On Pauli pairs

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. In this paper we provide a new set of examples of Pauli pairs, being the pairs of quantum states indistinguishable by measuring the spatial location and momentum. In particular, we construct a new set of spatially localized Pauli pairs.

Methane cross-validation between three Fourier Transform Spectrometers: SCISAT ACE-FTS, GOSAT TANSO-FTS, and ground-based FTS measurements in the Canadian high Arctic

We present cross-validation of remote sensing measurements of methane profiles in the Canadian high Arctic. Accurate and precise measurements of methane are essential to understand quantitatively its role in the climate system and in global change. Here, we show a cross-validation between three datasets: two from spaceborne instruments and one from a ground-based instrument. All are Fourier Transform Spectrometers (FTSs). We consider the Canadian SCISAT Atmospheric Chemistry Experiment (ACE)-FTS, a solar occultation infrared spectrometer operating since 2004, and the thermal infrared band of the Japanese Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared Sensor for carbon Observation (TANSO)-FTS, a nadir/off-nadir scanning FTS instrument operating at solar and terrestrial infrared wavelengths, since 2009. The ground-based instrument is a Bruker 125HR Fourier Transform Infrared (FTIR) spectrometer, measuring mid-infrared solar absorption spectra at the Polar Environment Atmospheric Research Laboratory (PEARL) Ridge Lab at Eureka, Nunavut (80° N, 86° W) since 2006. For each pair of instruments, measurements are collocated within 500 km and 24 h. An additional criterion based on potential vorticity values was found not to significantly affect differences between measurements. Profiles are regridded to a common vertical grid for each comparison set. To account for differing vertical resolutions, ACE-FTS measurements are smoothed to the resolution of either PEARL-FTS or TANSO-FTS, and PEARL-FTS measurements are smoothed to the TANSO-FTS resolution. Differences for each pair are examined in terms of profile and partial columns. During the period considered, the number of collocations for each pair is large enough to obtain a good sample size (from several hundred to tens of thousands depending on pair and configuration). Considering full profiles, the degrees of freedom for signal (DOFS) are between 0.2 and 0.7 for TANSO-FTS and between 1.5 and 3 for PEARL-FTS, while ACE-FTS has considerably more information (roughly 1° of freedom per altitude level). We take partial columns between roughly 5 and 30 km for the ACE-FTS–PEARL-FTS comparison, and between 5 and 10 km for the other pairs. The DOFS for the partial columns are between 1.2 and 2 for PEARL-FTS collocated with ACE-FTS, between 0.1 and 0.5 for PEARL-FTS collocated with TANSO-FTS or for TANSO-FTS collocated with either other instrument, while ACE-FTS has much higher information content. For all pairs, the partial column differences are within ± 3 × 1022 molecules cm−2. Expressed as median ± median absolute deviation (expressed in absolute or relative terms), these differences are 0.11 ± 9.60 × 10^20 molecules cm−2 (0.012 ± 1.018 %) for TANSO-FTS–PEARL-FTS, −2.6 ± 2.6 × 10^21 molecules cm−2 (−1.6 ± 1.6 %) for ACE-FTS–PEARL-FTS, and 7.4 ± 6.0 × 10^20 molecules cm−2 (0.78 ± 0.64 %) for TANSO-FTS–ACE-FTS. The differences for ACE-FTS–PEARL-FTS and TANSO-FTS–PEARL-FTS partial columns decrease significantly as a function of PEARL partial columns, whereas the range of partial column values for TANSO-FTS–ACE-FTS collocations is too small to draw any conclusion on its dependence on ACE-FTS partial columns.

Assessment of maturity degree of composts from domestic solid wastes by fluorescence and fourier transform infrared spectroscopies

Methods of assessment of compost maturity are needed so the application of composted materials to lands will provide optimal benefits. The aim of the present paper is to assess the maturity reached by composts from domestic solid wastes (DSW) prepared under periodic and permanent aeration systems and sampled at different composting time, by means of excitation-emission matrix (EEM) fluorescence spectroscopy and Fourier transform infrared spectroscopy (FT-IR). EEM spectra indicated the presence of two different fluorophores centered, respectively, at Ex/Em wavelength pairs of 330/425 and 280/330 nm. The fluorescence intensities of these peaks were also analyzed, showing trends related to the maturity of composts. The contour density of EEM maps appeared to be strongly reduced with composting days. After 30 and 45 days of composting, FT-IR spectra exhibited a decrease of intensity of peaks assigned to polysaccharides and in the aliphatic region. EEM and FT-IR techniques seem to produce spectra that correlate with the degree of maturity of the compost. Further refinement of these techniques should provide a relatively rapid method of assessing the suitability of the compost to land application.

