting aberrant observations in regression models ( Atkinson, 1994 ) and in multivariate methods such as cluster and discriminant analysis ( Atkinson, Riani, & Cerioli, 2004 ). Three data sets and a sim...

Recently, several papers have re-examined the so called production efficiency theorem and the Atkinson and Stiglitz theorem on commodity taxes in the optimal taxation literature. Naito (1998) showed that indirect redistribution through production distortion or consumption distortion can Pareto-improve welfare and that the two theorems do not necessarily hold when different factors are imperfect...

Haddon (1996) proposes a theoretical model for earthquake source spectra in eastern North America (ENA), based on certain assumptions regarding the rupture process. He shows that if ENA earthquakes are characterized by very high rupture velocities and fractional stress drop, then their high-frequency S-wave radiation is strongly enhanced relative to that predicted by the simple Brune (1970) sou...

Recently, several papers have re-examined the so called production efficiency theorem and the Atkinson and Stiglitz theorem on commodity taxes in the optimal taxation literature. Naito (1998) showed that indirect redistribution through production distortion or consumption distortion can Pareto-improve welfare and that the two theorems do not necessarily hold when different factors are imperfect...

Health inequality aversion parameters can be used to represent alternative value judgements about policy concern for reducing health inequality versus improving total health. In this study, we use data from an online survey of the general public in England (n = 244) to elicit health inequality aversion parameters for both Atkinson and Kolm social welfare functions. We find median inequality ave...

We analyse the problem of finding an allocation of resources in a multiagent system that is as fair as possible in terms of minimising inequality between the utility levels enjoyed by the individual agents. We use the well-known Atkinson index to measure inequality and we focus on the distributed approach to multiagent resource allocation, where new allocations emerge as the result of a sequenc...

Atkinson attempts to link “phoneme diversity” with the spread of language from Africa, explicitly attempting to draw parallels with human genetic diversity, frequently shown to be highest in Africa and lowest outside that continent. There are four major flaws in Atkinson’s reasoning, which we discuss separately in the sections following: (i) conflating independent dimensions of phonological ela...

This paper revisits the Atkinson–Stiglitz result on uselessness of commodity taxation in the presence of optimal non-linear income taxation in a more general setup, namely when tastes are heterogeneous. This general analysis displays the key economic assumptions under which the Atkinson–Stiglitz result is robust. A small tax on a given commodity is desirable if high income earners have a relati...