Krätzel Function as a Function of Hypergeometric Type

2000 Mathematics Subject Classification: 33C60, 33C20, 44A15

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

Fractional Calculus of P-transforms

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99

On the approximation by convolution operators in homogeneous Banach spaces on R^d

AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20

Analysis of Ultrasonic Techniques for the Characterization of Microfiltration Polymeric Membranes

The use of polymeric membranes is extremely important in several industries such as nuclear, biotechnology, chemical and pharmaceutical. In the nuclear area, for instance, systems based on membrane separation technologies are currently being used in the treatment of radioactive liquid effluent, and new technologies using membranes are being developed at a great rate. The knowledge of the physical characteristics of these membranes, such as, pore size and the pore size distribution, is very important to the membranes separation processes. Only after these characteristics are known is it possible to determine the type and to choose a particular membrane for a specific application. In this work, two ultrasonic non destructive techniques were used to determine the porosity of membranes: pulse echo and transmission. A 25 MHz immersion transducer was used. Ultrasonic signals were acquired, for both techniques, after the ultrasonic waves passed through a microfiltration polymeric membrane of pore size of 0.45 μm and thickness of 180 μm. After the emitted ultrasonic signal crossed the membrane, the received signal brought several information on the influence of the membrane porosity in the standard signal of the ultrasonic wave. The ultrasonic signals were acquired in the time domain and changed to the frequency domain by application of the Fourier Fast Transform (FFT), thus generating the material frequency spectrum. For the pulse echo technique, the ultrasonic spectrum frequency changed after the ultrasonic wave crossed the membrane. With the transmission technique there was only a displacement of the ultrasonic signal at the time domain.

Image Processing Algorithms applied to Radio SLAM using MIMO Radars

Radio Simultaneous Location and Mapping (SLAM) consists of the simultaneous tracking of the target and estimation of the surrounding environment, to build a map and estimate the target movements within it. It is an increasingly exploited technique for automotive applications, in order to improve the localization of obstacles and the target relative movement with respect to them, for emergency situations, for example when it is necessary to explore (with a drone or a robot) environments with a limited visibility, or for personal radar applications, thanks to its versatility and cheapness. Until today, these systems were based on light detection and ranging (lidar) or visual cameras, high-accuracy and expensive approaches that are limited to specific environments and weather conditions. Instead, in case of smoke, fog or simply darkness, radar-based systems can operate exactly in the same way. In this thesis activity, the Fourier-Mellin algorithm is analyzed and implemented, to verify the applicability to Radio SLAM, in which the radar frames can be treated as images and the radar motion between consecutive frames can be covered with registration. Furthermore, a simplified version of that algorithm is proposed, in order to solve the problems of the Fourier-Mellin algorithm when working with real radar images and improve the performance. The INRAS RBK2, a MIMO 2x16 mmWave radar, is used for experimental acquisitions, consisting of multiple tests performed in Lab-E of the Cesena Campus, University of Bologna. The different performances of Fourier-Mellin and its simplified version are compared also with the MatchScan algorithm, a classic algorithm for SLAM systems.

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.