Analysis Of The Dna Fourier Transform-infrared Microspectroscopic Signature Using An All-reflecting Objective.

The Fourier transform-infrared (FT-IR) signature of dry samples of DNA and DNA-polypeptide complexes, as studied by IR microspectroscopy using a diamond attenuated total reflection (ATR) objective, has revealed important discriminatory characteristics relative to the PO2(-) vibrational stretchings. However, DNA IR marks that provide information on the sample's richness in hydrogen bonds have not been resolved in the spectral profiles obtained with this objective. Here we investigated the performance of an all reflecting objective (ARO) for analysis of the FT-IR signal of hydrogen bonds in DNA samples differing in base richness types (salmon testis vs calf thymus). The results obtained using the ARO indicate prominent band peaks at the spectral region representative of the vibration of nitrogenous base hydrogen bonds and of NH and NH2 groups. The band areas at this spectral region differ in agreement with the DNA base richness type when using the ARO. A peak assigned to adenine was more evident in the AT-rich salmon DNA using either the ARO or the ATR objective. It is concluded that, for the discrimination of DNA IR hydrogen bond vibrations associated with varying base type proportions, the use of an ARO is recommended.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

Estimation of hexenuronic acids and kappa number in kraft pulps of Eucalyptus globulus by Fourier transform near infrared spectroscopy and multivariate analysis

Fourier transform near infrared (FT-NIR) spectroscopy was evaluated as an analytical too[ for monitoring residual Lignin, kappa number and hexenuronic acids (HexA) content in kraft pulps of Eucalyptus globulus. Sets of pulp samples were prepared under different cooking conditions to obtain a wide range of compound concentrations that were characterised by conventional wet chemistry analytical methods. The sample group was also analysed using FT-NIR spectroscopy in order to establish prediction models for the pulp characteristics. Several models were applied to correlate chemical composition in samples with the NIR spectral data by means of PCR or PLS algorithms. Calibration curves were built by using all the spectral data or selected regions. Best calibration models for the quantification of lignin, kappa and HexA were proposed presenting R-2 values of 0.99. Calibration models were used to predict pulp titers of 20 external samples in a validation set. The lignin concentration and kappa number in the range of 1.4-18% and 8-62, respectively, were predicted fairly accurately (standard error of prediction, SEP 1.1% for lignin and 2.9 for kappa). The HexA concentration (range of 5-71 mmol kg(-1) pulp) was more difficult to predict and the SEP was 7.0 mmol kg(-1) pulp in a model of HexA quantified by an ultraviolet (UV) technique and 6.1 mmol kg(-1) pulp in a model of HexA quantified by anion-exchange chromatography (AEC). Even in wet chemical procedures used for HexA determination, there is no good agreement between methods as demonstrated by the UV and AEC methods described in the present work. NIR spectroscopy did provide a rapid estimate of HexA content in kraft pulps prepared in routine cooking experiments.

Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Analysis of financial indices by means of the windowed Fourier transform

The goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

The comb signal and its Fourier transform

SignalProcessing, Vol. 81, nº 3

Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Transmission Fourier transform infrared microspectroscopy allows simultaneous assessment of cutin and cell-wall polysaccharides of Arabidopsis petals.

A procedure for the simultaneous analysis of cell-wall polysaccharides, amides and aliphatic polyesters by transmission Fourier transform infrared microspectroscopy (FTIR) has been established for Arabidopsis petals. The combination of FTIR imaging with spectra derivatization revealed that petals, in contrast to other organs, have a characteristic chemical zoning with high amount of aliphatic compounds and esters in the lamina and of polysaccharides in the stalk of the petal. The hinge region of petals was particular rich in amides as well as in vibrations potentially associated with hemicellulose. In addition, a number of other distribution patterns have been identified. Analyses of mutants in cutin deposition confirmed that vibrations of aliphatic compounds and esters present in the lamina were largely associated with the cuticular polyester. Calculation of spectrotypes, including the standard deviation of intensities, allowed detailed comparison of the spectral features of various mutants. The spectrotypes not only revealed differences in the amount of polyesters in cutin mutants, but also changes in other compound classes. For example, in addition to the expected strong deficiencies in polyester content, the long-chain acyl CoA synthase 2 mutant showed increased intensities of vibrations in a wavelength range that is typical for polysaccharides. Identical spectral features were observed in quasimodo2, a cell-wall mutant of Arabidopsis with a defect in pectin formation that exhibits increased cellulose synthase activity. FTIR thus proved to be a convenient method for the identification and characterization of mutants affected in the deposition of cutin in petals.