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...

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...

The theory and instrumentation for Fourier transform infrared spectrometry are discussed. These instruments measure infrared spectra of the same quality as spectra measured on grating spectrometers in about one thousandth of the time. Their sensitivity advantage for spectra measured in equal times is between a factor of 10 and 100. Commercial spectrometers are now available from nine vendors in...

platinum is a metallic element, which may react with our cellular component through its involvement in cancer chemotherapy medications. cisplatin is one of the most useful antineoplastic drugs against human ovarian carcinoma, which has the central element of platinum in its structure. the nature of chemical interaction between platinum and cellular macromolecules is yet to be understood. we exa...

drug resistance enables cancer cells to break away from cytotoxic effect of anticancer drugs. identification of resistant phenotype is very important because it can lead to effective treatment plan. there is an interest in developing classifying models of resistance phenotype based on the multivariate data. we have investigated a vibrational spectroscopic approach in order to characterize a sen...