Fractal descriptors based on Fourier spectrum applied to texture analysis

This work proposes the development and study of a novel technique lot the generation of fractal descriptors used in texture analysis. The novel descriptors are obtained from a multiscale transform applied to the Fourier technique of fractal dimension calculus. The power spectrum of the Fourier transform of the image is plotted against the frequency in a log-log scale and a multiscale transform is applied to this curve. The obtained values are taken as the fractal descriptors of the image. The validation of the proposal is performed by the use of the descriptors for the classification of a dataset of texture images whose real classes are previously known. The classification precision is compared to other fractal descriptors known in the literature. The results confirm the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.

Tailoring Molecular Architectures with Cobalt Tetrasulfonated Phthalocyanine: Immobilization in Layer-by-Layer Films and Sensing Applications

In the field of organic thin films, manipulation at the nanoscale can be obtained by immobilization of different materials on platforms designed to enhance a specific property via the layer-by-layer technique. In this paper we describe the fabrication of nanostructured films containing cobalt tetrasulfonated phthalocyanine (CoTsPc) obtained through the layer-by-layer architecture and assembled with linear poly(allylamine hydrochloride) (PAH) and poly(amidoamine) dendrimer (PAMAM) polyelectrolytes. Film growth was monitored by UV-vis spectroscopy following the Q band of CoTsPc and revealed a linear growth for both systems. Fourier transform infrared (FTIR) spectroscopy showed that the driving force keeping the structure of the films was achieved upon interactions of CoTsPc sulfonic groups with protonated amine groups present in the positive polyelectrolyte. A comprehensive SPR investigation on film growth reproduced the deposition process dynamically and provided an estimation of the thicknesses of the layers. Both FTIR and SPR techniques suggested a preferential orientation of the Pc ring parallel to the substrate. The electrical conductivity of the PAH films deposited on interdigitated electrodes was found to be very sensitive to water vapor. These results point to the development of a phthalocyanine-based humidity sensor obtained from a simple thin film deposition technique, whose ability to tailor molecular organization was crucial to achieve high sensitivity.

Hilbert transform

The Hilbert transform is an important tool in both pure and applied mathematics. It is largely used in the field of signal processing. Lately has been used in mathematical finance as the fast Hilbert transform method is an efficient and accurate algorithm for pricing discretely monitored barrier and Bermudan style options. The purpose of this report is to show the basic properties of the Hilbert transform and to check the domain of definition of this operator.

La trasformata veloce di Fourier (FFT): analisi e implementazione in C++

La trasformata di Fourier (FT) è uno strumento molto potente implementato, oggi, in un enorme numero di tecnologie. Il suo primo esempio di applicazione fu proprio il campionamento e la digitalizzazione di segnali analogici. Nel tempo l'utilizzo della FT è stato ampliato a più orizzonti in ambito digitale, basti pensare che il formato di compressione '.jpg' utilizza una FT bidimensionale, mentre uno degli ultimi esempi di applicazione si ha nell'imaging digitale in ambito medico (risonanza magnetica nucleare, tomografia assiale computerizzata TAC ecc...). Nonostante gli utilizzi della FT siano molto diversificati il suo basilare funzionamento non è mai cambiato: essa non fa altro che modificare il dominio di una funzione del tempo (un segnale) in un dominio delle frequenze, permettendo così lo studio della composizione in termini di frequenza, ampiezza e fase del segnale stesso. Parallelamente all'evoluzione in termini di applicazioni si è sviluppato uno studio volto a migliorare e ottimizzare la computazione della stessa, data l'esponenziale crescita del suo utilizzo. In questa trattazione si vuole analizzare uno degli algoritmi di ottimizzazione più celebri e utilizzati in tal senso: la trasformata veloce di Fourier (Fast Fourier Transformation o FFT). Si delineeranno quindi le caratteristiche salienti della FT, e verrà introdotto l'algoritmo di computazione tramite linguaggio C++ dedicando particolare attenzione ai limiti di applicazione di tale algoritmo e a come poter modificare opportunamente la nostra funzione in modo da ricondurci entro i limiti di validità.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Integração da equação de movimento através da Transformada de Fourier com o uso de ponderadores de ordem elevada

Baseando-se em um sistema com um grau de liberdade, é apresentada neste trabalho a equação de movimento, bem como a sua resolução através das Transformadas de Fourier e da Transformada Rápida de Fourier (FFT). Através da análise da forma como são feitas as integrações nas transformadas, foram estudados e aplicados os ponderadores de Newton-Cotes na resolução da equação de movimento, de forma a aumentar substancialmente a precisão dos resultados em comparação com a forma convencional da Transformada de Fourier.

Immobilization of aluminum chloride on MCM-41 as a new catalyst system for liquid-phase isopropylation of naphthalene

A great deal of effort has been made at searching for alternative catalysts to replace conventional Lewis acid catalyst aluminum trichloride (AlCl3). In this paper, immobilization of AlCl3 on mesoporous MCM-41 silica with and without modification was carried out. The catalytic properties of the immobilized catalyst systems for liquid-phase isopropylation of naphthalene were studied and compared with those of H/MCM-41 and H/mordenite. The structures of the surface-immobilized aluminum chloride catalysts were studied and identified by using solid-state magic angle spinning nuclear magnetic resonance (MAS NMR), Fourier transform infrared (FTIR) spectroscopy, X-ray photoelectron spectroscopy (XPS), nitrogen adsorption, and X-ray diffraction (XRD) techniques. The catalytic activity of the immobilized catalysts was found to be similar to that of acidic mordenite zeolite. A significant enhancement in the selectivity of 2,6-diisopropylnaphthalene (2,6-DIPN) was observed over the immobilized aluminum chloride catalysts. Immobilization of aluminum chloride on mesoporous silica coupled with surface silylation is a promising way of developing alternative catalyst system for liquid-phase Friedel-Crafts alkylation reactions. (C) 2002 Elsevier Science B.V. All rights reserved.

