Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains

By the potential method, we investigate the Dirichlet and Neumann boundary value problems of the elasticity theory of hemitropic (chiral) materials in the case of Lipschitz domains. We study properties of the single‐ and double‐layer potentials and of certain, generated by them, boundary integral operators. These results are applied to reduce the boundary value problems to the equivalent first and the second kind integral equations and the uniqueness and existence theorems are proved in various function spaces. Copyright © 2005 John Wiley & Sons, Ltd.     

Some remarks on a class of inverse problems related to the parabolic approximation to the Maxwell equations: a controllability approach

We consider a class of inverse source problems for the parabolic approximation to the Maxwell equations.We relate this to an exact controllability problem; the regularisation of the considered source problems is studied with an optimal control method. Copyright © 2014 John Wiley & Sons, Ltd.     

Chemometrical approaches to evaluate analytical data from aquatic macrophytes and marine algae

The possibility of using aquatic macrophytes and algae as bioindicators of water pollution is investigated. The use of cluster analysis enables the treatment of the analytical data in a global way, revealing hidden clusters of similar behaviour between various biological species or sampling sites. A great number of species was collected from four rivers and fourteen coastal sites in Greece and were analysed for zinc, copper, cadmium, lead and manganese. The analytical data obtained were treated by hierarchical clustering, for marine algae and aquatic macrophytes separately.     

Transmission problems in the theory of elastic hemitropic materials

The purpose of this article is to investigate mixed transmission-boundary value problems for the differential equations of the theory of hemitropic (chiral) elastic materials. We consider the differential equations corresponding to the time harmonic dependent case, the so called pseudo-oscillation equations. Applying the potential method and the theory of pseudodifferential equations we prove uniqueness and existence theorems of solutions to the Dirichlet, Neumann and mixed transmission-boundary value problems for piecewise homogeneous hemitropic composite bodies and analyze their regularity properties. We investigate also interface crack problems and establish almost best regularity results.     

Optimized microwave-assisted decomposition method for multi-element analysis of glass standard reference material and ancient glass specimens by inductively coupled plasma atomic emission spectrometry

A novel microwave-assisted wet-acid decomposition method for the multi-element analysis of glass samples using inductively coupled plasma atomic emission spectrometry (ICP-AES) was developed and optimized. The SRM 621 standard reference glass material was used for this purpose, because it has similar composition with either archaeological glass specimens or common modern glasses. For the main constituents of SRM 621 (Ca, Na, Al, Fe, Mg, Ba and Ti), quality control data are given for all the examined procedures. The chemical and instrumental parameters of the method were thoroughly optimized. Thirteen acid mixtures of hydrochloric, nitric, and hydrofluoric acids in relation to two different microwave programs were examined in order to establish the most efficient protocol for the determination of metals in glass matrix. For both microwave programs, an intermediate step was employed with addition of H₃BO₃ in order to compensate the effect of HF, which was used in all protocols. The suitability of the investigated protocols was evaluated for major (Ca, Na, Al), and minor (Fe, Mg, Ba, Ti, Mn, Cu, Sb, Co, Pb) glass constituents. The analytes were determined using multi-element matrix matched standard solutions. The analytical data matrix was processed chemometrically in order to evaluate the examined protocols in terms of their accuracy, precision and sensitivity, and eventually select the most efficient method for ancient glass. ICP-AES parameters such as spectral line, RF power and sample flow rate were optimized using the proposed protocol. Finally, the optimum method was successfully applied to the analysis of a number of ancient glass fragments.     

Characterization by gas chromatography-mass spectrometry of diterpenoid resinous materials in Roman-age amphorae from northern Greece

A combined gas chromatography-mass spectrometry approach has been used for the characterization of two lumps of resin and 17 adsorbed residues on Roman-age vessels, mainly amphorae, from northern Greece. The data show that a diterpenic resin from plants of the Pinacae family is the main component of the tarry material associated with the analyzed archaeological samples. The identification and mass spectrometric fragmentation of several characteristic diterpenoid biomarkers is discussed. The abundance of secondary products identified in the archaeological samples suggests that the oxidative degradation of abietic acid and dehydroabietic acid to aromatic products was the main pathway. Of particular interest is the presence of characteristic saturated abietane hydrocarbons in one sample, which indicate that a reductive process also occurred on a small scale. The overall similarity in the composition of the residues suggests the common use of pine tar as a waterproofing and sealing agent at different sites in northern Greece during the Roman period.     

Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low‐frequency theory

The scattering of plane time‐harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far‐field patterns are derived. A low‐frequency theory for the approximation of the solution to the above problem, and the derivation of the far‐field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

On the domain derivative for scattering by impenetrable obstacles in chiral media

For scattering of electromagnetic waves in a chiral medium bysome perfectly conducting inclusions, we study the dependenceof the scattered field on the boundary of the inclusions andshow its Fréchet differentiability in appropriate spaces.Further, we derive a characterization of the derivative as asolution to some corresponding chiral boundary value problem.Our proof contains a new approach to rigorously derive thischaracterization.     

A Transmission problem for bi-isotropic media

In this work we study the solvability of the transmission problem describing the scattering of a plane time-harmonic electromagnetic wave by a penetrable bi-isotropic obstacle. Existence and uniqueness of the solution to this problem is established by a weak solutions approach, with the use of the Dirichlet-to-Neumann operator. Moreover, in the low frequency case, we reduce the problem to a sequence of potential problems which can be solved iteratively.     

Simultaneous Voltammetric Determination of Molybdenum and Copper in Manganese Compounds

 Adsorptive voltammetry was employed for the determination of copper and molybdenum in manganese compounds. As working electrode the hanging mercury drop electrode (HMDE) was used. The method was applied in aqueous solutions of MnCl₂ and Mn(NO₃)₂, as well as in pre-treated manganese dioxide and manganese ores. The detection limits are 3 μg/g for copper and 5 μg/g for molybdenum in the sample. The RSDs at concentration level of 8 μg/g are 2.2 and 3.2% for copper and molybdenum, respectively.