Solubility Thermodynamics of CyMe$$_{}$$-BTBP in Various Diluents Mixed with TBP

The two organic ligands 6,6′-bis(5,5,8,8-tetramethyl-5,6,7,8-tetrahydrobenzo[1,2,4]triazin-3-yl)[2,2′]bipyridine (CyMe\(_{4}\)-BTBP) and tri-butyl phosphate (TBP) have previously been investigated in different diluents for use within recycling of used nuclear fuel through solvent extraction. The thermodynamic parameters, \(K_{\mathrm{S}}\), \(\Delta C_{p}\), \(\Delta H^{0}\) and \(\Delta S^{0}\), of the CyMe\(_{4}\)-BTBP solubility in three diluents (cyclohexanone, octanol and phenyl trifluoromethyl sulfone) mixed with TBP have been studied at 288, 298 and 308 K, both as pristine solutions and pre-equilibrated with 4 mol\(\cdot \)L\(^{-1}\) nitric acid. In addition, the amount of acid in the organic phase and density change after pre-equilibration have been measured. The solubility of CyMe\(_{4}\)-BTBP increases with an increased temperature in all systems, especially after acid pre-equilibration. This increased CyMe\(_{4}\)-BTBP solubility after pre-equilibration could be explained by acid dissolution into the solvent. Comparing the \(\Delta H^{0}\) and \(\Delta S^{0}\) calculated using \(\Delta C_{p}\) with the same parameters derived from a linear fit indicates temperature independence of all three thermodynamic systems. The change in enthalpy is positive in all solutions.     

Column switching in zone electrophoresis on a chip

This feasibility study deals with column switching in zone electrophoresis (ZE) separations on a column coupling (CC) chip. The column switching implemented into the ZE separations an on-chip sample clean up applicable for both the multicomponent and high salinity samples. In addition, complemented by different separation mechanisms in the coupled columns (channels), it provided benefits of two-dimensional separations. Properly timed column switching gave column-to-column transfers of the analytes, characterized by 99-102% recoveries, delivered to the second separation stage on the chip the analyte containing fractions contaminated only with minimum amounts of the matrix constituents. A diffusion driven transport of the matrix constituents to the second channel of the chip (due to direct contacts of the electrolyte solutions in the bifurcation region), representing 0.1-0.2% of the loaded sample constituents, was found to accompany the sample clean up performed on the CC chip. This source of potential disturbances to the separation in the second channel, however, is not detectable in a majority of practical situations. With respect to a 900 nl volume of the sample channel on the CC chip, the electric field and isotachophoresis (ITP) stackings were employed to minimize the injection dispersion in the separations and concentrate the analytes. Here, the column switching, removing a major part of the stacker from the separation system, provided a tool effective in a control of the destacking of analytes. Highly reproducible ZE separations as attained in this work also for the chip-to-chip and equipment-to-equipment frames can be ascribed, at least in part, to suppressions of electroosmotic and hydrodynamic flows of the solutions in which the separations were performed.     

Gelfand pairs,K-spherical means and injectivity on the Heisenberg group

We study the injectivity properties of the spherical mean value operators associated to the Gelfand pairs (H ⁿ,K), whereK is a compact subgroup ofU(n). We show that these spherical mean value operators are injective onL ^p Hⁿ) for 1≤p<∞. Forp=∞, these operators are not injective. Nevertheless, if the spherical meansf*μ _i overK-orbits of sufficiently many points (z _i,t _i) ∈H ⁿ vanish, we identify a necessary and sufficient condition on the points (z _i,t _i) which guaranteesf=0. ForK=U(n), this is equivalent to the condition for the two-radius theorem. Research supported by N.B.H.M. Research Grant, Govt. of India.     

On Schrödinger Propagator for the Special Hermite Operator

We establish a Strichartz type estimate for the Schrödinger propagator e ^it? for the special Hermite operator ? on ? ⁿ . Our method relies on a regularization technique. We show that no admissibility condition is required on (q,p) when 1≤q≤2.     

Analyticity of the Schr?dinger propagator on the Heisenberg group

We discuss the analytic extension property of the Schr?dinger propagator for the Heisenberg sublaplacian and some related operators. The result for the sublaplacian is proved by interpreting the sublaplacian as a direct integral of an one parameter family of dilated special Hermite operators.     

Spherical maximal operator on symmetric spaces, an end point estimate

We establish an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial functions on real rank-1 symmetric spaces of dimension n ≥ 2. More explicitly, we prove the Lorentz space estimate

     

Spherical maximal operator on symmetric spaces of constant curvature

We prove an endpoint weak-type maximal inequality for the spherical maximal operator applied to radial funcions on symmetric spaces of constant curvature and dimension . More explicitly, in the Lorentz space associated with the natural isometry-invariant measure, we show that, for every radial function ,

The proof uses only geometric arguments and volume estimates, and applies uniformly in every dimension.