Exact $n$th derivatives

Approximating real functions which possess nth derivatives of bounded variation and applications

The main aim of this paper is to provide an approximation for the function f which possesses continuous derivatives up to the order n−1 (n ≥ 1) and has the n−th derivative of bounded variation, in terms of the chord that connects its end points A = (a, f (a)) and B = (b, f (b)) and some more terms which depend on the values of the k derivatives of the function taken at the end points a and b, w...

A random nth-price auction

Second-price auctions are designed to induce people to reveal their private preferences for a good. Laboratory evidence suggests that while these auctions do a reasonable job on aggregate, they fall short at the individual level, especially for bidders who are off-margin of the market-clearing price. Herein we introduce and explore whether a random nth-price auction can engage all bidders to bi...

Flowsheet optimization and optimal sensitivity analysis using exact derivatives

Ultrastability of nth minimal errors

We use the ultraproduct technique to study local properties of basic quantities of information-based complexity theory – the n-th minimal errors. We consider linear and nonlinear operators in normed spaces, information consists of continuous linear functionals and is assumed to be adaptive. We establish ultrastability and disprove regularity of n-th minimal errors. As a consequence, we answer a...

HSI based colour image equalization using iterative nth root and nth power

In this paper an equalization technique for colour images is introduced. The method is based on n th root and n th power equalization approach but with optimization of the mean of the image in different colour channels such as RGB and HSI. The performance of the proposed method has been measured by the means of peak signal to noise ratio. The proposed algorithm has been compared with convention...