Thermosetting Blends of Polybenzoxazine and Poly(ε-caprolactone): Phase Behavior and Intermolecular Specific Interactions

Polybenzoxazine (PBA-a)/poly(epsilon-caprolactone) (PCL) blends were prepared by an in situ curing reaction of benzoxazine (BA-a) in the presence of PCL. Before curing, the benzoxazine (BA-a)/PCL blends are miscible, which was evidenced by the behaviors of single and composition-dependant glass transition temperature and equilibrium melting point depression. However, the phase separation induced by polymerization was observed after curing at elevated temperature. It was expected that after curing, the PBA-a/PCL blends would be miscible since the phenolic hydroxyls in the PBA-a molecular backbone have the potential to form inter- molecular hydrogen-bonding interactions with the carbonyls of PCL and thus would fulfil the miscibility of the blends. The resulting morphology of the blends prompted an investigation of the status of association between PBA-a and PCL under the curing conditions. Although Fourier-transform infrared spectroscopy (FT-IR) showed that there were intermolecular hydrogen-bonding interactions between PBA-a and PCL at room temperature, especially for the PCL-rich blends, the results of variable temperature FT-IR spectroscopy by the model compound indicate that the phenolic hydroxyl groups could not form efficient intermolecular hydrogen-bonding interactions at elevated temperatures, i.e., the phenolic hydroxyl groups existed mainly in the non-associated form in the system during curing. The results are valuable to understand the effect of curing temperature on the resulting morphology of the thermosetting blends. SEM micrograph of the dichloromethane-etched fracture surface of a 90:10 PBA-a PCL blend showing a heterogeneous morphology.

Organic-inorganic poly(methyl methacrylate) hybrids with confined polyhedral oligosilsesquioxane macromonomers

We herein report the synthesis of organic-inorganic hybrid poly(methyl methacrylate) containing 1 polyhedral oligosilsesquioxanes. Octakis(3-hydroxypropyldimethylsiloxy)octasilsesquioxane (OHPS) was synthesized from octakis(hydridodimethylsiloxy)octasilsesquioxane [Si8O12(OSiMe2H)(8), Q(8)M(8)(H)] following literature procedures. Octakis(tnethacryloxypropyldimethylsiloxy) octasilsesquioxane (OMPS) was synthesized via the reaction of methacryloyl chloride or methacrylic acid anhydride with OHPS, with the latter giving improved purity. Polymerization of OMPS with methyl inethacrylate using a dibenzoylperoxide initiator gave a highly cross-linked polymer. Characterization of the polymer was performed using Fourier transform IR spectroscopy, Si-29 NMR, differential scanning calorimetry, thermogravimetric analysis, atomic force microscopy, and transmission electron microscopy with energy-dispersive X-ray analysis. The polymer was found to be largely homogeneous. Increasing the OMPS concentration in the polymer gave increased decomposition and glass transition temperatures.

The in-vitro bioactivity of mesoporous bioactive glasses

Ordered mesoporous bioactive glasses (MBGs) with different compositions were prepared by using nonionic block copolymer surfactants as structure-directing agents through an evaporation-induced self-assembly process. Their in-vitro bioactivities were studied in detail by electron microscopy, Fourier-transform infrared spectroscopy, and inductively coupled plasma (ICP) atomic emission spectroscopy. The ICP element analysis results were further calculated in terms of the total consumption of Ca and P, Delta[Ca]/Delta[P] ratios, and ionic activity product (IP) of hydroxyapatite. Through the above analysis, it is clear that MBGs show a different structure-bioactivity correlation compared to conventional sol-gel-derivcd BGs. The in vitro bioactivity of MBGs is dependent on the Si/Ca ratio in the network when the other material parameters such as the mesostructure and texture properties (pore size, pore volume) are controlled. MBG 80S15C with relatively lower calcium content exhibits the best in vitro bioactivity, in contrast to conventional sol-gel-derived BGs where usually higher calcium percentage BGs (e.g. 60S35C) show better bioactivity. Calcination temperature is another important factor that influences the in vitro bioactivity. According to our results, MBGs calcined at 973 K may possess the best in vitro bioactivity. The influences of the composition and calcination temperature upon bioactivity are explained in terms of the unique structures of MBGs. (c) 2006 Elsevier Ltd. All rights reserved.

Full-field Fourier-domain optical coherence tomography

Full-field Fourier-domain optical coherence tomography (3F-OCT) is a full-field version of spectraldomain/swept-source optical coherence tomography. A set of two-dimensional Fourier holograms is recorded at discrete wavenumbers spanning the swept-source tuning range. The resultant three-dimensional data cube contains comprehensive information on the three-dimensional morphological layout of the sample that can be reconstructed in software via three-dimensional discrete Fourier-transform. This method of recording of the OCT signal confers signal-to-noise ratio improvement in comparison with "flying-spot" time-domain OCT. The spatial resolution of the 3F-OCT reconstructed image, however, is degraded due to the presence of a phase cross-term, whose origin and effects are addressed in this paper. We present theoretical and experimental study of imaging performance of 3F-OCT, with particular emphasis on elimination of the deleterious effects of the phase cross-term.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Hankel Transform in Quantum Calculus and Applications

Mathematics Subject Classification: 44A15, 33D15, 81Q99

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets

Mathematics Subject Classification: 42A38, 42C40, 33D15, 33D60