Weak solutions of the forward problem in EEG for different conductivity values

The potential distribution on the scalp produced by current sources in the brain can be measured by an EEG recorder. The relationship between these sources and the scalp potential distribution may be described by a well-known mathematical model where some simplifications are usually introduced. The head is modeled as a multicompartment nested set and the conductivity of the different tissues is approximated by a positive piecewise constant function. This simplified model is used to solve the forward problem (FP), i.e., to calculate the scalp potential for a current source configuration. In this work, we prove that the weak solutions of the FP are continuous with respect to the conductivity values, that is, the difference between the scalp potentials is small if the conductivity values are closed enough. We present numerical examples that illustrates this property.     

Polyisophthalamides with heteroaromatic pendent rings: Synthesis,physical properties,and water uptake

A set of novel aromatic polyamides containing pyridine pendent groups was prepared from aromatic diamines and new monomers that are 5‐substituted derivatives of isophthalic acid bearing nicotinamide, isonicotinamide, or picolinamide groups. The polymers were obtained in high yield and high molecular weight by the phosphorylation method of polycondensation. They were characterized by spectroscopic and chromatographic methods and several of their properties were investigated. All of the polymers were soluble in polar aprotic solvents and gave films of good mechanical properties. Glass transition temperatures were higher than that of the reference polymer, poly(m‐phenyleneisophthalamide) (IP‐MPD), while the thermal resistance, defined by the initial decomposition temperature observed by thermogravimetry, was in the range 370–420 °C, lower by 30–70 °C than that of IP‐MPD. The presence of a pendent pyridine group and an additional amide side group per repeat unit made the polymers essentially amorphous and greatly improved their abilities to absorb water in comparison with nonsubstituted polyamides. Water uptake values up to 15% were observed at 65% relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5300–5311, 2005     

Polynomial first integrals of quadratic vector fields

We classify all quadratic polynomial differential systems having a polynomial first integral, and provide explicit normal forms for such systems and for their first integrals.     

Application of a Microwave Helium Plasma Torch Operating at Atmospheric Pressure to Destroy Trichloroethylene

We examined the influence of the gas flow-rate, microwave power and trichloroethylene concentration on the destruction of trichloroethylene with a system based on a microwave helium plasma operating at atmospheric pressure. Based on the experimental results obtained, the proposed system allows input concentrations of C₂HCl₃ in the ppmv range to be reduced to output concentrations in the ppbv range (i.e. virtually quantitative destruction) by using a microwave plasma power below 1000 W. High helium flow-rates and C₂HCl₃ concentrations allow energy efficiency values above 600 g/kW h to be obtained. Analyses of the output gases by gas chromatography and species present in the plasma by optical emission spectroscopy confirmed the negligible presence of halogen compounds resulting from the destruction of C₂HCl₃, and that of CCl₄ and C₂Cl₄ as the sole chlorine species exceeding levels of 30 ppbv. Gaseous by-products consisted mainly of CO₂, NO and N₂O in addition to Cl₂ traces.     

Conic Set-Valued Maps in Vector Optimization

The paper deals with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems. The results here about the continuity and derivability of this conic set-valued map, can be used to get information about the sensitivity of the problem and the stability of the order associated to every ideal point. Furthermore, it is proved that certain contingent cones are determined by the ideal conic set-valued map.      

The Mössbauer spectrum of synthetic hureaulite: Fe5 2+(H2O)4(PO4H)2(PO4)2

The crystal structure of synthetic ferrous hureaulite, Fe₅ ²⁺ (H₂O)₄(PO₄H)₂(PO₄)₂, was refined from single-crystal X-ray data. It is monoclinic, space group C2/c, with a=17.487(4), b=9.017(2), c=9.338(2) Å, β=96.27(3)°, V=1463.6(6) Å³, Z=4 and D _calc=3.327 g/cm³. This end member of the hureaulite series was crystallized under distinctly acidic conditions, by a method that gives perfect crystals, large enough for X-ray single crystal studies. The main feature of the hureaulite structure is that it has an equal number of normal (PO₄)³⁺ and acid (PO₄H)²⁺ tetradentate groups. These are centered on Fe²⁺ atoms and share corners with edge-linked octahedra, forming pentamer units. The five Fe²⁺ atoms are distributed on three distinct sites in these units. This can be directly observed in the Mössbauer spectrum at 295 K, which contains three doublets whose relative intensities correspond to the 1:2:2 distributions of crystallographic sites.     

On the adjacencies of triangular meshes based on skeleton-regular partitions

For any 2D triangulation τ, the 1-skeleton mesh of τ is the wireframe mesh defined by the edges of τ, while that for any 3D triangulation τ, the 1-skeleton and the 2-skeleton meshes, respectively, correspond to the wireframe mesh formed by the edges of τ and the “surface” mesh defined by the triangular faces of τ. A skeleton-regular partition of a triangle or a tetrahedra, is a partition that globally applied over each element of a conforming mesh (where the intersection of adjacent elements is a vertex or a common face, or a common edge) produce both a refined conforming mesh and refined and conforming skeleton meshes. Such a partition divides all the edges (and all the faces) of an individual element in the same number of edges (faces). We prove that sequences of meshes constructed by applying a skeleton-regular partition over each element of the preceding mesh have an associated set of difference equations which relate the number of elements, faces, edges and vertices of the nth and (n−1)th meshes. By using these constitutive difference equations we prove that asymptotically the average number of adjacencies over these meshes (number of triangles by node and number of tetrahedra by vertex) is constant when n goes to infinity. We relate these results with the non-degeneracy properties of longest-edge based partitions in 2D and include empirical results which support the conjecture that analogous results hold in 3D.     

Arsenic speciation using HPLC-HG-ICP-AES with gas-liquid separator

Summary The determination of different chemical species of arsenic in aquatic media has been carried out using several separation and detection techniques. As separation techniques GC, HPLC, HG and cold trap-selective thermal desorption are the most frequently used. As detection techniques FAAS, ETAAS or, to a lesser extent, ICP-AES are applied. In this work the optimization conditions are presented for As(III), As(V), monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA) determination using (IC)HPLC coupled to HG with gas-liquid separator, and using ICP-AES as detector is presented. The gas-liquid separator impedes the entrance of mobile phase into the nebulizer and consequently into the plasma torch. The experimental conditions for HG (kind of acids and concentration, borohydride concentration, reagent flows) as well as plasma conditions have been optimized.The quality parameters: LOD, precision and accuracy are reported for all the species studied.