Solubilities of chromium(III) in molten potassium hydrogensulfate

The behavior of chromium(III) in molten potassium hydrogensulfate (220° C, P(H₂O) = 0.04 atm) is reported. Chromium(III) exists as Cr³⁺ in acidic medium, and as chromium(III) sulfate, which is insoluble in neutral medium but soluble in basic medium as Cr(SO₄)^?₂. The values of acidity constants and the solubilities of Cr(III) are reported.     

Acidobasic properties of molten potassium tetrahalogenogallates (X=Cl,I)

Molten potassium tetrachlorogallate and potassium tetraiodogallate were studied in terms of halogenoacidity, based on X^? ion-exchange. Titration of KX solution with GaX₃ were achieved and characterized by the shift of cathodic voltammetric curves. Autodissociation constants K_i,X/mol² kg^?1 were determined: ?log K_i,Cl=4.25±0.05 and ?log K_i,I=2.6±0.05, as well as the solubility values of KX: 0.41±0.02 and 0.80±0.02 mol kg^?1 for KCl and KI respectively.     

Evidence of radial-axial motion couplings in an rf stored ion cloud

Received: 21 February 1997/Revised version: 13 May 1997     

A continuous parametric shape model

In this paper we propose a flexible continuous parametric shape model for star-shaped planar objects. The model is based on a polar Fourier expansion of the normalized radius-vector function. The expected phase amplitudes are modelled by a simple regression with parameters having nice geometric interpretations. The suggestedgeneralized p-order model is an extension of first- and second-order Gaussian shape models, and in particular the Gaussian assumption is relaxed. The statistical analysis is straightforward, as demonstrated by an application concerning shape discrimination of two cell nuclei populations.     

Recent developments in the stereological analysis of particles

Recent developments in the stereological analysis of particles are reviewed. The trend has been towards methods which are applicable without specific assumptions about particle shape. Geometric samples of a local 3-d character are used. Stereological estimators of particle intensity, particle size distribution and particle interaction are presented and discussed.An earlier version of this article was presented at the Symposium on the Analysis of Statistical Information held in the Institute of Statistical Mathematics, Tokyo during December 5–8, 1989.     

Wavelet Bases for Confinements of the Infrared Divergence

We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces , s−n/2∈ℕ. They provide a confinement of the infrared divergence by decomposing as a direct sum X ⊕ Y where X is a “small” space which carries the divergence and Y can be embedded in . In the case of we also construct such an orthonormal basis, which provides a confinement of the Mumford process.     

Confinement of the infrared divergence for the Mumford process

The Mumford process X is a stochastic distribution modulo constant and cannot be defined as a stochastic distribution invariant in law by dilations. We present two expansions of X—using wavelet bases—in X=X₀+X₁ which allow us to confine the divergence on the “small term” X₁ and which respect the invariance in law by dyadic dilations of the process.     

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ? ^d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ?³, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.     

Experimental lifetime of the metastable 5D 3/2 state in Ba+

A discrepancy exists between theoretical and experimental lifetimes of the metastable 5D _3/2 state in Ba⁺. In order to redertermine that lifetime, we probe the population of the metastable 5D _3/2 state of a Ba⁺ ion cloud stored in a Paul ion trap in the presence of He buffer gas as the function of time delay after pulsed laser excitation of this state. The measured decay rates at different buffer gas pressures are extrapolated to zero pressure and we obtain a radiative decay time of 48.0±5.9 s. This is not in agreement with theoretical predictions of about 80 s, but reduces the discrepancy from a previously reportet experimental value of 17.5 s. If the possibility of finestructure mixing to an adjacent 5D _5/2 level by collisions is considered our value represents a lower limit of the radiative lifetime for the 5D _3/2 state.     

ESR study of lithium incorporation by V2O5 single crystals

Lithium has been chemically and electrochemically incorporated into V₂O₅ single crystals. The ESR spectra of these room temperature bronzes are characterized by the same g tensor as α-Li_xV₂O₅ high temperature bronzes. This suggests that V₂O₅ acts as a three-dimensional framework host and that lithium is inserted into the channels of the orthorhombic structure. However, Li⁺ ions are not randomly distributed into the lattice. A clustering of the paramagnetic centers surrounding these ions is observed, giving an exchange narrowed ESR signal. The usual 29 hyperfine line ESR spectrum of high temperature α-Li_xV₂O₅ is again observed after heating the crystal above 300°C showing that these new bronzes convert to the previously reported Li_xV₂O₅ bronzes.