Many scientific and engineering investigations require the extraction of the first derivative from experimental data. Direct numerical differentiation is usually impractical because this amplifies the noise in the data, leading to unreliable results. This investigation shows that the problem of differentiating experimental data can be converted into one of solving an integral equation of the first kind. Tikhonov regularization is used to solve this integral equation, leading to a smooth first derivative. By using the built‐in regularization parameter in the method noise amplification is kept under control. The performance of this method is demonstrated by applying it to data taken from the literature. © 2005 American Institute of Chemical Engineers AIChE J, 2006

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This article describes a procedure for obtaining the partial derivatives of experimental data that depend on two independent variables. The starting equation is an ill‐posed integral equation of the first kind. Tikhonov regularization is used to keep noise amplification under control. Implementation of the computation steps is described and the performance of the procedure is demonstrated by four practical examples. © 2010 American Institute of Chemical Engineers AIChE J, 2010

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The frequent occurrence of hard X-ray emission from the top of Ñaring loops was one of the discoveries by the Hard X-Ray Telescope on board the Japanese Y ohkoh satellite. In this paper we take a Ñare current-sheet geometry and show how the combined e †ect of magnetic Ðeld convergence and pitchangle scattering of nonthermal electrons injected at the top of the loop results in the generation of a looptop source with properties akin to those observed by Y ohkoh. We demonstrate that a looptop source can be produced in both impulsive and gradual phase loops. We further present a possible mechanism for the generation of high-temperature "" ridges ÏÏ in the loop legs.

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