| Some applications of the Discrete Fourier Transform (DFT) in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in general commutative rings. I. The (Usual) Discrete Fourier Transform Let be a primitive N th root of uni...

To investigate the effect of fluorination on the surface of polydimethylsiloxane (PDMS) film, direct fluorination was performed under a mild condition (approx. 2000 micromol/mol F(2) in nitrogen) for 120 min. No structural damage of PDMS films was observed on the scanning electron microscopic images under the condition. Fourier-transform infrared/attenuated total reflectance (FTIR/ATR) and ener...

Formulæ are derived for expressing Cauchy and Hilbert transforms of a function f in terms of Cauchy and Hilbert transforms of f(xr). When r is an integer, this corresponds to evaluating the Cauchy transform of f(xr) at all choices of z1/r. Related formuæ for rational r result in a reduction to a generalized Cauchy transform living on a Riemann surface, which in turn is reducible to the standard...

the necessary conditions to transform hydroxyamide (1) and 2-oxazolines (2, 3) into 3- or 4-methyl benzo[f] isoquinolines (4, 5) has been established. the mechanism of these reactions has been proposed claiming the existence of the protonated 2-oxazoline (6) and the styrylamides (7) as intermediates.

The purpose of this paper is to present an algorithm for evaluating Han-kel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates the proposed algorithm. T...

We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a function. We also show two applications of the theorem. The first is the two weight problem for the Fourier transform, and the second is estimating the number of ...

We present a quantum algorithm for the dihedral hidden subgroup problem with time and query complexity 2O( √ log N). In this problem an oracle computes a function f on the dihedral group DN which is invariant under a hidden reflection in DN . By contrast the classical query complexity of DHSP is O( √ N). The algorithm also applies to the hidden shift problem for an arbitrary finitely generated ...

We have designed and constructed a Fourier Transform Spectrometer (FTS) for the study of submillimeter-wave mixers and optical components. The FTS has a large aperture (up to 25.4 cm) and small focal ratio (as fast as f/2.5) to achieve a large throughput. It operates in the 100-3750 GHz (3.3125 cm 1) frequency range with a resolution of up to 75 MHz (0.0025 cm ). Here we discuss the design goal...