Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

Can we make a Bohmian electron reach the speed of light, at least for one instant?

In Bohmian mechanics, a version of quantum mechanics that ascribes world lines to electrons, we can meaningfully ask about an electron's instantaneous speed relative to a given inertial frame. Interestingly, according to the relativistic version of Bohmian mechanics using the Dirac equation, a massive particle's speed is less than or equal to the speed of light, but not necessarily less. That is, there are situations in which the particle actually reaches the speed of light-a very nonclassical behavior. That leads us to the question of whether such situations can be arranged experimentally. We prove a theorem, Theorem 5, implying that for generic initial wave functions the probability that the particle ever reaches the speed of light, even if at only one point in time, is zero. We conclude that the answer to the question is no. Since a trajectory reaches the speed of light whenever the quantum probability current (psi) over bar gamma(mu)psi is a lightlike 4-vector, our analysis concerns the current vector field of a generic wave function and may thus be of interest also independently of Bohmian mechanics. The fact that the current is never spacelike has been used to argue against the possibility of faster-than-light tunneling through a barrier, a somewhat similar question. Theorem 5, as well as a more general version provided by Theorem 6, are also interesting in their own right. They concern a certain property of a function psi : R(4) -> C(4) that is crucial to the question of reaching the speed of light, namely being transverse to a certain submanifold of C(4) along a given compact subset of space-time. While it follows from the known transversality theorem of differential topology that this property is generic among smooth functions psi : R(4) -> C(4), Theorem 5 asserts that it is also generic among smooth solutions of the Dirac equation. (C) 2010 American Institute of Physics. [doi:10.1063/1.3520529]

Direct evidence of singlet molecular oxygen generation from peroxynitrate, a decomposition product of peroxynitrite

The decomposition of peroxynitrite to nitrite and dioxygen at neutral pH follows complex kinetics, compared to its isomerization to nitrate at low pH. Decomposition may involve radicals or proceed by way of the classical peracid decomposition mechanism. Peroxynitrite (ONOOH/ONOO(-)) decomposition has been proposed to involve formation of peroxynitrate (O(2)NOOH/O(2)NOO(-)) at neutral pH (D. Gupta, B. Harish, R. Kissner and W. H. Koppenol, Dalton Trans., 2009, DOI: 10.1039/b905535e, see accompanying paper in this issue). Peroxynitrate is unstable and decomposes to nitrite and dioxygen. This study aimed to investigate whether O(2)NOO(-) formed upon ONOOH/ONOO(-) decomposition generates singlet molecular oxygen [O(2) ((1)Delta(g))]. As unequivocally revealed by the measurement of monomol light emission in the near infrared region at 1270 nm and by chemical trapping experiments, the decomposition of ONOO(-) or O(2)NOOH at neutral to alkaline pH generates O(2) ((1)Delta(g)) at a yield of ca. 1% and 2-10%, respectively. Characteristic light emission, corresponding to O(2) ((1)Delta(g)) monomolecular decay was observed for ONOO(-) and for O(2)NOOH prepared by reaction of H(2)O(2) with NO(2)BF(4) and of H(2)O(2) with NO(2)(-) in HClO(4). The generation of O(2) ((1)Delta(g)) from ONOO(-) increased in a concentration-dependent manner in the range of 0.1-2.5 mM and was dependent on pH, giving a sigmoid pro. le with an apparent pK(a) around pD 8.1 (pH 7.7). Taken together, our results clearly identify the generation of O(2) ((1)Delta(g)) from peroxynitrate [O(2)NOO(-) -> NO(2)(-) + O(2) ((1)Delta(g))] generated from peroxynitrite and also from the reactions of H(2)O(2) with either NO(2)BF(4) or NO(2)(-) in acidic media.

Autocatalysis in the open circuit interaction of alcohol molecules with oxidized Pt surfaces

We studied the open circuit interaction of methanol and ethanol with oxidized platinum electrodes using in situ infrared spectroscopy. For methanol, it was found that formic acid is the main species formed in the initial region of the transient and that the steep decrease of the open circuit potential coincides with an explosive increase in the CO(2) production, which is followed by an increase in the coverage of adsorbed CO. For ethanol, acetaldehyde was the main product detected and only traces of dissolved CO(2) and adsorbed CO were found after the steep potential decay. In both cases, the transients were interpreted in terms of (a) the emergence of sub-surface oxygen in the beginning of the transient, where the oxide content is high, and (b) the autocatalytic production of free platinum sites for lower oxide content during the steep decay of the open circuit potential.

