913 resultados para Fourier and Laplace Transforms


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This study aimed to evaluate the chemical interaction of collagen with some substances usually applied in dental treatments to increase the durability of adhesive restorations to dentin. Initially, the similarity between human dentin collagen and type I collagen obtained from commercial bovine membranes of Achilles deep tendon was compared by the Attenuated Total Reflectance technique of Fourier Transform Infrared (ATR-FTIR) spectroscopy. Finally, the effects of application of 35% phosphoric acid, 0.1M ethylenediaminetetraacetic acid (EDTA), 2% chlorhexidine, and 6.5% proanthocyanidin solution on microstructure of collagen and in the integrity of its triple helix were also evaluated by ATR-FTIR. It was observed that the commercial type I collagen can be used as an efficient substitute for demineralized human dentin in studies that use spectroscopy analysis. The 35% phosphoric acid significantly altered the organic content of amides, proline and hydroxyproline of type I collagen. The surface treatment with 0.1M EDTA, 2% chlorhexidine, or 6.5% proanthocyanidin did not promote deleterious structural changes to the collagen triple helix. The application of 6.5% proanthocyanidin on collagen promoted hydrogen bond formation. (c) 2012 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2012.

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Thermal infrared (IR, 10.5 – 12.5 m) images from the Meteosat Visible and Infrared Imager (MVIRI) of cold cloud episodes (cloud top brightness temperature < 241 K) are used as a proxy of precipitating clouds to derive a warm season (May-August) climatology of their coherency, duration, span, and speed over Europe and the Mediterranean. The analysis focuses over the 30°-54°N, 15°W-40°E domain in May-August 1996-2005. Harmonic analysis using discrete Fourier transforms is applied together with a statistical analysis and an investigation of the diurnal cycle. This study has the objective to make available a set of results on the propagation dynamics of the cloud systems with the aim of assist numerical modellers in improving summer convection parameterization. The zonal propagation of cold cloud systems is accompanied by a weak meridional component confined to narrow latitude belts. The persistence of cold clouds over the area evidences the role of orography, the Pyrenees, the Alps, the Balkans and Anatolia. A diurnal oscillation is found with a maximum marking the initiation of convection in the lee of the mountains and shifting from about 1400 UTC at 40°E to 1800 UTC at 0°. A moderate eastward propagation of the frequency maximum from all mountain chains across the domain exists and the diurnal maxima are completely suppressed west of 5°W. The mean power spectrum of the cold cloud frequency distribution evidences a period of one day all over Europe disappearing over the ocean (west of 10°W). Other maxima are found in correspondence of 6 to 10 days in the longitudes from 15° W to 0° and indicate the activity of the westerlies with frontal passage over the continent. Longer periods activities (from 15 up to 30 days) were stronger around 10° W and from 5° W to 15° E and are likely related to the Madden Julian Oscillation influence. The maxima of the diurnal signal are in phase with the presence of elevated terrain and with land masses. A median zonal phase speed of 16.1 ms-1 is found for all events ≥ 1000 km and ≥ 20 h and a full set of results divided by years and recurrence categories is also presented.

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Aim of this thesis was to further extend the applicability of the Fourier-transform (FT) rheology technique especially for non-linear mechanical characterisation of polymeric materials on the one hand and to investigated the influence of the degree of branching on the linear and non-linear relaxation behaviour of polymeric materials on the other hand. The latter was achieved by employing in particular FT-rheology and other rheological techniques to variously branched polymer melts and solutions. For these purposes, narrowly distributed linear and star-shaped polystyrene and polybutadiene homo-polymers with varying molecular weights were anionically synthesised using both high-vacuum and inert atmosphere techniques. Furthermore, differently entangled solutions of linear and star-shaped polystyrenes in di-sec-octyl phthalate (DOP) were prepared. The several linear polystyrene solutions were measured under large amplitude oscillatory shear (LAOS) conditions and the non-linear torque response was analysed in the Fourier space. Experimental results were compared with numerical predictions performed by Dr. B. Debbaut using a multi-mode differential viscoelastic fluid model obeying the Giesekus constitutive equation. Apart from the analysis of the relative intensities of the harmonics, a detailed examination of the phase information content was developed. Further on, FT-rheology allowed to distinguish polystyrene melts and solutions due to their different topologies where other rheological measurements failed. Significant differences occurred under LAOS conditions as particularly reflected in the phase difference of the third harmonic, Ħ3, which could be related to shear thinning and shear thickening behaviour.

