Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Empirical mode decomposition: a novel technique for the study of tremor time series

Tremor is a clinical feature characterized by oscillations of a part of the body. The detection and study of tremor is an important step in investigations seeking to explain underlying control strategies of the central nervous system under natural (or physiological) and pathological conditions. It is well established that tremorous activity is composed of deterministic and stochastic components. For this reason, the use of digital signal processing techniques (DSP) which take into account the nonlinearity and nonstationarity of such signals may bring new information into the signal analysis which is often obscured by traditional linear techniques (e.g. Fourier analysis). In this context, this paper introduces the application of the empirical mode decomposition (EMD) and Hilbert spectrum (HS), which are relatively new DSP techniques for the analysis of nonlinear and nonstationary time-series, for the study of tremor. Our results, obtained from the analysis of experimental signals collected from 31 patients with different neurological conditions, showed that the EMD could automatically decompose acquired signals into basic components, called intrinsic mode functions (IMFs), representing tremorous and voluntary activity. The identification of a physical meaning for IMFs in the context of tremor analysis suggests an alternative and new way of detecting tremorous activity. These results may be relevant for those applications requiring automatic detection of tremor. Furthermore, the energy of IMFs was visualized as a function of time and frequency by means of the HS. This analysis showed that the variation of energy of tremorous and voluntary activity could be distinguished and characterized on the HS. Such results may be relevant for those applications aiming to identify neurological disorders. In general, both the HS and EMD demonstrated to be very useful to perform objective analysis of any kind of tremor and can therefore be potentially used to perform functional assessment.

Electronic transitions and bonding properties in a series of five-coordinate “16-electron” complexes [Mn(CO)3(L2)]− (L2=chelating redox-active π-donor ligand)

In this article we present for the first time accurate density functional theory (DFT) and time-dependent (TD) DFT data for a series of electronically unsaturated five-coordinate complexes [Mn(CO)(3)(L-2)](-), where L-2 stands for a chelating strong pi-donor ligand represented by catecholate, dithiolate, amidothiolate, reduced alpha-diimine (1,4-dialkyl-1,4-diazabutadiene (R-DAB), 2,2'-bipyridine) and reduced 2,2'-biphosphinine types. The single-crystal X-ray structure of the unusual compound [Na(BPY)][Mn(CO)(3)(BPY)]center dot Et2O and the electronic absorption spectrum of the anion [Mn(CO)(3)(BPY)](-) are new in the literature. The nature of the bidentate ligand determines the bonding in the complexes, which varies between two limiting forms: from completely pi-delocalized diamagnetic {(CO)(3)Mn-L-2}(-) for L-2 = alpha-diimine or biphosphinine, to largely valence-trapped {(CO)(3)Mn-1-L-2(2-)}(-) for L-2(2-) = catecholate, where the formal oxidation states of Mn and L-2 can be assigned. The variable degree of the pi-delocalization in the Mn(L-2) chelate ring is indicated by experimental resonance Raman spectra of [Mn(CO)(3)(L-2)](-) (L-2=3,5-di-tBu-catecholate and iPr-DAB), where accurate assignments of the diagnostically important Raman bands have been aided by vibrational analysis. The L-2 = catecholate type of complexes is known to react with Lewis bases (CO substitution, formation of six-coordinate adducts) while the strongly pi-delocalized complexes are inert. The five-coordinate complexes adopt usually a distorted square pyramidal geometry in the solid state, even though transitions to a trigonal bipyramid are also not rare. The experimental structural data and the corresponding DFT-computed values of bond lengths and angles are in a very good agreement. TD-DFT calculations of electronic absorption spectra of the studied Mn complexes and the strongly pi-delocalized reference compound [Fe(CO)(3)(Me-DAB)] have reproduced qualitatively well the experimental spectra. Analyses of the computed electronic transitions in the visible spectroscopic region show that the lowest-energy absorption band always contains a dominant (in some cases almost exclusive) contribution from a pi(HOMO) -> pi*(LUMO) transition within the MnL2 metallacycle. The character of this optical excitation depends strongly on the composition of the frontier orbitals, varying from a partial L-2 -> Mn charge transfer (LMCT) through a fully delocalized pi(MnL2) -> pi*(MnL2) situation to a mixed (CO)Mn -> L-2 charge transfer (LLCT/MLCT). The latter character is most apparent in the case of the reference complex [Fe(CO)(3)(Me-DAB)]. The higher-lying, usually strongly mixed electronic transitions in the visible absorption region originate in the three lower-lying occupied orbitals, HOMO - 1 to HOMO - 3, with significant metal-d contributions. Assignment of these optical excitations to electronic transitions of a specific type is difficult. A partial LLCT/MLCT character is encountered most frequently. The electronic absorption spectra become more complex when the chelating ligand L-2, such as 2,2'-bipyridine, features two or more closely spaced low-lying empty pi* orbitals.

