A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

Factorial design to optimize microwave-assisted synthesis of FDU-1 silica with a new triblock copolymer

The synthesis of FDU-1 silica with large cage-like mesopores prepared with a new triblock copolymer Vorasurf 504 (R) (Eo)(38)(BO)(46)(EO)(38) was developed. The hydrothermal treatment temperature, the dissolution of the copolymer in ethanol, the HCl concentration, the solution stirring time and the hydrothermal treatment time in a microwave oven were evaluated with factorial design procedures. The dissolution in ethanol is important to produce a material with better porous morphology. Increases in the hydrothermal temperature (100 degrees C) and HCl concentration (2 M) improved structural, textural and chemical properties of the cubic ordered mesoporous silica. Also, longer times induced better physical and chemical property characteristics. (C) 2010 Elsevier Inc. All rights reserved.

Field on Poincare Group and Quantum Description of Orientable Objects

We propose an approach to the quantum-mechanical description of relativistic orientable objects. It generalizes Wigner`s ideas concerning the treatment of nonrelativistic orientable objects (in particular, a nonrelativistic rotator) with the help of two reference frames (space-fixed and body-fixed). A technical realization of this generalization (for instance, in 3+1 dimensions) amounts to introducing wave functions that depend on elements of the Poincar, group G. A complete set of transformations that test the symmetries of an orientable object and of the embedding space belongs to the group I =GxG. All such transformations can be studied by considering a generalized regular representation of G in the space of scalar functions on the group, f(x,z), that depend on the Minkowski space points xaG/Spin(3,1) as well as on the orientation variables given by the elements z of a matrix ZaSpin(3,1). In particular, the field f(x,z) is a generating function of the usual spin-tensor multi-component fields. In the theory under consideration, there are four different types of spinors, and an orientable object is characterized by ten quantum numbers. We study the corresponding relativistic wave equations and their symmetry properties.

Investigation of AISI 1040 steel corrosion H(2)S solution containing chloride ions by digital image processing coupled with in electrochemical techniques

This paper presents a study of AISI 1040 steel corrosion in aqueous electrolyte of acetic acid buffer containing 3.1 and 31 x 10(-3) mol dm(-3) of Na(2)S in both the presence and absence of 3.5 wt.% NaCl. This investigation of steel corrosion was carried out using potential polarization, and open-circuit and in situ optical microscopy. The morphological analysis and classification of types of surface corrosion damage by digital image processing reveals grain boundary corrosion and shows a non-uniform sulfide film growth, which occurs preferentially over pearlitic grains through successive formation and dissolution of the film. (C) 2011 Elsevier Ltd. All rights reserved.

Vanadium complexes with 2-pyridineformamide thiosemicarbazones: In vitro studies of insulin-like activity

Reaction of VOCl(2) with 2-pyridineformamide thiosemicarbazone (H2Am4DH) and its N(4)-methyl (H2Am4Me), N(4)-ethyl (H2Am4Et) and N(4)-phenyl (H2Am4Ph) derivatives in ethanol gave as products [VO(H2Am4DH) Cl(2)] (1), [VO(H2Am4Me) Cl(2)] center dot 1/2HCl (2), [VO(H2Am4Et) Cl(2)] center dot HCl (3) and [VO(2Am4Ph) Cl] (4). Upon the dissolution of 1-4 in water, oxidation immediately occurs with the formation of [VO(2)(2Am4DH)] (5), [VO(2)(2Am4Me)] (6), [VO(2)(2Am4Et)] (7) and [VO(2)(2Am4Ph)] (8). The crystal and molecular structures of 5 and 6 were determined. Complexes 5-8 inhibited glycerol release in a similar way to that observed with insulin but showed a low enhancing effect on glucose uptake by rat adipocytes. (C) 2008 Elsevier B.V. All rights reserved.

Geochemistry of natural chromium occurrence in a sandstone aquifer in Bauru Basin, Sao Paulo State, Brazil

