The asymptotical estimates for the cross-ratio distortion with respect to a smooth monotone function of one variable in terms of its Schwarz derivative are established.

We prove asymptotic formulae for the cross-ratio distortion with respect to a smooth monotone function of one variable in terms of its Schwartz derivative.

Three simple, economical, precise, and accurate methods are described for the simultaneous determination of Tenofovir disoproxil fumarate (TE) and Emtricitabine (EM) in combined tablet dosage form. The first method is ratio derivative spectra, second is first-order derivative spectrophotometry and third is absorption corrected method. The amplitudes at 271.07 and 302.17 nm in the ratio derivati...

We show how Adjoint Algorithmic Differentiation can be combined with the so-called Pathwise Derivative and Likelihood Ratio Method to construct efficient Monte Carlo estimators of second order price sensitivities of derivative portfolios. We demonstrate with a numerical example how the proposed technique can be straightforwardly implemented to greatly reduce the computation time of second order...

Derivative free optimization (DFO) methods are typically designed to solve optimization problems whose objective function is computed by a “black box”; hence, the gradient computation is unavailable. Each call to the “black box” is often expensive, so estimating derivatives by finite differences may be prohibitively costly. Finally, the objective function value may be computed with some noise, ...

The precise analysis of mineral abundance is a key content of hyperspectral technology research. In the present paper, a new spectral unmixing method based on derivative of ratio spectroscopy (DRS) was employed for visible to short-wave infrared (VIS–SWIR; 0.4–2.5 μm) reflectance data. The mixtures of plaster and allochite with different proportions were analyzed by DRS, Fully Constrained Least...