in this work we synthesized of mesoporous silica nanoparticles and functionalized with 3-aminopropyltriethoxysilane to improve the loading and release of ibuprofen bonded to 3-aminopropyltriethoxysilane. sample were characterized by fourier transform infrared spectroscopy, scanning electron microscopy , x-ray diffraction, and ultraviolet-visible. the fourier transform infrared spectroscopy resu...

Abstract. The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions. The Fourier transform is calculated as an improper integral and the limit coincides with the Fourier transform in the distributional sense. The inver...

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of...

Disclaimer: These notes are intended to be an accessible introduction to the subject, with no pretense at completeness. In general, you can find more thorough discussions in Oppenheim's book. Please let me know if you find any typos. In this lecture, we discuss the Discrete Fourier Transform (DFT), which is a fourier representation for finite length signals. The main practical importance of thi...

We give a quantum algorithm for solving a shifted multiplicative character problem over Z/nZ and finite fields. We show that the algorithm can be interpreted as a matrix factorization or as solving a deconvolution problem and give sufficient conditions for a shift problem to be solved efficiently by our algorithm. We also show that combining the shift problem with the hidden subgroup problem re...

We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N time-domain measurements using a compressive-sensing reconstruction algorithm. We demonstrate the technique by resolving sparse vibrational spectra using <25% of ...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and i...

Abstract. In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of t...

A FT spectrometer is an interferometer. Its historical and most widely known configuration is the Michelson interferometer, shown on Fig. 1. A beam-splitter is used for dividing the light to be spectrally analyzed into two beams. After they have been reflected on two distinct mirrors, the two beams are recombined by the same beam-splitter and sent to a detector. One of the mirrors is fixed, whi...

Fourier transform is a reserved teaching topic for science and engineering students in almost all universities. Among the large audience, some of them feel it is too difficult. This article is written for them in a casual and friendly way, with the humble aim of giving them more confidence in reading formal textbooks. A few features and efforts have been introduced in this article, such as link...