Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

Profile and crowding of currents in mesoscopic superconductors with an array of antidots

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Compressible modes in a square lid-driven cavity

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Square stepping exercise: uma nova atividade física para idosos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Validation of a stability-indicating HPLC method with diode array detection for the determination of beclomethasone dipropionate in aqueous suspension for nebulizer

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Correntes críticas e comportamento dinâmico dos vórtices em fitas supercondutoras do tipo II com arranjos conformes de centros de aprisionamento

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Correntes críticas e comportamento dinâmico dos vórtices em fitas supercondutoras do tipo II com arranjos conformes de centros de aprisionamento

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of salinity on the interannual heat storage trends in the Atlantic estimated from altimeters and Pilot Research Moored Array in the Tropical Atlantic data

Changes in the oceanic heat storage (HS) can reveal important evidences of climate variability related to ocean heat fluxes. Specifically, long-term variations in HS are a powerful indicator of climate change as HS represents the balance between the net surface energy flux and the poleward heat transported by the ocean currents. HS is estimated from sea surface height anomaly measured from the altimeters TOPEX/Poseidon and Jason 1 from 1993 to 2006. To characterize and validate the altimeter-based HS in the Atlantic, we used the data from the Pilot Research Moored Array in the Tropical Atlantic (PIRATA) array. Correlations and rms differences are used as statistical figures of merit to compare the HS estimates. The correlations range from 0.50 to 0.87 in the buoys located at the equator and at the southern part of the array. In that region the rms differences range between 0.40 and 0.51 x 10(9) Jm(-2). These results are encouraging and indicate that the altimeter has the precision necessary to capture the interannual trends in HS in the Atlantic. Albeit relatively small, salinity changes can also have an effect on the sea surface height anomaly. To account for this effect, NCEP/GODAS reanalysis data are used to estimate the haline contraction. To understand which dynamical processes are involved in the HS variability, the total signal is decomposed into nonpropagating basin-scale and seasonal (HS(l)) planetary waves, mesoscale eddies, and small-scale residual components. In general, HS(l) is the dominant signal in the tropical region. Results show a warming trend of HS(l) in the past 13 years almost all over the Atlantic basin with the most prominent slopes found at high latitudes. Positive interannual trends are found in the halosteric component at high latitudes of the South Atlantic and near the Labrador Sea. This could be an indication that the salinity anomaly increased in the upper layers during this period. The dynamics of the South Atlantic subtropical gyre could also be subject to low-frequency changes caused by a trend in the halosteric component on each side of the South Atlantic Current.

Formation of an extended CoSi2 thin nanohexagons array coherently buried in silicon single crystal

A Co-doped silica film was deposited on the surface of a Si(100) wafer and isothermally annealed at 750 degrees C to form spherical Co nanoparticles embedded in the silica film and a few atomic layer thick CoSi2 nanoplatelets within the wafer. The structure, morphology, and spatial orientation of the nanoplatelets were characterized. The experimental results indicate that the nanoplatelets exhibit hexagonal shape and a uniform thickness. The CoSi2 nanostructures lattice is coherent with the Si lattice, and each of them is parallel to one of the four planes belonging to the {111} crystallographic form of the host lattice. (C) 2012 American Institute of Physics. [doi:10.1063/1.3683493]

Constrained least square pre-distortion scheme for multiuser ultra-wideband

The study proposes a constrained least square (CLS) pre-distortion scheme for multiple-input single-output (MISO) multiple access ultra-wideband (UWB) systems. In such a scheme, a simple objective function is defined, which can be efficiently solved by a gradient-based algorithm. For the performance evaluation, scenarios CM1 and CM3 of the IEEE 802.15.3a channel model are considered. Results show that the CLS algorithm has a fast convergence and a good trade-off between intersymbol interference (ISI) and multiple access interference (MAI) reduction and signal-to-noise ratio (SNR) preservation, performing better than time-reversal (TR) pre-distortion.

Use of Hg-Electroplated-Pt Ultramicroelectrode for Determining Elemental Sulphur in Naphtha Samples

This paper describes the applicability of a Hg-electroplated-Pt ultramicroelectrode in the quantification of elemental sulphur in naphtha samples by square-wave voltammetry. A reproducible deposition methodology was studied and is reported in this paper. This methodology is innovative and relies on the quality of the mercury stock solution to obtain reproducible surfaces required for the analytical methodology. All analyses were performed using a Hg-electroplated-Pt ultramicroelectrode (Hg-Pt UME) due to the low sensibility of such devices to ohmic drops in resistive solutions. The responses of the peak areas in voltammetric experiments were linear in all of the range studied. The method developed here is accurate and reproducible, with a detection limit of 0.010 mg L-1 and a good recovery range for both standard solutions of elemental sulphur (85 to 99%) and real naphtha sample (79%). These results attest to the potential for the application of this electroanalytical methodology in determining elemental sulphur in naphtha samples containing mercaptans and disulphides.

Turing patterns in the chlorine dioxide-iodine-malonic acid reaction with square spatial periodic forcing

We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns to two-dimensional "square" spatial forcing, implemented as orthogonal sets of bright bands projected onto the reaction medium. Various resonant structures emerge in a broad range of forcing wavelengths and amplitudes, including square lattices and superlattices, one-dimensional stripe patterns and oblique rectangular patterns. Numerical simulations using a model that incorporates additive two-dimensional spatially periodic forcing reproduce well the experimental observations.

MSX2 copy number increase and craniosynostosis: copy number variation detected by array comparative genomic hybridization

Fleury Group

Microelectrode array in mixed alkanethiol self-assembled monolayers: Electrochemical studies

We report an efficient alternative to obtain recessed microelectrodes device on gold electrode surface, in which mixed self-assembled monolayer of long and short carbon alkanethiol chains was used for this purpose. Development of the modified electrodes included the chemical adsorption of 11-mercaptoundecanoic acid and 2-mercaptoethanol solution, as well as their mixtures, on gold surface, resulting in the final mixed self-assembled monolayer configuration. For comparison, the electrochemical performance of self-assembled monolayer of 11-mercaptoundecanoic acid. 3-mercaptopropionic acid, 4-mercapto-1-butanol and 6-mercapto-1-hexanol modified electrodes was also investigated. It was verified that, in the mixed self-assembled monolayer, the 11-mercaptoundecanoic acid acts as a barrier for electron transfer while the short alkanethiol chair is deposited in an island-like shape through which electrons can be freely transferred to ions in solution, allowing electrochemical reactions to occur. The performance of the modified electrodes toward microelectrode behavior was investigated via cyclic voltammetry and electrochemical impedance spectroscopy measurements using [Fe(CN)(6)](3-/4-) redox couple as a probe. In this case, sigmoidal voltammetric responses were obtained, very similar to those observed for microelectrodes. Such behavior reinforces the proposition of electron transfer through the short alkanethiol chain layer and surface blockage by the long chain one. Electrochemical impedance results allowed calculated the mean radius value of each microelectrode disks of 3.8 mu m with about 22 mu m interval between them. The microelectrode environment provided by the mixed self-assembled monolayer can be conveniently used to provide an efficient catalytic conversion in biosensing applications. (C) 2012 Elsevier Ltd. All rights reserved.