Certain solutions to Harper’s equation are discrete analogues of (and approximations to) the Hermite–Gaussian functions. They are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator, and they lead to a definition of a discrete fractional Fourier transform (FT). The discrete fractional FT is essentially the time-evolution operator of the discrete harmonic oscill...

Integrable equations with second order Lax pair like KdV and CamassaHolm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy are discussed in this contribution. The squared eigenfunctions of the spectral problem, associated to the Camassa-Holm equation represent a complete basis of ...

Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack-Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector-matrix-multiply rec...

BACKGROUND In metabolomics researches using mass spectrometry (MS), systematic searching of high-resolution mass data against compound databases is often the first step of metabolite annotation to determine elemental compositions possessing similar theoretical mass numbers. However, incorrect hits derived from errors in mass analyses will be included in the results of elemental composition sear...

Copper (II) carboxylate, (Cu-BDC), metal-organic-framework (MOF) has been synthesized undersolvothermalconditions and used as a new adsorbent for the methane. The Lithium doping intoCu-BDC, (Li-Cu-BDC), is made by impregnating Cu-BDC with an ethanol solution ofLiNO3, followed by heat treatment in vacuum. The adsorbent was characterized by X-ray diffraction (XRD), Fourier transform infrared ...

In this study at first, in laboratory, three types of vanadium oxide were produced by using porous graphene and amine framework in hydrothermal method nanostructures such as: vanadium oxide - octadecyl amine - graphene, vanadium oxide - dodecyl amine - graphene and vanadium oxide – aniline - graphene (V-ODA-G، V-DDA-G، V-A-G). Then their structures and functions in propane dehydrogenation react...

The structural elucidation of oligosaccharides remains a major challenge. Mass spectrometry provides a rapid and convenient method for structural elucidation based on tandem mass spectrometry. Ions commonly are selected and subjected to collision-induced dissociation (CID) to obtain structural information. Unfortunately, N-linked oligosaccharides are relatively large compounds and are not readi...

Pyrolysis characteristics and mechanism of tobacco stem were studied by pyrolysis coupled with gas chromatography/mass spectrometry (PyGC/MS), thermogravimetric analyzer coupled with Fourier transform infrared spectrometry, and mass spectrometry (TG-FTIR and TG-MS) techniques. The composition of evolved volatiles from fast pyrolysis of tobacco stem was determined by Py-GC/MS analysis, and the e...

Energy-dispersive X-ray fluorescence (EDXRF) spectrometry was previously proposed to measure the thickness of the cellulose nitrate layer of he commonly used LR 115 solid-state nuclear track detector (SSNTD). The present work is devoted to the investigation whether the X-ray radiation nvolved in EDXRF spectrometry will induce degradation of the cellulose nitrate. For this purpose, Fourier trans...

In this article, recent measurements made with LIFTIRS, the Livermore Imaging Fourier Transform InfraRed Spectrometer, are presented. The experience gained with this instrument has produced a variety of insights into the tradeoffs between signal to noise ratio (SNR), spectral resolution and temporal resolution for time multiplexed Fourier transform imaging spectrometers. This experience has als...