Tensor Products of Torsion Free C n -Modules of Finite Degree and Finite Dimensional Modules

It is known that every torsion free C _n -module of finite degree is completely reducible. In this article, we provide a formula for the decomposition of the tensor product of a simple torsion free C _n -module of finite degree with a simple finite dimensional C _n -module. As a byproduct we obtain a recursion formula for the decomposition of the tensor product of any two simple finite dimensional C _n -modules.     

Study of structural and electronic transport properties of Ce-doped LaMnO3

The structural and electronic transport properties of La_1−x Ce _x MnO₃ (x=0.0–1.0) have been studied. All the samples exhibit orthorhombic crystal symmetry and the unit cell volume decreases with Ce doping. They also make a metal-insulator transition (MIT) and transition temperature increases with increase in Ce concentration up to 50% doping. The system La_0.5Ce_0.5MnO₃ also exhibits MIT instead of charge-ordered state as observed in the hole doped systems of the same composition.     

Direct determination of 226Ra in environmental matrices using collision cell inductively coupled plasma mass-spectrometry

Direct determination of ²²⁶Ra in complex environmental matrices (biological and uranium ore samples) by collision-cell inductively coupled plasma mass-spectrometry was investigated. Possible polyatomic interferences were studied and their effects on ²²⁶Ra measurements were determined. The instrumental conditions for optimal signal-to-noise ratio for ²²⁶Ra were found. Concentrations of ²²⁶Ra in certified reference samples were measured using both external calibration and standard addition approaches. The best precision was obtained by applying standard additions. The absolute detection limit for ²²⁶Ra was 1 fg with optimal gas flow rates for the collision cell of 7 ml^.min^-1 for helium and 4 ml^.min^-1 for hydrogen.     

Collision cell chemistry for the analysis of radioisotopes by inductively coupled plasma mass spectrometry

A new method is presented for rapid and selective enrichment of radium in natural samples using ²²⁵Ra as a chemical yield tracer. The new technique allows a complete separation of the target nuclide from the sample matrix with high separation factors for thorium and uranium. The use of EmporeÔ Radium Rad Disks combines the easy handling of column chromatography with the high selectivity and rapid extraction kinetics of solvent extraction chromatography. Following this new chemical approach, eluates are obtained which are well suited for a-spectrometric analysis of Ra, Th and U.     

Two connected inverse spectral transforms

We establish a transformation which connects the potentials of the one-dimensional Dirac and Klein-Gordon operators. This transformation links the solutions of the nonlinear evolution equations solvable by means of the two inverse spectral transforms which use the Dirac and Klein-Gordon direct and inverse spectral problems.