Statistical analysis of eight surface ozone measurement series for various sites in Ireland

Data from various stations having different measurement record periods between 1988 and 2007 are analyzed to investigate the surface ozone concentration, long-term trends, and seasonal changes in and around Ireland. Time series statistical analysis is performed on the monthly mean data using seasonal and trend decomposition procedures and the Box-Jenkins approach (autoregressive integrated moving average). In general, ozone concentrations in the Irish region are found to have a negative trend at all sites except at the coastal sites of Mace Head and Valentia. Data from the most polluted Dublin city site have shown a very strong negative trend of −0.33 ppb/yr with a 95% confidence limit of 0.17 ppb/yr (i.e., −0.33 ± 0.17) for the period 2002−2007, and for the site near the city of Cork, the trend is found to be −0.20 ± 0.11 ppb/yr over the same period. The negative trend for other sites is more pronounced when the data span is considered from around the year 2000 to 2007. Rural sites of Wexford and Monaghan have also shown a very strong negative trend of −0.99 ± 0.13 and −0.58 ± 0.12, respectively, for the period 2000−2007. Mace Head, a site that is representative of ozone changes in the air advected from the Atlantic to Europe in the marine planetary boundary layer, has shown a positive trend of about +0.16 ± 0.04 ppb per annum over the entire period 1988−2007, but this positive trend has reduced during recent years (e.g., in the period 2001−2007). Cluster analysis for back trajectories are performed for the stations having a long record of data, Mace Head and Lough Navar. For Mace Head, the northern and western clean air sectors have shown a similar positive trend (+0.17 ± 0.02 ppb/yr for the northern sector and +0.18 ± 0.02 ppb/yr for the western sector) for the whole period, but partial analysis for the clean western sector at Mace Head shows different trends during different time periods with a decrease in the positive trend since 1988 indicating a deceleration in the ozone trend for Atlantic air masses entering Europe.

Identification of partial resetting using De as a function of illumination time

Modern age samples from various depositional environments were examined for signal resetting. For 19 modern aeolian/beach samples all De values obtained were View the MathML source, with ∼70% having View the MathML source. For 21 fluvial/colluvial samples, all De values were View the MathML source with ∼80% being View the MathML source. De as a function of illumination (OSL measurement) time (De(t)) plots were examined for all samples. Based on previous laboratory experiments, increases in De(t) were expected for partially reset samples, and constant De(t) for fully reset samples. All aeolian samples, both modern age and additional ‘young’ samples (<1000 years), showed constant (flat) De(t) while all modern, non-zero De, fluvial/colluvial samples showed increasing De(t). ‘Replacement plots’, where a regenerated signal is substituted for the natural, yielded constant (flat) De(t). These findings support strongly the use of De(t) as a method of identifying incomplete resetting in fluvial samples. Potential complicating factors, such as illumination (bleaching) spectrum, thermal instability and component composition are discussed and a series of internal checks on the applicability of the De(t) for each individual aliquot/grain level are outlined.

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.

Experience With Lacosamide in a Series of Children With Drug-Resistant Focal Epilepsy

We report our pediatric experience with lacosarnide, a new antiepileptic drug, approved by the US Food and Drug Administration as adjunctive therapy in focal epilepsy in patients more than 17 years old. We retrospectively reviewed charts for lacosamide use and seizure frequency outcome in patients with focal epilepsy (Wilcoxon signed rank test). Sixteen patients (7 boys) were identified (median dose 275 mg daily, 4.7 mg/kg daily; mean age 14.9 years, range 8-21 years). Patients were receiving a median of 2 antiepileptic drugs (interquartile range [IQR] 1.7-3) in addition to having undergone previous epilepsy surgery (n = 3), vagus nerve stimulation (n = 9), and ketogenic diet (n = 3). Causes included structural (encephalomalacia and diffuse encephalitis, 1 each; stroke in 2) and genetic abnormalities (Aarskog and Rett syndromes, 1 each) or cause not known (n = 10). Median seizure frequency at baseline was 57 per month (IQR 7-75), and after a median follow-up of 4 months (range 1-13 months) of receiving lacosamide, it was 12.5 per month (IQR 3-75), (P < 0.01). Six patients (37.5%; 3 seizure free) were classified as having disease that responded to therapy (>= 50% reduction seizure frequency) and 10 as having disease that did not respond to therapy (<50% in 3; increase in 1; unchanged in 6). Adverse events (tics, behavioral disturbance, seizure worsening, and depression with suicidal ideation in 1 patient each) prompted lacosamide discontinuation in 4/16 (25%). This retrospective study of 16 children with drug-resistant focal epilepsy demonstrated good response to adjunctive lacosamide therapy (median seizure reduction of 39.6%; 37.5% with >= 50% seizure reduction) without severe adverse events. (C) 2011 Elsevier Inc. All rights reserved.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

