Radon gas activity measurements in the frame of an international comparison

In order to validate its original method for the radon gas activity standardization and to assure the international metrological traceability and equivalence, the Radionuclide Metrology Laboratory of IFIN-HH participated recently in the international comparison CCRI(II)-K2.Rn-222, organized by the International Committee for Weights and Measures—CIPM-CCRI(II)-Radionuclide Measurements. The radon gas sample received, the measurement equipment and the experimental procedures are described. Because the comparison is underway, the results are presented only as relative values to the liquid scintillator vial measurement result. The uncertainty budget of the measurements performed is provided.     

Efficient computation of operator‐type response sensitivities for uncertainty quantification and predictive modeling: illustrative application to a spent nuclear fuel dissolver model

This work honors the 75th birthday of Professor Ionel Michael Navon by presenting original results highlighting the computational efficiency of the adjoint sensitivity analysis methodology for function‐valued operator responses by means of an illustrative paradigm dissolver model. The dissolver model analyzed in this work has been selected because of its applicability to material separations and its potential role in diversion activities associated with proliferation and international safeguards. This dissolver model comprises eight active compartments in which the 16 time‐dependent nonlinear differential equations modeling the physical and chemical processes comprise 619 scalar and time‐dependent model parameters, related to the model's equation of state and inflow conditions. The most important response for the dissolver model is the time‐dependent nitric acid in the compartment furthest away from the inlet, where measurements are available at 307 time instances over the transient's duration of 10.5 h. The sensitivities to all model parameters of the acid concentrations at each of these instances in time are computed efficiently by applying the adjoint sensitivity analysis methodology for operator‐valued responses. The uncertainties in the model parameters are propagated using the above‐mentioned sensitivities to compute the uncertainties in the computed responses. A predictive modeling formalism is subsequently used to combine the computational results with the experimental information measured in the compartment furthest from the inlet and then predict optimal values and uncertainties throughout the dissolver. This predictive modeling methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution for the a priori known mean values and uncertainties characterizing the model parameters and the computed and experimentally measured model responses. This approximate a priori distribution is subsequently combined using Bayes' theorem with the “likelihood” provided by the multi‐physics computational models. Finally, the posterior distribution is evaluated using the saddle‐point method to obtain analytical expressions for the optimally predicted values for the parameters and responses of both multi‐physics models, along with corresponding reduced uncertainties. This work shows that even though the experimental data pertains solely to the compartment furthest from the inlet (where the data were measured), the predictive modeling procedure used herein actually improves the predictions and reduces the predicted uncertainties for the entire dissolver, including the compartment furthest from the measurements, because this predictive modeling methodology combines and transmits information simultaneously over the entire phase‐space, comprising all time steps and spatial locations. Copyright © 2016 John Wiley & Sons, Ltd.     

On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions

The existence of solutions of an anti-periodic boundary value problem for fractional differential inclusions of order ????(2,3] is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.     

Hexaaquacobalt(II) and hexaaquanickel(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate

The title complexes, hexaaquacobalt(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate, [Co(H₂O)₆][Bi₂(C₇H₄NO₄)₄]·2H₂O, (I), and hexaaquanickel(II) bis(μ‐pyridine‐2,6‐dicarboxylato)bis[(pyridine‐2,6‐dicarboxylato)bismuthate(III)] dihydrate, [Ni(H₂O)₆][Bi₂(C₇H₄NO₄)₄]·2H₂O, (II), are isomorphous and crystallize in the triclinic space group P. The transition metal ions are located on the inversion centre and adopt slightly distorted MO₆ (M = Co or Ni) octahedral geometries. Two [Bi(pydc)₂]⁻ units (pydc is pyridine‐2,6‐dicarboxylate) are linked via bridging carboxylate groups into centrosymmetric [Bi₂(pydc)₄]²⁻ dianions. The crystal packing reveals that the [M(H₂O)₆]²⁺ cations, [Bi₂(pydc)₄]²⁻ anions and solvent water molecules form multiple hydrogen bonds to generate a supramolecular three‐dimensional network. The formation of secondary Bi...O bonds between adjacent [Bi₂(pydc)₄]²⁻ dimers provides an additional supramolecular synthon that directs and facilitates the crystal packing of both (I) and (II).     

Dilations of Some VH-Spaces Operator Valued Invariant Kernels

We investigate VH-spaces (Vector Hilbert spaces, or Loynes spaces) operator valued Hermitian kernels that are invariant under actions of *-semigroups from the point of view of generation of *-representations, linearizations (Kolmogorov decompositions), and reproducing kernel spaces. We obtain a general dilation theorem in both Kolmogorov and reproducing kernel space representations, that unifies many dilation results, in particular B. Sz.-Nagy??s and Stinesprings?? dilation type theorems.     

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.     

Wigner Functions and Spin Tomograms for Qubit States

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.