Preliminary studies of laser-induced breakdown spectrometry for the determination of Ba, Cd, Cr and Pb in toys

The performance of laser-induced breakdown spectrometry (LIBS) for the determination of Ba, Cd, Cr and Pb in toys has been evaluated by using a Nd:YAG laser operating at 1064 nm and an Echelle spectrometer with intensified charge-coupled device detector. Samples were purchased in different cities of Sao Paulo State market and analyzed directly without sample preparation. Laser-induced breakdown spectrometry experimental conditions (number of pulses, delay time. integration time gate and pulse energy) were optimized by using a Doehlert design. Laser-induced breakdown spectrometry signals correlated reasonably well with inductively coupled plasma optical emission spectrometry (ICP OES) concentrations after microwave-assisted acid digestion of selected samples. Thermal analysis was used for polymer identification and scanning electron microscopy to Visualize differences in crater geometry of different polymers employed for toy fabrication. Results indicate that laser-induced breakdown spectrometry can be proposed as a rapid screening method for investigation of potentially toxic elements in toys. The unique application of laser-induced breakdown spectrometry for identification of contaminants in successive layers of ink and polymer is also demonstrated. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of laser induced breakdown spectroscopy for the determination of micronutrients in plant materials

Laser induced breakdown spectroscopy (LIBS) has been evaluated for the determination of micronutrients (B, Cu, Fe, Mn and Zn) in pellets of plant materials, using NIST, BCR and GBW biological certified reference materials for analytical calibration. Pellets of approximately 2 mm thick and 15 mm diameter were prepared by transferring 0.5 g of powdered material to a 15 mm die set and applying 8.0 tons cm(-2). An experimental setup was designed by using a Nd:YAG laser operating at 1064 nm (200 mJ per pulse, 10 Hz) and an Echelle spectrometer with ICCD detector. Repeatability precision varied from 4 to 30% from measurements obtained in 10 different positions (8 laser shots per test portion) in the same sample pellet. Limits of detection were appropriate for routine analysis of plant materials and were 2.2 mg kg(-1) B, 3.0 mg kg(-1) Cu, 3.6 mg kg(-1) Fe, 1.8 mg kg(-1) Mn and 1.2 mg kg(-1) Zn. Analysis of different plant samples were carried out by LIBS and results were compared with those obtained by ICP OES after wet acid decomposition. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of laser induced breakdown spectroscopy for the determination of macronutrients in plant materials

Laser induced breakdown spectroscopy (LIBS) has become an analytical tool for the direct analysis of a large variety of materials in order to provide qualitative and/or quantitative information. However, there is a lack of information for LIBS analysis of agricultural and environmental samples. In this work a LIBS system has been evaluated for the determination of macronutrients (P, K, Ca, Mg) in pellets of vegetal reference materials. An experimental setup was designed by using a Nd:YAG laser operating at 1064 nm and an Echelle spectrometer with ICCD detector. The plasma temperature was estimated by Boltzmann plots and instrumental paragmeters such as delay time, lens-to-sample distance and pulse energy were evaluated. Certified reference materials as well as reference materials were used for analytical calibrations of P, K, Ca, and Mg. Most results of the direct analysis of plant samples by LIBS were in reasonable agreement with those obtained by ICP OES after wet acid decomposition. (C) 2008 Elsevier B.V. All rights reserved.

