Wiener’s criterion for the unique solvability of the Dirichlet problem in arbitrary open sets with non-compact boundaries

This paper establishes a necessary and sufficient condition for the existence of a unique bounded solution to the classical Dirichlet problem in arbitrary open subset of R^N${\mathbb{R}}^N$ (N≥3$N\ge 3$) with a non-compact boundary. The criterion is the exact analogue of Wiener’s test for the boundary regularity of harmonic functions and characterizes the “thinness” of a complementary set at infinity. The Kelvin transformation counterpart of the result reveals that the classical Wiener criterion for the boundary point is a necessary and sufficient condition for the unique solvability of the Dirichlet problem in a bounded open set within the class of harmonic functions having a “fundamental solution” kind of singularity at the fixed boundary point. Another important outcome is that the classical Wiener’s test at the boundary point presents a necessary and sufficient condition for the “fundamental solution” kinds of singularities of the solution to the Dirichlet problem to be removable.     

The thermoluminescence response of Ge-doped optical fibre subjected to photon irradiation

A radiation dosimeter based on Ge-doped silica fibre is described. Parameters concerning thermoluminescence (TL) induced by ⁶⁰Co irradiation are investigated, including activation energies, frequency factors, and reproducibility with dose and fading. It is concluded that Ge-doped silica fibres provide a good basis for medical radiation dosimetry at therapy levels. In particular, doses are reproducible to within 3%, the fibres are reusable and show linearity of dose versus TL output over the approximate range of dose 1 Gy to in excess of 100 Gy. At room temperatures, fading within the first 30 d following irradiation has been found to be of the order of 7%.     

Radiation Polymerization of 4-(Acryloylamido)benzonitrile: Zinc and Copper Complexes

The new polymer containing cyano groups was synthesized by γ-irradiation. The oximated polymer was prepared using hydroxylamine hydrochloride in basic medium. The characterization of monomer, polymer, and oximated ones was confirmed by infrared and nuclear magnetic resonance spectroscopy. The complex formation of the amidoxime salt towards Zn^II, Cu^II, and Zn^II/Cu^II mixture in aqueous solution was studied by atomic absorption spectroscopy, energy dispersive spectroscopy, and electron spin resonance spectrometry. The significant binding capacity of these metal ions revealed its selectivity to Zinc(II) ion. The thermal stability of polymers and complexed ones was investigated using thermogravimetry analysis. The change in their morphology was observed by scanning electron microscopy (SEM).     

Comparative Studies on the Development of a 188W-188Re Generator

A comparative study on the sorption behaviour of tungsten and rhenium between anion exchange resin, charcoal and alumina and aqueous media of HNO₃, HCl and NaCl were carried out. The equilibrium distribution coefficient obtained for the different systems were evaluated and discussed in terms of the separation factor between W and Re. It is found that the systems based on alumina and HCl or NaCl are the most promising systems to be used for development of ¹⁸⁸W-¹⁸⁸Re generator. The capacity of a chromatographic column loaded with alumina for ¹⁸⁸W from 0.01 M HCl, 0.7% NaCl and 1.2% NaCl was found to equals 75.3, 91.0 and 126.0 mg/cm, respectively. A recommended procedure was adopted for ¹⁸⁸W-¹⁸⁸Re generator.

Es wurde eine Vergleichsuntersuchung zum Sorptionsverhalten von W und Re zwischen einem Anionenaustauscherharz einer Aktivkohle und einer Tonerde und den wüβirigen Lösungen von HN0₃, HCl and NaCl ausgeführt. Die Gleichgeiwichlsverteilungskoeffizienten der unterschiedlichen Systeme wurden bestimmt und als Trennfaktoren zwischen W und Re diskutiert. Es wurde gefunden, daβ sich das System Tonerde/HCl oder NaCl sehr als Trennsystem für die Entuwicklung eines ¹⁸⁸W¹⁸⁸Re-Generators eignet. Die Kapazitäten einer mit Tonerde gefüllten Säule für ¹⁸⁸W mit 0.01 M HCl, 0.7% NaCl und 1.2% NaCl betrugen entsprechend 75.3, 90.0 und 126.0 mg/cm. Es wird eine geeignete Trennmethode für einen ¹⁸⁸.¹⁸⁸ Re-Generator empfohlen.     

Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the singularity of solutions to linear and semilinear fractional elliptic equations with a homogeneous singular potential related to the fractional Hardy inequality. As a consequence we obtain unique continuation properties for fractional elliptic equations.