Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping

The problem of projecting multidimensional data into lower dimensions has been pursued by many researchers due to its potential application to data analyses of various kinds. This paper presents a novel multidimensional projection technique based on least square approximations. The approximations compute the coordinates of a set of projected points based on the coordinates of a reduced number of control points with defined geometry. We name the technique Least Square Projections ( LSP). From an initial projection of the control points, LSP defines the positioning of their neighboring points through a numerical solution that aims at preserving a similarity relationship between the points given by a metric in mD. In order to perform the projection, a small number of distance calculations are necessary, and no repositioning of the points is required to obtain a final solution with satisfactory precision. The results show the capability of the technique to form groups of points by degree of similarity in 2D. We illustrate that capability through its application to mapping collections of textual documents from varied sources, a strategic yet difficult application. LSP is faster and more accurate than other existing high-quality methods, particularly where it was mostly tested, that is, for mapping text sets.

A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Development of a sequential injection-square wave voltammetry method for determination of paraquat in water samples employing the hanging mercury drop electrode

This work describes the development and optimization of a sequential injection method to automate the determination of paraquat by square-wave voltammetry employing a hanging mercury drop electrode. Automation by sequential injection enhanced the sampling throughput, improving the sensitivity and precision of the measurements as a consequence of the highly reproducible and efficient conditions of mass transport of the analyte toward the electrode surface. For instance, 212 analyses can be made per hour if the sample/standard solution is prepared off-line and the sequential injection system is used just to inject the solution towards the flow cell. In-line sample conditioning reduces the sampling frequency to 44 h(-1). Experiments were performed in 0.10 M NaCl, which was the carrier solution, using a frequency of 200 Hz, a pulse height of 25 mV, a potential step of 2 mV, and a flow rate of 100 mu L s(-1). For a concentration range between 0.010 and 0.25 mg L(-1), the current (i(p), mu A) read at the potential corresponding to the peak maximum fitted the following linear equation with the paraquat concentration (mg L(-1)): ip = (-20.5 +/- 0.3) Cparaquat -(0.02 +/- 0.03). The limits of detection and quantification were 2.0 and 7.0 mu g L(-1), respectively. The accuracy of the method was evaluated by recovery studies using spiked water samples that were also analyzed by molecular absorption spectrophotometry after reduction of paraquat with sodium dithionite in an alkaline medium. No evidence of statistically significant differences between the two methods was observed at the 95% confidence level.

Square wave adsorptive cathodic stripping voltarnmetry automated by sequential injection analysis - Potentialities and limitations exemplified by the determination of methyl parathion in water samples

This paper describes the development and evaluation of a sequential injection method to automate the determination of methyl parathion by square wave adsorptive cathodic stripping voltammetry exploiting the concept of monosegmented flow analysis to perform in-line sample conditioning and standard addition. Accumulation and stripping steps are made in the sample medium conditioned with 40 mmol L-1 Britton-Robinson buffer (pH 10) in 0.25 mol L-1 NaNO3. The homogenized mixture is injected at a flow rate of 10 mu Ls(-1) toward the flow cell, which is adapted to the capillary of a hanging drop mercury electrode. After a suitable deposition time, the flow is stopped and the potential is scanned from -0.3 to -1.0 V versus Ag/AgCl at frequency of 250 Hz and pulse height of 25 mV The linear dynamic range is observed for methyl parathion concentrations between 0.010 and 0.50 mgL(-1), with detection and quantification limits of 2 and 7 mu gL(-1), respectively. The sampling throughput is 25 h(-1) if the in line standard addition and sample conditioning protocols are followed, but this frequency can be increased up to 61 h(-1) if the sample is conditioned off-line and quantified using an external calibration curve. The method was applied for determination of methyl parathion in spiked water samples and the accuracy was evaluated either by comparison to high performance liquid chromatography with UV detection, or by the recovery percentages. Although no evidences of statistically significant differences were observed between the expected and obtained concentrations, because of the susceptibility of the method to interference by other pesticides (e.g., parathion, dichlorvos) and natural organic matter (e.g., fulvic and humic acids), isolation of the analyte may be required when more complex sample matrices are encountered. (C) 2007 Elsevier B.V. All rights reserved.

Electroanalytical determination of promethazine hydrochloride in pharmaceutical formulations on highly boron-doped diamond electrodes using square-wave adsorptive voltammetry

The electrochemical oxidation of promethazine hydrochloride was made on highly boron-doped diamond electrodes. Cyclic voltammetry experiments showed that the oxidation mechanisms involved the formation of an adsorbed product that is more readily oxidized, producing a new peak with lower potential values whose intensity can be increased by applying the accumulation potential for given times. The parameters were optimized and the highest current intensities were obtained by applying +0.78 V for 30 seconds. The square-wave adsorptive voltammetry results obtained in BR buffer showed two well-defined peaks, dependent on the pH and on the voltammetric parameters. The best responses were obtained at pH 4.0, frequency of 50 s(-1), step of 2 mV, and amplitude of 50 mV. Under these conditions, linear responses were obtained for concentrations from 5.96 x 10(-7) to 4.76 x 10(-6) mol L-1, and calculated detection limits of 2.66 x 10(-8) mol L-1 (8.51 mu g L-1) for peak 1 and of 4.61 x 10(-8) mol L-1 (14.77 mu g L-1) for peak 2. The precision and accuracy were evaluated by repeatability and reproducibility experiments, which yielded values of less than 5.00% for both voltammetric peaks. ne applicability of this procedure was tested on commercial formulations of promethazine hydrochloride by observing the stability, specificity, recovery and precision of the procedure in complex samples. All results obtained were compared to recommended procedure by British Pharmacopeia. The voltammetric results indicate that the proposed procedure is stable and sensitive, with good reproducibility even when the accumulation steps involve short times. It is therefore very suitable for the development of the electroanalytical procedure, providing adequate sensitivity and a reliable method.