Optimization and validation of a LIBS method for the determination of macro and micronutrients in sugar cane leaves

Laser induced breakdown spectrometry (LIBS) was applied for the determination of macro (P, K, Ca, Mg) and micronutrients (B, Cu, Fe, Mn and Zn) in sugar cane leaves, which is one of the most economically important crops in Brazil. Operational conditions were previously optimized by a neuro-genetic approach, by using a laser Nd:YAG at 1064 nm with 110 mJ per pulse focused on a pellet surface prepared with ground plant samples. Emission intensities were measured after 2.0 mu s delay time, with 4.5 mu s integration time gate and 25 accumulated laser pulses. Measurements of LIBS spectra were based on triplicate and each replicate consisted of an average of ten spectra collected in different sites (craters) of the pellet. Quantitative determinations were carried out by using univariate calibration and chemometric methods, such as PLSR and iPLS. The calibration models were obtained by using 26 laboratory samples and the validation was carried out by using 15 test samples. For comparative purpose, these samples were also microwave-assisted digested and further analyzed by ICP OES. In general, most results obtained by LIBS did not differ significantly from ICP OES data by applying a t-test at 95% confidence level. Both LIBS multivariate and univariate calibration methods produced similar results, except for Fe where better results were achieved by the multivariate approach. Repeatability precision varied from 0.7 to 15% and 1.3 to 20% from measurements obtained by multivariate and univariate calibration, respectively. It is demonstrated that LIBS is a powerful tool for analysis of pellets of plant materials for determination of macro and micronutrients by choosing calibration and validation samples with similar matrix composition.

Kernel machines for epilepsy diagnosis via EEG signal classification: A comparative study

Objective: We carry out a systematic assessment on a suite of kernel-based learning machines while coping with the task of epilepsy diagnosis through automatic electroencephalogram (EEG) signal classification. Methods and materials: The kernel machines investigated include the standard support vector machine (SVM), the least squares SVM, the Lagrangian SVM, the smooth SVM, the proximal SVM, and the relevance vector machine. An extensive series of experiments was conducted on publicly available data, whose clinical EEG recordings were obtained from five normal subjects and five epileptic patients. The performance levels delivered by the different kernel machines are contrasted in terms of the criteria of predictive accuracy, sensitivity to the kernel function/parameter value, and sensitivity to the type of features extracted from the signal. For this purpose, 26 values for the kernel parameter (radius) of two well-known kernel functions (namely. Gaussian and exponential radial basis functions) were considered as well as 21 types of features extracted from the EEG signal, including statistical values derived from the discrete wavelet transform, Lyapunov exponents, and combinations thereof. Results: We first quantitatively assess the impact of the choice of the wavelet basis on the quality of the features extracted. Four wavelet basis functions were considered in this study. Then, we provide the average accuracy (i.e., cross-validation error) values delivered by 252 kernel machine configurations; in particular, 40%/35% of the best-calibrated models of the standard and least squares SVMs reached 100% accuracy rate for the two kernel functions considered. Moreover, we show the sensitivity profiles exhibited by a large sample of the configurations whereby one can visually inspect their levels of sensitiveness to the type of feature and to the kernel function/parameter value. Conclusions: Overall, the results evidence that all kernel machines are competitive in terms of accuracy, with the standard and least squares SVMs prevailing more consistently. Moreover, the choice of the kernel function and parameter value as well as the choice of the feature extractor are critical decisions to be taken, albeit the choice of the wavelet family seems not to be so relevant. Also, the statistical values calculated over the Lyapunov exponents were good sources of signal representation, but not as informative as their wavelet counterparts. Finally, a typical sensitivity profile has emerged among all types of machines, involving some regions of stability separated by zones of sharp variation, with some kernel parameter values clearly associated with better accuracy rates (zones of optimality). (C) 2011 Elsevier B.V. All rights reserved.

Cardiac and peripheral adjustments induced by early exercise training intervention were associated with autonomic improvement in infarcted rats: role in functional capacity and mortality

Aims To test the effects of early exercise training (ET) on left ventricular (LV) and autonomic functions, haemodynamics, tissues blood flows (BFs), maximal oxygen consumption (VO(2) max), and mortality after myocardial infarction (MI) in rats. Methods and results Male Wistar rats were divided into: control (C), sedentary-infarcted (SI), and trained-infarcted (TI). One week after MI, TI group underwent an ET protocol (90 days, 50-70% VO2 max). Left ventricular function was evaluated noninvasively and invasively. Baroreflex sensitivity, heart rate variability, and pulse interval were measured. Cardiac output (CO) and regional BFs were determined using coloured microspheres. Infarcted area was reduced in TI (19 +/- 6%) compared with SI (34 +/- 5%) after ET. Exercise training improved the LV and autonomic functions, the CO and regional BF changes induced by MI, as well as increased SERCA2 expression and mRNA vascular endothelial growth factor levels. These changes brought about by ET resulted in mortality rate reduction in the TI (13%) group compared with the SI (54%) group. Conclusion Early aerobic ET reduced cardiac and peripheral dysfunctions and preserved cardiovascular autonomic control after MI in trained rats. Consequently, these ET-induced changes resulted in improved functional capacity and survival after MI.

