We give a detailed study of the discrete Fourier transform (DFT) of r-even arithmetic functions, which form a subspace of the space of r-periodic arithmetic functions. We consider the DFT of sequences of r-even functions, their mean values and Dirichlet series. Our results generalize properties of the Ramanujan sum. We show that some known properties of r-even functions and of the Ramanujan sum...

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and f...

In open-path Fourier Transform Infrared spectroscopy, the generation of a suitable background single-beam spectrum is of major concern. The Shifting Method is a derivative-like approach to correct for the background without the need to actually measure a background spectrum using the sample single-beam spectrum. A thorough study of the Shifting Method was conducted. A set of guidelines was deve...

polyethylene is a synthetic polymer which is used in our daily life for different purposes. increased use of polyethylene causes severe environmental problems. there are different methods to decrease problem caused by polyethylene for example source reduction, incineration and land filling and all of them have their own drawbacks. so, the best way to reduce the problem caused by polyethylene is...

the knoevenagel condensation of aromatic aldehydes with barbituric acid, dimedone and malononitrile occurred in the presence of bf3/nano-γ-al2o3 at room temperature in ethanol. this catalyst is characterized by powder x-ray diffraction (xrd), fourier transform infrared spectroscopy (ft-ir), thermal gravimetric analysis (tga), field emission scanning electron microscopy (fesem) and energy-disper...

introduction: the aim of this in vitro study was to evaluate the setting time, flow, film thickness, solubility, radiopacity and characterization analysis of three epoxy resin based sealers including two experimental sealers and ah-26. methods and materials: five samples of each material were evaluated for setting time, flow, film thickness, solubility and radiopacity according to iso 6876 stan...

By recourse to tempered ultradistributions, we show here that the effect of a q-Fourier transform (qFT) is to map equivalence classes of functions into other classes in a one-to-one fashion. This suggests that Tsallis’ q-statistics may revolve around equivalence classes of distributions and not individual ones, as orthodox statistics does. We solve here the qFT’s non-invertibility issue, but di...

For the first time, a tunable reflected phase reflectarray is demonstrated in the thermal infrared. This is done using thermochromic VO(2) square-patch elements in a reflectarray metamaterial configuration. A sixty degree change in reflected phase is measured using a Twyman-Green interferometer, and FTIR measurements show that the resonance reflection minima shifts from 9.2 to 11.2 mum as the s...