Anomalous concentrations of Cr(VI) occur in groundwaters of the Adamantina Aquifer, in a large region in the western state of Sao Paulo, sometimes exceeding the potability limit (0.05 mg L(-1)). To identify the possible geochemical reactions responsible for the occurrence of Cr in groundwater in Urania, borehole rock samples were collected in order to carry out mineralogical and chemical analyses. In addition, multilevel monitoring wells were installed and groundwater samples were analyzed. Analyses of the borehole rock samples show the occurrence of a geochemical anomaly of Cr in the quartzose sandstones (average concentrations of 221 ppm). Chrome-diopside is one of the main minerals contributing to this anomaly, having an average Cr content of 1505 ppm. Sequential extraction experiments indicated weakly adsorbed Cr in the order of 0.54 ppm, and this quantity is enough to provide the Cr concentrations observed in groundwater. Groundwaters from the monitoring wells proved to be stratified, with the highest concentrations of Cr(VI) (0.13 mg L(-1)) being associated with high redox and pH values (over 10) and high concentrations of Na. Geochemical reactions that may explain the release of Cr from the solid phase to groundwater involve the release of Cr(III) from minerals (like chrome-diopside and Cr-Fe hydroxide), followed by oxidation of Cr(III) to Cr(VI), probably related to the reduction of Mn oxides present in the aquifer. Then cation exchange occurs and dissolution of carbonates which increases the pH of groundwater, resulting in the desorption and mobilization of Cr(VI) into groundwater. (C) 2011 Elsevier Ltd. All rights reserved.

Geology and geochronology of the Betara region in south-southeastern Brazil: Evidence for possible Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extension events

The results of geological mapping, chemical analysis and radiometric dating of metabasic rocks of Betara Formation, and mapping and dating of those present in the Betara basement nucleus together with mylonitic granodiorite and syenogranite are reported here. U-Pb analysis of bulk zircon fractions from the metabasic rocks of the basement nucleus yielded a Statherian age of 1790 +/- 22 Ma, while the metabasic rocks from the upper part of the Betara Formation yielded a Calymmian age between 1500 and 1450 Ma. This age is a minimum for the deposition of the Betara Formation. The older metabasic rocks are associated with post-tectonic, possibly anorogenic syenogranite, while the younger ones are gabbro or very porphyritic ankaramite whose REE patterns are consistent with crystallization from an N-MORB parent magma. The observations and data point to the probable events associated with extensional processes of the end of Paleoproterozoic and early Mesoproterozoic. Similar registers of Statherian (1.80-1.75 Ga) and Calymmian (1.50-1.45 Ga) extensional events are recorded in other parts of the South American and African continents. The Neoproterozoic witnessed the formation and junction of the tectonic slices which formed the Apiai domain during the assemblage of western Gondwana. (C) 2010 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Characterization of anodic silicon oxide films grown in room temperature ionic liquids

The electroformation of silicon oxide was performed in two room temperature ionic liquids (RTIL), 1-butyl-3-methyl-imidazolium bis(trifluoromethane sulfonyl) imide (BMITFSI) and N-n-butyl-N-methylpiperidinium bis(trifluoromethane sulfonyl) imide (BMPTFSI). This phenomenon was studied by electrochemical techniques and it was observed that the oxide growth follows a high-field mechanism. X-ray Photoelectron Spectroscopy experiments have shown that a non-stoichiometric oxide film was formed, related to the low water content present in both RTILs (< 30 ppm). The roughness values obtained by using AFM technique of the silicon surface after etching with HF was 1.5 nm (RMS). The electrochemical impedance spectroscopy at low frequencies range was interpreted as a resistance in parallel with a CPE element, the capacitance obtained was associated with the dielectric nature of the oxide formed and the resistance was interpreted considering the chemical dissolution of the oxide by the presence of the TFSI anion. The CPE element was associated with the surface roughness and the very thin oxide film obtained. (C) 2007 Elsevier Ltd. All rights reserved.

Microwave-Assisted Derivatization of Cellulose in an Ionic Liquid: An Efficient, Expedient Synthesis of Simple and Mixed Carboxylic Esters

Microwave (MW)-assisted cellulose dissolution in ionic liquids (ILs) has routinely led either to incomplete biopolymer solubilization, or its degradation. We show that these problems can be avoided by use of low-energy MW heating, coupled with efficient stirring. Dissolution of microcrystalline cellulose in the IL 1-allyl-3-methylimidazolium chloride has been achieved without changing its degree of polymerization; regenerated cellulose showed pronounced changes in its index of crystallinity, surface area, and morphology. MW-assisted functionalization of MCC by ethanoic, propanoic, butanoic, pentanoic, and hexanoic anhydrides has been studied. Compared with conventional heating, MW irradiation has resulted in considerable decrease in dissolution and reaction times. The value of the degree of substitution (DS) was found to be DS(ethanoate) > DS(propanoate) > DS(butanoate). The values of DS(pentanoate) and DS(hexanoate) were found to be slightly higher than DS(ethanoate). This surprising dependence on the chain length of the acylating agent has been reported before, but not rationalized. On the basis of the rate constants and activation parameters of the hydrolysis of ethanoic, butanoic, and hexanoic anhydrides in aqueous acetonitrile (a model acyl transfer reaction), we suggest that this result may be attributed to the balance between two opposing effects, namely, steric crowding and (cooperative) hydrophobic interactions between the anhydride and the cellulosic surface, whose lipophilicity has increased, due to its partial acylation. Four ethanoate-based mixed esters were synthesized by the reaction with a mixture of the two anhydrides; the ethanoate moiety predominated in all products. The DS is reproducible and the IL is easily recycled. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 134-143, 2010