Post-resistance exercise hypotension in spontaneously hypertensive rats is mediated by nitric oxide

1. Postexercise hypotension (PEH) plays an important role in the non-pharmacological treatment of hypertension. It is characterized by a decrease in blood pressure (BP) after a single bout of exercise in relation to pre-exercise levels. 2. The present study investigated the effect of a single session of resistance exercise, as well as the effect of nitric oxide (NO) and the autonomic nervous system (ANS), in PEH in spontaneously hypertensive rats (SHR). 3. Catheters were inserted into the left carotid artery and left jugular vein of male SHR (n = 37) for the purpose of measuring BP or heart rate (HR) and drug or vehicle administration, respectively. Haemodynamic measurements were made before and after acute resistance exercise. The roles of NO and the ANS were investigated by using N(G)-nitro-L-arginine methyl ester (L-NAME; 15 mg/kg, i.v.) and hexamethonium (20 mg/kg, i.v.) after a session of acute resistance exercise. 4. Acute resistance exercise promoted a pronounced reduction in systolic and diastolic BP (-37 +/- 1 and -8 +/- 1 mmHg, respectively; P < 0.05), which was suppressed after treatment with L-NAME. The reduction in systolic BP caused by exercise (-37 +/- 1 mmHg) was not altered by the administration of hexamethonium (-38 +/- 2 mmHg; P > 0.05). After exercise, the decrease in diastolic BP was greater with hexamethonium (-26 +/- 1 mmHg; P < 0.05) compared with the decrease caused by exercise alone. 5. The results suggest that acute resistance exercise has an important hypotensive effect on SHR and that NO plays a crucial role in this response.

Characterization of nickel-niobium composite electrocoatings

The electrodeposition of nickel based composites is been performed in order to improve properties of nickel layers, such as hardness, wear resistance, lubrication, corrosion resistance and catalytic activity. In the present work Nb powders (20 mu m average size) and Ni were codeposited on 1020 carbon steel by galvanostatic electrolysis of Watts bath, using 10, 20 and 40 mA/cm(2) cathodic current density and 240, 400 and 550 rpm electrolyte stirring rate. The morphology and texture of the coatings, Nb incorporated volume fraction, microhardness, adhesion to the substrate and corrosion behavior were evaluated. The Ni-Nb composite layers presented a rough morphology with randomly oriented Ni grains, whereas pure Ni coatings were smooth and showed highly preferred orientation in the [110] or [100] direction. The volume fraction of Nb in the composites determined by image analysis ranged from 8.5 to 19%. The 400 rpm stirring rate led to the highest Nb content (16 to 19016) for all current densities investigated The microhardness of the composite layers was higher than that of pure Ni coatings due to refining of Ni grains induced by incoporation of Nb particles. The adhesion of the coatings estimated qualitatively by bend test was found satisfactory. The Ni-Nb composites presented lower corrosion rate than Ni coatings in both 3% NaCl and 20% H2SO4 solutions.

Characterization of copper-silicon nitride composite electrocoatings

Silicon nitride particles were incorporated to electrolytic copper by co-electrodeposition in acidic sulfate bath, aiming the improvement of its mechanical resistance. Smooth deposits containing well-distributed silicon nitride particles were obtained. The current density did not show significant influence on incorporated particle volume fraction, whereas the variation of particle concentration in the bath had a more pronounced effect. The microhardness of the composite layers was higher than that of pure copper deposits obtained under the same conditions and increased with the increase of incorporated particle volume fraction. The microhardness of composites also increased with the increase of current density due to copper matrix grain refining. The composite coatings were slightly more corrosion resistant than pure copper deposits in 3.5% NaCl solutions.