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The influence of shear fields on water-based systems was investigated within this thesis. The non-linear rheological behaviour of spherical and rod-like particles was examined with Fourier-Transform rheology under LAOS conditions. As a model system for spherical particles two different kinds of polystyrene dispersions, with a solid content higher than 0.3 each, were synthesised within this work. Due to the differences in polydispersity and Debye-length, differences were also found in the rheology. In the FT-rheology both kinds of dispersions showed a similar rise in the intensities of the magnitudes of the odd higher harmonics, which were predicted by a model. The in some cases additionally appearing second harmonics were not predicted. A novel method to analyse the time domain signal was developed, that splits the time domain signal up in four characteristic functions. Those characteristic functions correspond to rheological phenomena. In some cases the intensities of the Fourier components can interfere negatively. FD-virus particles were used as a rod-like model system, which already shows a highly non-linear behaviour at concentrations below 1. % wt. Predictions for the dependence of the higher harmonics from the strain amplitude described the non-linear behaviour well at large, but no so good at small strain amplitudes. Additionally the trends of the rheological behaviour could be described by a theory for rod-like particles. An existing rheo-optical set-up was enhanced by reducing the background birefringence by a factor of 20 and by increasing the time resolution by a factor of 24. Additionally a combination of FT-rheology and rheo-optics was achieved. The influence of a constant shear field on the crystallisation process of zinc oxide in the presence of a polymer was examined. The crystallites showed a reduction in length by a factor of 2. The directed addition of polymers in combination with a defined shear field can be an easy way for a defined change of the form of crystallites.

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The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

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This thesis focuses on studying molecular structure and internal dynamics by using pulsed jet Fourier transform microwave (PJ-FTMW) spectroscopy combined with theoretical calculations. Several kinds of interesting chemical problems are investigated by analyzing the MW spectra of the corresponding molecular systems. First, the general aspects of rotational spectroscopy are summarized, and then the basic theory on molecular rotation and experimental method are described briefly. ab initio and density function theory (DFT) calculations that used in this thesis to assist the assignment of rotational spectrum are also included. From chapter 3 to chapter 8, several molecular systems concerning different kind of general chemical problems are presented. In chapter 3, the conformation and internal motions of dimethyl sulfate are reported. The internal rotations of the two methyl groups split each rotational transition into several components line, allowing for the determination of accurate values of the V3 barrier height to internal rotation and of the orientation of the methyl groups with respect to the principal axis system. In chapter 4 and 5, the results concerning two kinds of carboxylic acid bi-molecules, formed via two strong hydrogen bonds, are presented. This kind of adduct is interesting also because a double proton transfer can easily take place, connecting either two equivalent or two non-equivalent molecular conformations. Chapter 6 concerns a medium strong hydrogen bonded molecular complex of alcohol with ether. The dimer of ethanol-dimethylether was chosen as the model system for this purpose. Chapter 7 focuses on weak halogen…H hydrogen bond interaction. The nature of O-H…F and C-H…Cl interaction has been discussed through analyzing the rotational spectra of CH3CHClF/H2O. In chapter 8, two molecular complexes concerning the halogen bond interaction are presented.

