Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

The effect of metal transfer modes and shielding gas composition on the emission of ultraafine particles in MAG steel welding

The present study aims to characterize ultrafine particles emitted during gas metal arc welding of mild steel and stainless steel, using different shielding gas mixtures, and to evaluate the effect of metal transfer modes, controlled by both processing parameters and shielding gas composition, on the quantity and morphology of the ultrafine particles. It was found that the amount of emitted ultrafine particles (measured by particle number and alveolar deposited surface area) are clearly dependent from the main welding parameters, namely the current intensity and the heat input of the Welding process. The emission of airborne ultrafine particles increases with the current intensity as fume formation rate does. When comparing the shielding gas mixtures, higher emissions were observed for more oxidizing mixtures, that is, with higher CO2 content, which means that these mixtures originate higher concentrations of ultrafine particles (as measured by number of particles. by cubic centimeter of air) and higher values of alveolar deposited surface area of particles, thus resulting in a more hazardous condition regarding welders exposure.

The effect of metal transfer stability (spattering) on fume generation, morphology and composition in short-circuit MAG welding

The main objective of this work was to evaluate the hypothesis that the greater transfer stability leads also to less volume of fumes. Using an Ar + 25%CO2 blend as shielding gas and maintaining constant the average current, wire feed speed and welding speed, bead-on-plate welds were carried out with plain carbon steel solid wire. The welding voltage was scanned to progressively vary the transfer stability. Using two conditions of low stability and one with high stability, fume generation was evaluated by means of the AWS F1.2:2006 standard. The influence of these conditions on fume morphology and composition was also verified. A condition with greater transfer stability does not generate less fume quantity, despite the fact that this condition produces fewer spatters. Other factors such as short-circuit current, arcing time, droplet diameters and arc length are the likely governing factors, but in an interrelated way. Metal transfer stability does not influence either the composition or the size/morphology of fume particulates. (c) 2014 Elsevier B.V. All rights reserved.

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Substituted P-Phenylene Ethynylene trimers as fluorescent sensors for nitroaromatic explosives

New sensory materials based on p-phenylene ethynylene trimers integrating calix[4]arene receptors (CALIX-PET) and tert-butylphenol (TBP-PET) moieties have been synthesized and their sensitivity and selectivity for the detection of nitroaromatic compounds (NACs) such as nitrobenzene (NB), 2,4-dinitrotoluene (2,4-DNT), 2,4,6-trinitrotoluene (TNT) and picric acid (PA) investigated in fluid phase and solid-state. It was found that both fluorophores displayed high sensitivities toward NACs detection in solution as evaluated by the Stern-Volmer formalism. For all the tested explosives, the ratio of fluorescence intensities (F-0/F) is a linear function of the quencher concentration only after appropriate correction of fluorescence quenching data for inner-filter effects. The quenching efficiencies for CALIX-PET and TBP-PET follow the order PA >> TNT > DNT > NB, which correlate well with the quenchers electron affinities as evaluated from their LUMOs energies thereby suggesting a photoinduced electron transfer as the dominant mechanism of fluorescence quenching. The selectivity of these sensors was checked against exemplar interferents possessing differentiated electronic properties (benzoic acid, 2,4-dichlorophenol and benzoquinone) and reduced quenching activity was detected. The quenching efficiencies and response times of the two fluorophores in the solid-state toward NB, 2,4-DNT and TNT vapors were evaluated through steady-state fluorescence quenching experiments with the materials dispersed in polymeric matrices or as neat films. The most significant fluorescence quenching responses were achieved for drop-casted films of TBP-PET upon exposure to nitroaromatics.

Numerical 3D modeling of heat transfer in human tissues for microwave radiometry monitoring of Brown fat metabolismo

Background: Brown adipose tissue (BAT) plays an important role in whole body metabolism and could potentially mediate weight gain and insulin sensitivity. Although some imaging techniques allow BAT detection, there are currently no viable methods for continuous acquisition of BAT energy expenditure. We present a non-invasive technique for long term monitoring of BAT metabolism using microwave radiometry. Methods: A multilayer 3D computational model was created in HFSS™ with 1.5 mm skin, 3-10 mm subcutaneous fat, 200 mm muscle and a BAT region (2-6 cm3) located between fat and muscle. Based on this model, a log-spiral antenna was designed and optimized to maximize reception of thermal emissions from the target (BAT). The power absorption patterns calculated in HFSS™ were combined with simulated thermal distributions computed in COMSOL® to predict radiometric signal measured from an ultra-low-noise microwave radiometer. The power received by the antenna was characterized as a function of different levels of BAT metabolism under cold and noradrenergic stimulation. Results: The optimized frequency band was 1.5-2.2 GHz, with averaged antenna efficiency of 19%. The simulated power received by the radiometric antenna increased 2-9 mdBm (noradrenergic stimulus) and 4-15 mdBm (cold stimulus) corresponding to increased 15-fold BAT metabolism. Conclusions: Results demonstrated the ability to detect thermal radiation from small volumes (2-6 cm3) of BAT located up to 12 mm deep and to monitor small changes (0.5°C) in BAT metabolism. As such, the developed miniature radiometric antenna sensor appears suitable for non-invasive long term monitoring of BAT metabolism.

New textures for the lepton mass matrices

We study predictive textures for the lepton mass matrices in which the charged-lepton mass matrix has either four or five zero matrix elements while the neutrino Majorana mass matrix has, respectively, either four or three zero matrix elements. We find that all the viable textures of these two kinds share many predictions: the neutrino mass spectrum is inverted, the sum of the light-neutrino masses is close to 0.1 eV, the Dirac phase delta in the lepton mixing matrix is close to either 0 or pi, and the mass term responsible for neutrinoless double-beta decay lies in between 12 and 22 meV. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.

Confronting predictive texture zeros in lepton mass matrices with current data

Several popular Ansatze of lepton mass matrices that contain texture zeros are confronted with current neutrino observational data. We perform a systematic chi(2) analysis in a wide class of schemes, considering arbitrary Hermitian charged-lepton mass matrices and symmetric mass matrices for Majorana neutrinos or Hermitian mass matrices for Dirac neutrinos. Our study reveals that several patterns are still consistent with all the observations at the 68.27% confidence level, while some others are disfavored or excluded by the experimental data. The well-known Frampton-Glashow-Marfatia two-zero textures, hybrid textures, and parallel structures (among others) are considered.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.