Determination of carbaryl in tomato ""in natura"" using an amperometric biosensor based on the inhibition of acetylcholinesterase activity

This work reports the utilization of two methodologies for carbaryl determination in tomatoes. The measurements were carried out using an amperometric biosensor technique based on the inhibition of acetylcholinesterase activity due to carbaryl adsorption and a HPLC procedure. The electrochemical experiments were performed in 0.1 mol L-1 phosphate buffer solutions at pH 7.4 with an incubation time of 8 min. The analytical curve obtained in pure solutions showed excellent linearity in the 5.0 x 10(-5) to 75 x 10(-5) mol L-1 range, with the limit of detection at 0.4 x 10(-3) gL(-1). The application of such a methodology in tomato samples involved solely liquidising the samples, which were spiked with 6.0 x 10(-6) and 5.0 x 10(-5) mol L-1 carbaryl. Recovery in such samples presented values of 99.0 and 92.4%, respectively. In order to obtain a comparison, HPLC experiments were also conducted under similar conditions. However, the tomato samples have to be manipulated by an extraction procedure (MSPD), which yielded much lower recovery values (78.3 and 84.8%, respectively). On the other hand, the detection limit obtained was much lower than that for the biosensor, i.e., 3.2 x 10(-6) g L-1. Finally, the biosensor methodology was employed to analyze carbaryl directly inside the tomato, without any previous manipulation. In this case, the biosensor was immersed in the tomato pulp, which had previously been spiked with the pesticide for 8 min, removed and inserted in the electrochemical cell. A recovery of 83.4% was obtained, showing very low interference of the matrix constituents. (C) 2007 Elsevier B.V. All rights reserved.

Polydimethylsiloxane/polypyrrole stir bar sorptive extraction and liquid chromatography (SBSE/LC-UV) analysis of antidepressants in plasma samples

A new polymeric coating consisting of a dual-phase, polydimethylsiloxane (PDMS) and polypyrrole (PPY) was developed for the stir bar sorptive extraction (SBSE) of antidepressants (mirtazapine, citalopram, paroxetine, duloxetine, fluoxetine and sertraline) from plasma samples, followed by liquid chromatography analysis (SBSE/LC-UV). The extractions were based on both adsorption (PPY) and sorption (PDMS) mechanisms. SBSE variables, such as extraction time, temperature, pH of the matrix, and desorption time were optimized, in order to achieve suitable analytical sensitivity in a short time period. The PDMS/PPY coated stir bar showed high extraction efficiency (sensitivity and selectivity) toward the target analytes. The quantification limits (LOQ) of the SBSE/LC-UV method ranged from 20 ng mL(-1) to 50 ng mL(-1), and the linear range was from LOQ to 500 ng mL(-1), with a determination coefficient higher than 0.99. The inter-day precision of the SBSE/LC-UV method presented a variation coefficient lower than 15%. The efficiency of the SBSE/LC-UV method was proved by analysis of plasma samples from elderly depressed patients. (C) 2008 Elsevier B.V. All rights reserved.

The role of HBF(4) in electro-catalysis: Arsenic contamination and anion adsorption

We present in this work a comprehensive investigation of the role played by dissolved tetrafluoroboric acid on the electrochemical response of a polycrystalline platinum electrode in acidic media. HBF(4) from two different suppliers was employed and characterized in terms of the amount of arsenic contamination by Inductively Coupled Plasma-Optical Emission Spectroscopy. The effect of different amounts of HBF(4) on the voltammetric profile of the Pt vertical bar HClO(4)(aq) interface was investigated by means of electrochemical quartz crystal nanobalance (EQCN). Despite the comparable cyclic voltammograms, the presence of arsenic in one of the two HBF(4) used resulted in dramatic variations in the mass change profile, which evidences the deposition/dissolution of arsenic prior to the surface oxidation. For the arsenic-free HBF(4), its effect on the mass change profile was mainly associated to anion adsorption. The impact of dissolved HBF(4) on the electro-oxidation of formic acid was rationalized in terms of two contributions: current enhancement at low potentials due to the arsenic-assisted formic acid electro-oxidation and inhibition at high potentials due to anion adsorption. (C) 2011 Elsevier B.V. All rights reserved.