Comparison of thermal ionization mass spectrometry and Multiple Collector Inductively Coupled Plasma Mass Spectrometry for cesium isotope ratio measurements

In the nuclear domain, precise and accurate isotopic composition determination of elements in spent nuclear fuels is mandatory to validate neutron calculation codes and for nuclear waste disposal. The present study presents the results obtained on Cs isotope ratio by mass spectrometric measurements. Natural cesium is monoisotopic (¹³³Cs) whereas cesium in spent fuels has 4 isotopes (¹³³Cs, ¹³⁴Cs, ¹³⁵Cs, and ¹³⁷Cs). As no standard reference material is available to evaluate the accuracy of Cs isotopic measurements, a comparison of cesium isotopic composition in spent nuclear fuels has been performed between Thermal Ionization Mass Spectrometry (TIMS) and a new method involving Multiple Collector Inductively Coupled Plasma Mass Spectrometry (MC-ICPMS) measurements. For TIMS measurements, isotopic fractionation has been evaluated by studying the behavior of cesium isotope ratios (¹³³Cs/¹³⁷Cs and ¹³⁵Cs/¹³⁷Cs) during the analyses. For MC-ICPMS measurements, the mass bias effects have been corrected with an external mass bias correction using elements (Eu and Sb) close to cesium masses. The results obtained by the two techniques show good agreement: relative difference on ¹³³Cs/¹³⁷Cs and ¹³⁵Cs/¹³⁷Cs ratios for two nuclear samples, analyzed after chemical separation, ranges from 0.2% to 0.5% depending on the choice of reference value for mass bias correction by MC-ICPMS. Finally the quantification of the ¹³⁵Cs/²³⁸U ratio by the isotope dilution technique is presented in the case of a MOx (mixed oxide) spent fuel sample. Evaluation of the global uncertainties shows that this ratio could be defined at an uncertainty of 0.5% (k = 2). The intercomparison between two independent mass spectrometric techniques is fundamental for the evaluation of uncertainty when no isotopic standard is available.     

Structural properties of graphs of diameter 2 with maximal repeats

It was shown using eigenvalue analysis by Erdös et al. that with the exception of C₄, there are no graphs of diameter 2, of maximum degree d and of order d², that is, one less than the Moore bound. These graphs belong to a class of regular graphs of diameter 2, and having certain interesting structural properties, which will be proved in this paper.     

Ab initio study of the hydration of carbon dioxide: Additional comments based on refined calculations

Ab initio calculations on the formation of carbonic acid from the hydration of carbon dioxide with water dimer are re-examined. Fully optimized geometries of the three stationary points (minima and transition state) with the 3-21G basis set are reported. They possess non-planar structures. The inclusion of polarization (with the 6-31G* basis) and electron correlation (via Møller-Plesset perturbation theory to second through to fourth-order using the 6-31G basis) tends to enlarge the energy barrier (35–40 kcal mol⁻¹) for the double hydrogen transfer. This suggests that the neutral hydrolysis of CO₂ could require more water molecules (an oligomer) in an autocatalytic process rather than a dimer.     

Fast and continuous isolation of short-lived mercury isotopes from diluted sulphuric acid solution

The seconds living mercury isotopes have been isolated from nuclear reaction products arising in the bombardment of ¹⁴⁷Sm target with ⁴⁰Ar ions at the U-400 cyclotron of JINR-Dubna.     

Optimality Conditions and Stability Analysis via the Mordukhovich Subdifferential

This article shows that finite-dimensional multiplier rules, which are based on the limiting subdifferential, can be proved by Ekeland's variational principle and some basic calculus tools of the generalized differentiation theory introduced by B. S. Mordukhovich. Consequences of a limiting constraint qualification, which yields the normal form of the multiplier rules, stability and calmness of optimization problems, are investigated in detail.     

Equi-surjective systems of linear operators and applications

In this paper we study a system of linear operators between finite-dimensional Euclidean spaces. Emphasis is made on unbounded systems and sufficient conditions are established for their equi-surjectivity. An application is presented in which a system of approximate Jacobian matrices is used to obtain a parametric interior mapping theorem. A multiplier rule for vector problems is also derived.