Performance Evaluation of Different PV-Array Configurations under Weak Light Conditions and Partial Shadings

The paper analyses empirical performance data of five commercial PV-plants in Germany. The purpose was on one side to investigate the weak light performance of the different PV-modules used. On the other hand it was to quantify and compare the shading losses of different PV-array configurations. The importance of this study relies on the fact that even if the behavior under weak light conditions or the shading losses might seem to be a relatively small percentage of the total yearly output; in projects where a performance guarantee is given, these variation can make the difference between meeting or not the conditions.When analyzing the data, a high dispersion was found. To reduce the optical losses and spectral effects, a series of data filters were applied based on the angle of incidence and absolute Air Mass. To compensate for the temperature effects and translate the values to STC (25°C), five different methods were assessed. At the end, the Procedure 2 of IEC 60891 was selected due to its relative simplicity, usage of mostly standard parameters found in datasheets, good accuracy even with missing values, and its potential to improve the results when the complete set of inputs is available.After analyzing the data, the weak light performance of the modules did not show a clear superiority of a certain technology or technology group over the others. Moreover, the uncertainties in the measurements restrictive the conclusiveness of the results.In the partial shading analysis, the landscape mounting of mc-Si PV-modules in free-field showed a significantly better performance than the portrait one. The cross-table string using CIGS modules did not proved the benefits expected and performed actually poorer than a regular one-string-per-table layout. Parallel substrings with CdTe showed a proper functioning and relatively low losses. Among the two product generations of CdTe analyzed, none showed a significantly better performance under partial shadings.

V(2)O(5)/TiO(2) catalytic xerogels raman and EPR studies

Raman spectroscopy and Electron Paramagnetic Resonance (EPR) studies were performed on a series of V(2)O(5)/TiO(2) catalysts prepared by a modified sol-gel method in order to identify the vanadium species. Two species of surface vanadium were identified by Raman measurements, monomeric vanadyls and polymeric vanadates. Monomeric vanadyls are characterized by a narrow Raman band at 1030 cm(-1) and polymeric vanadates by two broad bands in the region from 900 to 960 cm(-1) and 770 to 850 cm(-1). The Raman spectra do not exhibit characteristic peaks of crystalline V(2)O(5). These results are in agreement with those of X-ray Diffractometry (XRD) and Fourier Transform Infrared (FT-IR) previously reported (C.B. Rodella et al., J. Sol-Gel Sci. Techn., submitted). At least three families of V(4+) ions were identified by EPR investigations. The analysis of the EPR spectra suggests that isolated V(4+) ions are located in sites with octahedral symmetry substituting for Ti(4+) ions in the rutile structure. Magnetically interacting V(4+) ions are also present as pairs or clusters giving rise to a broad and structureless EPR line. At higher concentration of V(2)O(5), a partial oxidation of V(4+) to V(5+) is apparent from the EPR results.

Carbon Nuclear Magnetic Resonance Spectroscopic Profiles coupled to Partial Least-Squares Multivariate Regression for Prediction of Several Physicochemical Parameters of Brazilian Commercial Gasoline

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Partial characterization of the polluting load of swine wastewater treated with an integrated biodigestion system

The stabilization of swine wastewaters from swine confined housing by the combination of a upflow anaerobic sludge blanket (UASB) reactor and waste stabilization ponds is a viable alternative to minimize the environmental impact caused by inadequate disposal of swine wastewaters. In the present study, the polluting load of pre-decanted swine wastewater treated with a series of two 0.705 m(3) UASB reactors and then in parallel in aerated and non-aerated stabilization tanks was investigated from January to July, 2000. Physicochemical and microbiological analyses were made adopting standard methods (Standard Methods for Examination of Water and Wastewater, 19th ed., American Public Health Association, Washington, DC, 1995). COD values decreased as the wastewater ran through the integrated biodigestion system dropping from about 3492 +/- 511-4094 mg l(-1) +/- 481 to 124 +/- 52-490 mg l(-1) +/- 230, while nitrate and nitrite levels increased in stabilization tanks, ranging respectively from 4 +/- 0 to 20 mg l(-1) +/- 3 and 3 +/- 1 to 11 mg l(-1) +/- 24. Although the removal of Escherichia coli was more than 97% +/- 6, the effluents of the treatment system still contained unacceptable levels of E. coli (1.6 x 10(3)-1.2 x 10(6) 100 ml(-1)) according to WHO guidelines for use of wastewater in agriculture and aquaculture. These results indicate the necessity of changes on operational characteristics of the treatment system such as an increase of the hydraulic retention time in UASB reactors or in stabilization tanks. (C) 2003 Published by Elsevier Ltd.

Estimativa do expoente de Hurst de séries temporais de chuvas do estado de São Paulo usando as transformadas de Fourier, Wavelets e análise R/S

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

New biphasic mono-component composite material obtained by partial oxypropylation of bacterial cellulose

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.