A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form are somewhat complex - usually invoking the use of new spaces, and what not. These demonstrations are usually too difficult for an average Mathematics student to understand how he or she can obtain the Jordan Canonical Form for any square matrix. The method here proposed not only demonstrates the existence of such forms but, additionally, shows how to find them in a step by step manner. I do not claim that the following demonstration is in any way “elegant” (by the standards of elegance in fashion nowadays among mathematicians) but merely simple (undergraduate students taking a fist course in Matrix Algebra would understand how it works).

Minimum size for the occurrence of vortex matter in a square mesoscopic superconductor

The study of superconducting samples in mesoscopic scale presented a remarkable improvement during the last years. Certainly, such interest is based on the fact that when the size of the samples is close to the order of the temperature dependent coherence length xi(T), and/or the size of the penetration depth lambda(T), there are some significant modifications on the physical properties of the superconducting state. This contribution tests the square cross-section size limit for the occurrence (or not) of vortices in mesoscopic samples of area L-2, where L varies discretely from 1 xi(0) to 8 xi(0).The time dependent Ginzburg-Landau (TDGL) equations approach is used upon taking the order parameter and the local magnetic field invariant along the z-direction. The vortex configurations at the equilibrium can be obtained from the TDGL equations for superconductivity as the system relaxes to the stationary state.The obtained results show that the limit of vortex penetration is for the square sample of size 3 xi(0) x 3 xi(0) in which only a single vortex are allowed into the sample. For smaller specimens, no vortex can be formed and the field entrance into the sample is continuous and the total flux penetration occurs at higher values of H/H-c2(0), where H-c2(T) is the upper critical field. Otherwise, for larger samples different vortices patterns can be observed depending on the sample size. (c) 2007 Elsevier B.V. All rights reserved.

Vortex dynamics in mesoscopic superconducting square of variable surface

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

Vortex-antivortex annihilation dynamics in a square mesoscopic superconducting cylinder

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

Determination of 5-aminosalicylic acid in pharmaceutical formulations by square wave voltammetry at pencil graphite electrodes

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

DETERMINATION of SILICON IN LUBRICANT OIL BY HIGH-RESOLUTION CONTINUUM SOURCE FLAME ATOMIC ABSORPTION SPECTROMETRY USING LEAST-SQUARE BACKGROUND CORRECTION and INTERNAL STANDARDIZATION

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

Determination of sulfur compounds in gasoline using mercury film electrode by square wave voltammetry

A sensitive method based on square wave voltammetry is described for the quantitative determination of elemental sulfur, disulfide and mercaptan in gasoline using a mercury film electrode. These sulfur compounds can be quantified by direct dissolution of gasoline in a supporting electrolyte followed by subsequent voltammetric measurement. The supporting electrolyte is 1.4 mol L-1 sodium acetate and No acetic acid in methanol. Chemical and optimum operational conditions for the formation of the mercury film were analyzed in this study. The values obtained were a 4.3 mu m thickness for the mercury film, a 1000 rpm rotation frequency, -0.9 V applied potential and 600 s depositing time. Voltammetric measurements were obtained using square wave voltammetry with detection limits of the 3.0 x 10(-9), 1.6 x 10(-7) and 4.9 x 10(-7) mol L-1 for elemental sulfur, disulfide and mercaptan, respectively. (C) 2007 Elsevier Ltd. All rights reserved.

Depairing critical current density of a mesoscopic square superconductor

In the present paper we consider the vortex lattice properties of a square superconductor such as the vortex patterns, the Gibbs free energy, the magnetization, and the depairing critical current density. We show that this last quantity shows a matching effect, that is, it shows a discontinuous behavior as a function of the applied magnetic field.

Temperature-dependent vortex motion in a square mesoscopic superconducting cylinder: Ginzburg-Landau calculations

In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

Preconcentration of rutin at a poly glutamic acid modified electrode and its determination by square wave voltammetry

The voltammetric determination of rutin in 0.04 mol l(-1) B-R buffer (pH 4.0) by square wave voltammograms (+0.41 V vs. Ag/AgCl(sat.)) at a poly glutamic acid modified glassy carbon electrode was found to be several orders of magnitude lower than that on a bare glassy carbon electrode. Rutin can be preconcentrated on the films of poly glutamic acid and presented linear relationship from concentration of 7 x 10(-7) to 1 x 10(-5) mol l(-1) in 0.04 mol l(-1) B-R buffer pH 4.0. The method was successfully applied to the determination of rutin in pharmaceutical formulation without any pretreatment.