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Nella tesi viene descritto il Network Diffusion Model, ovvero il modello di A. Ray, A. Kuceyeski, M. Weiner inerente i meccanismi di progressione della demenza senile. In tale modello si approssima l'encefalo sano con una rete cerebrale (ovvero un grafo pesato), si identifica un generale fattore di malattia e se ne analizza la propagazione che avviene secondo meccanismi analoghi a quelli di un'infezione da prioni. La progressione del fattore di malattia e le conseguenze macroscopiche di tale processo(tra cui principalmente l'atrofia corticale) vengono, poi, descritte mediante approccio matematico. I risultati teoretici vengono confrontati con quanto osservato sperimentalmente in pazienti affetti da demenza senile. Nella tesi, inoltre, si fornisce una panoramica sui recenti studi inerenti i processi neurodegenerativi e si costruisce il contesto matematico di riferimento del modello preso in esame. Si presenta una panoramica sui grafi finiti, si introduce l'operatore di Laplace sui grafi e si forniscono stime dall'alto e dal basso per gli autovalori. Al fine di costruire una cornice matematica completa si analizza la relazione tra caso discreto e continuo: viene descritto l'operatore di Laplace-Beltrami sulle varietà riemanniane compatte e vengono fornite stime dall'alto per gli autovalori dell'operatore di Laplace-Beltrami associato a tali varietà a partire dalle stime dall'alto per gli autovalori del laplaciano sui grafi finiti.

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The performance of the parallel vector implementation of the one- and two-dimensional orthogonal transforms is evaluated. The orthogonal transforms are computed using actual or modified fast Fourier transform (FFT) kernels. The factors considered in comparing the speed-up of these vectorized digital signal processing algorithms are discussed and it is shown that the traditional way of comparing th execution speed of digital signal processing algorithms by the ratios of the number of multiplications and additions is no longer effective for vector implementation; the structure of the algorithm must also be considered as a factor when comparing the execution speed of vectorized digital signal processing algorithms. Simulation results on the Cray X/MP with the following orthogonal transforms are presented: discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete sine transform (DST), discrete Hartley transform (DHT), discrete Walsh transform (DWHT), and discrete Hadamard transform (DHDT). A comparison between the DHT and the fast Hartley transform is also included.(34 refs)

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A high resolution luminescence study of NaLaF4: 1%Pr3+, 5%Yb3+ and NaLaF4: 1%Ce3+, 5%Yb3+ in the UV to NIR spectral range using a InGaAs detector and a fourier transform interferometer is reported. Although the Pr3+(P-3(0) -> (1)G(4), Yb3+(F-2(7/2) -> F-2(5/2)) energy transfer step takes place, significant Pr3+ (1)G(4) emission around 993, 1330 and 1850 nm is observed. No experimental proof for the second energy transfer step in the down-conversion process between Pr3+ and Yb3+ can be given. In the case of NaLaF4: Ce3+, Yb3+ it is concluded that the observed Yb3+ emission upon Ce3+ 5d excitation is the result of a charge transfer process instead of down-conversion. (C) 2010 Elsevier B.V. All rights reserved.

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Abstract We demonstrate the use of Fourier transform infrared spectroscopy (FTIRS) to make quantitative measures of total organic carbon (TOC), total inorganic carbon (TIC) and biogenic silica (BSi) concentrations in sediment. FTIRS is a fast and costeffective technique and only small sediment samples are needed (0.01 g). Statistically significant models were developed using sediment samples from northern Sweden and were applied to sediment records from Sweden, northeast Siberia and Macedonia. The correlation between FTIRS-inferred values and amounts of biogeochemical constituents assessed conventionally varied between r = 0.84–0.99 for TOC, r = 0.85– 0.99 for TIC, and r = 0.68–0.94 for BSi. Because FTIR spectra contain information on a large number of both inorganic and organic components, there is great potential for FTIRS to become an important tool in paleolimnology.

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We present an image quality assessment and enhancement method for high-resolution Fourier-Domain OCT imaging like in sub-threshold retina therapy. A Maximum-Likelihood deconvolution algorithm as well as a histogram-based quality assessment method are evaluated.

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