Puiseux parametric equations of analytic sets

We prove the existence of local Puiseux-type parameterizations of complex analytic sets via Laurent series convergent on wedges. We describe the wedges in terms of the Newton polyhedron of a function vanishing on the discriminant locus of a projection. The existence of a local parameterization of quasi-ordinary singularities of complex analytic sets of any codimension will come as a consequence of our main result.

     

On-line preconcentration and determination of mercury in biological samples by flow injection vapour generation inductively coupled plasma atomic emission spectrometry

An FI-ICP-AES method for the determination of trace levels of mercury in biological samples has been described, which is based on the extraction of the mercury complex with 1,5-bis (di-2-pyridyl)methylene thiocarbonohydrazide (DPTH) on-line into isobuthyl-methyl ketone (IBMK). The organic phase (containing the complex) has been mixed on-line with SnCl₂ in N,N-dimethylformamide. Thus, mercury vapour can be generated directly from the organic phase and separated in a gas-liquid separation device. The detection limit for mercury is 4 ng/ml and the calibration curve is linear at least from 10 to 2500 ng/ml. The relative standard deviation for 10 replicate measurements is ±1% for 100 ng/ml of Hg(II). Results from the analysis of some certified biological reference materials are given.     

Separation and Preconcentration by Dispersive Liquid�CLiquid Microextraction Procedure: Recent Applications

Dispersive liquid?Cliquid microextraction (DLLME) is a relatively novel miniaturized sample pre-treatment technique. DLLME has been applied for the analysis of a large variety of organic compounds and metal ions in different samples. This paper reviews the more recent applications of this procedure for sample preparation.     

The Dirichlet problem associated to the relativistic heat equation

We prove existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation.     

A Review of Stir Bar Sorptive Extraction

Stir bar sorptive extraction (SBSE) is an extraction technique for enrichment of volatile and semi-volatile organic compounds from aqueous and gaseous media. After exposure to a sample, the stir bar, which is covered in a layer of a polysiloxane is subsequently removed and the sorbed compounds are then either thermally desorbed, and analysed by GC-MS or desorbed by means of a liquid, for improved selectivity or for interfacing to an LC system.The technique has been applied successfully to trace analysis in environmental, biomedical and food applications. Applications of SBSE to environmental, foodstuffs and pharmaceutical and biomedical samples are given.

     

Synthesis and acid digestion of biomorphic ceramics: determination of alkaline and alkaline earth ions

Ceramic and glass are some of the more recent engineering materials and those that are most resistant to environmental conditions. They belong to advanced materials in that they are being developed for the aerospace and electronics industries. In the last decade, a new class of ceramic materials has been the focus of particular attention. The materials were produced with natural, renewable resources (wood or wood-based products). In this work, we have synthesised a new biomorphic ceramic material from oak wood and Si infiltration. After the material characterization, we have optimized the dissolution of the sample by acid attack in an oven under microwave irradiation. Experimental designs were used as a multivariate strategy for the evaluation of the effects of varying several variables at the same time. The optimization was performed in two steps using factorial design for preliminary evaluation and a Draper-Lin design for determination of the critical experimental conditions. Five variables (time, power, volume of HNO3, volume H2SO4 and volume of HF) were considered as factors and as a response the concentration of different metal ions in the optimization process. Interactions between analytical factors and their optimal levels were investigated using a Draper-Lin design.     

On-line preconcentration of palladium(II) using a microcolumn packed with a chelating resin, and its subsequent determination by graphite furnace atomic absorption spectrometry

Palladium(II) is preconcentrated on a chelating resin microcolumn [1,5-Bis(2-pyridyl)-3-sulphophenyl methylene thiocarbonohydrazide immobilized on an anion-exchange resin (Dowex 1 X8-200)] placed in the autosampler arm, followed by the elution of the Pd-chelate with nitric acid and subsequent determination of Pd from the eluate by graphite furnace atomic absorption spectrometry. The method was applied to the recovery of Pd(II) ions from different samples.     

A Strongly Degenerate Quasilinear Equation: the Parabolic Case

We prove the existence and uniqueness of entropy solutions of the Neumann problem for the quasilinear parabolic equation u_t=÷ a(u, Du), where a(z,)=f(z,), and f is a convex function of with linear growth as ||||, satisfying other additional assumptions. In particular, this class includes the case where f(z,)=(z)(), >0, and is a convex function with linear growth as ||||.     

Existence and approximation of nonlocal optimal design problems driven by parabolic equations

This work is a follow‐up to a series of articles by the authors where the same topic for the elliptic case is analyzed. In this article, a class of nonlocal optimal design problem driven by parabolic equations is examined. After a review of results concerning existence and uniqueness for the state equation, a detailed formulation of the nonlocal optimal design is given. The state equation is of nonlocal parabolic type, and the associated cost functional belongs to a broad class of nonlocal integrals. In the first part of the work, a general result on the existence of nonlocal optimal design is proved. The second part is devoted to analyzing the convergence of nonlocal optimal design problems toward the corresponding classical problem of optimal design. After a slight modification of the problem, either on the cost functional or by considering a new set of admissibility, the G‐convergence for the state equation and, consequently, the convergence of the nonlocal optimal design problem are proved.